(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, array_tmp1 1 temp2], array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : -----------, 1 1 1 1 array_x 1 array_tmp2 array_tmp3 1 1 array_tmp3 : -----------, array_tmp4 : -----------, 1 array_x 1 array_x 1 1 array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_m1 array_const_2D0 , 2 2 1 array_tmp1 - array_tmp2 array_x 2 1 2 array_tmp2 : ----------------------------------, 2 array_x 1 array_tmp2 - array_tmp3 array_x 2 1 2 array_tmp3 : ----------------------------------, 2 array_x 1 array_tmp3 - array_tmp4 array_x 2 1 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 2 array_x 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp1 - array_tmp2 array_x 3 2 2 array_tmp2 : ----------------------------------, 3 array_x 1 array_tmp2 - array_tmp3 array_x 3 2 2 array_tmp3 : ----------------------------------, 3 array_x 1 array_tmp3 - array_tmp4 array_x 3 2 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 3 array_x 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp1 - array_tmp2 array_x 4 3 2 array_tmp2 : ----------------------------------, 4 array_x 1 array_tmp2 - array_tmp3 array_x 4 3 2 array_tmp3 : ----------------------------------, 4 array_x 1 array_tmp3 - array_tmp4 array_x 4 3 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 4 array_x 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp1 - array_tmp2 array_x 5 4 2 array_tmp2 : ----------------------------------, 5 array_x 1 array_tmp2 - array_tmp3 array_x 5 4 2 array_tmp3 : ----------------------------------, 5 array_x 1 array_tmp3 - array_tmp4 array_x 5 4 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 5 array_x 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 - ats(kkk, array_x, array_tmp2, 2) array_tmp2 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp3, 2) array_tmp3 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp4, 2) array_tmp4 : ----------------------------------, kkk array_x 1 array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, array_tmp1 1 temp2], array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : -----------, 1 1 1 1 array_x 1 array_tmp2 array_tmp3 1 1 array_tmp3 : -----------, array_tmp4 : -----------, 1 array_x 1 array_x 1 1 array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_m1 array_const_2D0 , 2 2 1 array_tmp1 - array_tmp2 array_x 2 1 2 array_tmp2 : ----------------------------------, 2 array_x 1 array_tmp2 - array_tmp3 array_x 2 1 2 array_tmp3 : ----------------------------------, 2 array_x 1 array_tmp3 - array_tmp4 array_x 2 1 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 2 array_x 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp1 - array_tmp2 array_x 3 2 2 array_tmp2 : ----------------------------------, 3 array_x 1 array_tmp2 - array_tmp3 array_x 3 2 2 array_tmp3 : ----------------------------------, 3 array_x 1 array_tmp3 - array_tmp4 array_x 3 2 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 3 array_x 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp1 - array_tmp2 array_x 4 3 2 array_tmp2 : ----------------------------------, 4 array_x 1 array_tmp2 - array_tmp3 array_x 4 3 2 array_tmp3 : ----------------------------------, 4 array_x 1 array_tmp3 - array_tmp4 array_x 4 3 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 4 array_x 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp1 - array_tmp2 array_x 5 4 2 array_tmp2 : ----------------------------------, 5 array_x 1 array_tmp2 - array_tmp3 array_x 5 4 2 array_tmp3 : ----------------------------------, 5 array_x 1 array_tmp3 - array_tmp4 array_x 5 4 2 array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 , 5 array_x 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 - ats(kkk, array_x, array_tmp2, 2) array_tmp2 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp3, 2) array_tmp3 : ----------------------------------, kkk array_x 1 - ats(kkk, array_x, array_tmp4, 2) array_tmp4 : ----------------------------------, kkk array_x 1 array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) 1.0 --- x (%i55) exact_soln_y(x) := block(---) x 1.0 --- x (%o55) exact_soln_y(x) := block(---) x (%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing3postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:0.7,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.0001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0/x/x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 1.0, x_end : 0.7, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:43:37-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing3"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "sing3 diffeq.max"), logitem_str(html_log_file, "sing3 maxima results" ), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing3postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:0.7,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.0001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0/x/x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 1.0, x_end : 0.7, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T01:43:37-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing3"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "sing3 diffeq.max"), logitem_str(html_log_file, "sing3 maxima results" ), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/sing3postode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-1.0," "x_end:0.7," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.0001," "glob_look_poles:true," "glob_max_iter:100," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0/x/x) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 1.7 "" estimated_steps = 1700. "" step_error = 5.8823529411764710000000000000E-14 "" est_needed_step_err = 5.8823529411764710000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.154401977258852900000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" max_value3 = 1.154401977258852900000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" value3 = 1.154401977258852900000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -1. " " y[1] (analytic) = 1. " " y[1] (numeric) = 1. " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1. " " y[1] (analytic) = 1. " " y[1] (numeric) = 1. " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.999 " " y[1] (analytic) = 1.002003004005006 " " y[1] (numeric) = 1.002003004005006 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.998 " " y[1] (analytic) = 1.0040120320801924 " " y[1] (numeric) = 1.0040120320801926 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.21157314683750900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.7098275596423034 " " Order of pole = 1.474020905334327800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.997 " " y[1] (analytic) = 1.0060271084064631 " " y[1] (numeric) = 1.0060271084064634 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.207143356969254200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.997000000000008 " " Order of pole = 2.02504679691628550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.996 " " y[1] (analytic) = 1.0080482572861729 " " y[1] (numeric) = 1.008048257286173 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.202718007993098600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9960000000000049 " " Order of pole = 1.24344978758017530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.995 " " y[1] (analytic) = 1.01007550314386 " " y[1] (numeric) = 1.0100755031438602 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.19829709990904120000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9950000000000081 " " Order of pole = 2.06057393370429050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.994 " " y[1] (analytic) = 1.0121088705269847 " " y[1] (numeric) = 1.012108870526985 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.193880632717082600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9940000000000003 " " Order of pole = 1.065814103640150300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.993 " " y[1] (analytic) = 1.014148384106672 " " y[1] (numeric) = 1.0141483841066723 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.189468606417222200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.993000000000006 " " Order of pole = 1.56319401867222040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.992 " " y[1] (analytic) = 1.0161940686784598 " " y[1] (numeric) = 1.01619406867846 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.185061021009460000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9920000000000043 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.991 " " y[1] (analytic) = 1.0182459491630527 " " y[1] (numeric) = 1.0182459491630529 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.180657876493796700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.99 " " y[1] (analytic) = 1.020304050607081 " " y[1] (numeric) = 1.020304050607081 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9900000000000039 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.989 " " y[1] (analytic) = 1.022368398183865 " " y[1] (numeric) = 1.022368398183865 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.5904831289558315 " " Order of pole = 2.0943247136528953000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.988 " " y[1] (analytic) = 1.0244390171941844 " " y[1] (numeric) = 1.0244390171941846 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.167475088299397600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9880000000000009 " " Order of pole = 2.131628207280300600000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.987 " " y[1] (analytic) = 1.0265159330670552 " " y[1] (numeric) = 1.0265159330670552 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.986 " " y[1] (analytic) = 1.0285991713605076 " " y[1] (numeric) = 1.0285991713605076 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9860000000000068 " " Order of pole = 1.74082970261224550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.985 " " y[1] (analytic) = 1.0306887577623747 " " y[1] (numeric) = 1.0306887577623747 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9850000000000031 " " Order of pole = 7.81597009336110200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.984 " " y[1] (analytic) = 1.0327847180910834 " " y[1] (numeric) = 1.0327847180910834 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.9840000000000014 " " Order of pole = 3.55271367880050100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.983 " " y[1] (analytic) = 1.0348870782964519 " " y[1] (numeric) = 1.0348870782964517 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.145592592484035500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used" Radius of convergence = 0.983000000000008 " " Order of pole = 2.09610107049229550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.982 " " y[1] (analytic) = 1.0369958644604924 " " y[1] (numeric) = 1.0369958644604924 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.8580903982701059 " " Order of pole = 8.974154752650065000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.981 " " y[1] (analytic) = 1.0391111027982223 " " y[1] (numeric) = 1.0391111027982223 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 7.37357541423516700E-2 " " Order of pole = 8.327560863108374000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9795252849171528 " " y[1] (analytic) = 1.042242306003412 " " y[1] (numeric) = 1.0422423060034118 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.13045089079606400000000000000E-14 "%" Correct digits = 16 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.979525284917159 " " Order of pole = 1.56319401867222040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9787879273757293 " " y[1] (analytic) = 1.0438132176885266 " " y[1] (numeric) = 1.0438132176885262 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.25448923547333930000000000000E-14 "%" Correct digits = 16 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9787879273757324 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9773132122928821 " " y[1] (analytic) = 1.0469657146749676 " " y[1] (numeric) = 1.0469657146749667 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.48335726042243800000000000000E-14 "%" Correct digits = 16 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9773132122928828 " " Order of pole = 1.776356839400250500000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9765758547514586 " " y[1] (analytic) = 1.0485473214779006 " " y[1] (numeric) = 1.0485473214778998 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.47056114213577300000000000000E-14 "%" Correct digits = 16 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9765758547514674 " " Order of pole = 2.23820961764431560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.975838497210035 " " y[1] (analytic) = 1.0501325148894394 " " y[1] (numeric) = 1.0501325148894385 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.45777468183274900000000000000E-14 "%" Correct digits = 16 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9758384972100388 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9743637821271879 " " y[1] (analytic) = 1.0533137049900918 " " y[1] (numeric) = 1.0533137049900905 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26483461027664140000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9743637821271888 " " Order of pole = 2.131628207280300600000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9736264245857643 " " y[1] (analytic) = 1.05490972350797 " " y[1] (numeric) = 1.0549097235079685 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.47340781854446160000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.9426168666334437 " " Order of pole = 5.5777604757167860000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9728890670443407 " " y[1] (analytic) = 1.0565093722923575 " " y[1] (numeric) = 1.0565093722923562 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2610088130685532000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9728890670443451 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9714143519614936 " " y[1] (analytic) = 1.0597196047749458 " " y[1] (numeric) = 1.059719604774944 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6762517475341960000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9714143519614981 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.97067699442007 " " y[1] (analytic) = 1.0613302106350602 " " y[1] (numeric) = 1.0613302106350584 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.67370797665068350000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9706769944200737 " " Order of pole = 9.59232693276135300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9699396368786465 " " y[1] (analytic) = 1.0629444910858952 " " y[1] (numeric) = 1.0629444910858934 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.67116613736389860000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9699396368786467 " " Order of pole = 3.552713678800501000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9684649217957993 " " y[1] (analytic) = 1.0661841205486962 " " y[1] (numeric) = 1.0661841205486944 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.66608825358051130000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.9066826682043555 " " Order of pole = 3.472599985343549600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9677275642543758 " " y[1] (analytic) = 1.067809492061846 " " y[1] (numeric) = 1.0678094920618442 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6635522090839090000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.9395334045554141 " " Order of pole = 2.051336878139409200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9669902067129522 " " y[1] (analytic) = 1.069438583168475 " " y[1] (numeric) = 1.0694385831684727 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.0762726202300420000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9669902067129557 " " Order of pole = 9.23705556488130200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9655154916301051 " " y[1] (analytic) = 1.0727079696382447 " " y[1] (numeric) = 1.0727079696382422 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.2769390396148910000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9655154916301151 " " Order of pole = 2.62900812231237070000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9647781340886815 " " y[1] (analytic) = 1.0743482878480906 " " y[1] (numeric) = 1.0743482878480881 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.27346260221406420000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9647781340886897 " " Order of pole = 2.16715534406830560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9633034190058344 " " y[1] (analytic) = 1.077640231662567 " " y[1] (numeric) = 1.0776402316625644 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.4725647584533580000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9633034190058377 " " Order of pole = 8.52651282912120200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9625660614644108 " " y[1] (analytic) = 1.0792918803772276 " " y[1] (numeric) = 1.0792918803772245 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.8802444690531080000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9618287039229872 " " y[1] (analytic) = 1.0809473291107086 " " y[1] (numeric) = 1.0809473291107055 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.87583343353823960000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9603539888401401 " " y[1] (analytic) = 1.0842696733433397 " " y[1] (numeric) = 1.0842696733433363 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 3.0718087536335580000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9596166312987165 " " y[1] (analytic) = 1.0859365923093074 " " y[1] (numeric) = 1.0859365923093038 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.2715664100105957000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9596166312987227 " " Order of pole = 1.56319401867222040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.958879273757293 " " y[1] (analytic) = 1.0876073582281458 " " y[1] (numeric) = 1.087607358228142 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 3.47069947179753000000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9588792737572956 " " Order of pole = 7.10542735760100200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9574045586744458 " " y[1] (analytic) = 1.0909604783563023 " " y[1] (numeric) = 1.0909604783562985 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 3.4600321080492114000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9574045586744483 " " Order of pole = 6.39488462184090200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9566672011330223 " " y[1] (analytic) = 1.0926428563958566 " " y[1] (numeric) = 1.0926428563958528 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 3.4547045831396210000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9566672011330261 " " Order of pole = 9.94759830064140300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9559298435915987 " " y[1] (analytic) = 1.0943291290491775 " " y[1] (numeric) = 1.0943291290491735 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 3.65228593715972770000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9559298435916045 " " Order of pole = 1.52766688188421540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9544551285087516 " " y[1] (analytic) = 1.0977134063651064 " " y[1] (numeric) = 1.097713406365102 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.0455842779636764000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.953717770967328 " " y[1] (analytic) = 1.0994114352281437 " " y[1] (numeric) = 1.0994114352281392 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.0393359175667270000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9537177709673331 " " Order of pole = 1.35003119794419040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9529804134259044 " " y[1] (analytic) = 1.1011134071062385 " " y[1] (numeric) = 1.101113407106234 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.03309238616159750000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9529804134259112 " " Order of pole = 1.84741111297626050000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9515056983430573 " " y[1] (analytic) = 1.1045292288254613 " " y[1] (numeric) = 1.1045292288254565 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.42268179135947350000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9515056983430585 " " Order of pole = 2.84217094304040100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9507683408016337 " " y[1] (analytic) = 1.106243103244134 " " y[1] (numeric) = 1.1062431032441291 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.41582984248683250000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9507683408016342 " " Order of pole = 1.065814103640150300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9492936257187866 " " y[1] (analytic) = 1.1096828410016322 " " y[1] (numeric) = 1.1096828410016273 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.40214188041455350000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.948556268177363 " " y[1] (analytic) = 1.1114087292054735 " " y[1] (numeric) = 1.1114087292054682 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.7948791278708147000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9485562681773646 " " Order of pole = 3.90798504668055100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9478189106359395 " " y[1] (analytic) = 1.1131386469500228 " " y[1] (numeric) = 1.1131386469500175 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.7874274537159367000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9478189106359399 " " Order of pole = 1.065814103640150300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9463441955530923 " " y[1] (analytic) = 1.1166106213253808 " " y[1] (numeric) = 1.1166106213253753 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 4.9713973851840926000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9463441955530951 " " Order of pole = 7.10542735760100200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9456068380116688 " " y[1] (analytic) = 1.1183527032108014 " " y[1] (numeric) = 1.1183527032107958 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 4.9636533333254146000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9456068380116696 " " Order of pole = 2.131628207280300600000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9448694804702452 " " y[1] (analytic) = 1.1200988651466137 " " y[1] (numeric) = 1.1200988651466082 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 4.9559153177065113000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9433947653873981 " " y[1] (analytic) = 1.12360348022281 " " y[1] (numeric) = 1.1236034802228043 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 5.1380756909955450000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9433947653874042 " " Order of pole = 1.63424829224823040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9426574078459745 " " y[1] (analytic) = 1.1253619590147512 " " y[1] (numeric) = 1.1253619590147452 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 5.3273564873515160000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9426574078459784 " " Order of pole = 1.03028696685214530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.941920050304551 " " y[1] (analytic) = 1.1271245691606675 " " y[1] (numeric) = 1.1271245691606615 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 5.3190255070389210000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9419200503045582 " " Order of pole = 1.95399252334027550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9404453352217038 " " y[1] (analytic) = 1.1306622353720033 " " y[1] (numeric) = 1.130662235371997 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 5.4987676632317320000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.4370539834708473 " " Order of pole = 5.757172516496212000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9397079776802802 " " y[1] (analytic) = 1.132437317493435 " " y[1] (numeric) = 1.1324373174934288 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 5.4901484098583840000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9397079776802811 " " Order of pole = 2.131628207280300600000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9389706201388567 " " y[1] (analytic) = 1.134216583081347 " " y[1] (numeric) = 1.1342165830813407 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 5.6773050569690680000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.6075557547777449 " " Order of pole = 1.029931695484265200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9374959050560095 " " y[1] (analytic) = 1.1377877173336177 " " y[1] (numeric) = 1.137787717333611 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 5.8546405856460190000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9374959050560174 " " Order of pole = 2.13162820728030060000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.936758547514586 " " y[1] (analytic) = 1.1395796124661213 " " y[1] (numeric) = 1.1395796124661144 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 6.0402824667772890000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.9309023683431222 " " Order of pole = 7.608136343151273000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9352838324317388 " " y[1] (analytic) = 1.1431761253057273 " " y[1] (numeric) = 1.1431761253057204 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 6.0212793114753870000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.93528383243174 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9345464748903153 " " y[1] (analytic) = 1.1449807697952141 " " y[1] (numeric) = 1.144980769795207 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 6.2057176373991370000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9338091173488917 " " y[1] (analytic) = 1.1467896909409045 " " y[1] (numeric) = 1.1467896909408974 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 6.1959288732105920000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9338091173489009 " " Order of pole = 2.45137243837234560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9323344022660446 " " y[1] (analytic) = 1.1504204173496198 " " y[1] (numeric) = 1.1504204173496122 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 6.562397931743871000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.931597044724621 " " y[1] (analytic) = 1.152242249821008 " " y[1] (numeric) = 1.1522422498210003 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 6.7447285269945170000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9315970447246238 " " Order of pole = 7.46069872548105200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9308596871831974 " " y[1] (analytic) = 1.154068413365837 " " y[1] (numeric) = 1.1540684133658292 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 6.7340558691060270000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9308596871831987 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9293849721003503 " " y[1] (analytic) = 1.1577337886876748 " " y[1] (numeric) = 1.157733788687667 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 6.7127359055360970000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9286476145589267 " " y[1] (analytic) = 1.1595730281071834 " " y[1] (numeric) = 1.1595730281071754 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 6.8935768455647880000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9286476145589297 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9279102570175032 " " y[1] (analytic) = 1.1614166538856527 " " y[1] (numeric) = 1.1614166538856447 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 6.8826340233348660000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9279102570175035 " " Order of pole = 7.105427357601002000000000000000E-15 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.926435541934656 " " y[1] (analytic) = 1.1651171204110289 " " y[1] (numeric) = 1.1651171204110207 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 7.0513515236372550000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9264355419346586 " " Order of pole = 7.10542735760100200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9256981843932325 " " y[1] (analytic) = 1.16697398924291 " " y[1] (numeric) = 1.1669739892429016 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 7.2304053602987820000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9256981843932388 " " Order of pole = 1.74082970261224550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9249608268518089 " " y[1] (analytic) = 1.1688353006042338 " " y[1] (numeric) = 1.1688353006042251 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 7.4088621276235720000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9249608268518127 " " Order of pole = 1.03028696685214530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9234861117689618 " " y[1] (analytic) = 1.1725713077033952 " " y[1] (numeric) = 1.1725713077033864 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 7.5746218064956450000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9234861117689644 " " Order of pole = 7.46069872548105200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9227487542275382 " " y[1] (analytic) = 1.174446031977209 " " y[1] (numeric) = 1.1744460319771999 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 7.751593989039890000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9227487542275402 " " Order of pole = 5.329070518200751000000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9212740391446911 " " y[1] (analytic) = 1.1782089937417515 " " y[1] (numeric) = 1.1782089937417421 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 7.9152964002033650000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.4245793181075523 " " Order of pole = 1.270628047222999200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9205366816032675 " " y[1] (analytic) = 1.1800972601124184 " " y[1] (numeric) = 1.1800972601124087 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 8.2789469537202990000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.6912587041211338 " " Order of pole = 1.359801160560891700000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.919799324061844 " " y[1] (analytic) = 1.1819900694918186 " " y[1] (numeric) = 1.1819900694918088 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 8.2656892548190760000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9197993240618548 " " Order of pole = 3.0198066269804260000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9183246089789968 " " y[1] (analytic) = 1.1857893756760156 " " y[1] (numeric) = 1.1857893756760056 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 8.4264604040072380000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9175872514375732 " " y[1] (analytic) = 1.1876959018271387 " " y[1] (numeric) = 1.1876959018271287 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 8.4129339894621270000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9168498938961497 " " y[1] (analytic) = 1.1896070296802148 " " y[1] (numeric) = 1.1896070296802046 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 8.5860721832630220000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9168498938961566 " " Order of pole = 1.88293824976426550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9153751788133025 " " y[1] (analytic) = 1.1934431498366218 " " y[1] (numeric) = 1.1934431498366114 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 8.7445274899815180000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9153751788133055 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.914637821271879 " " y[1] (analytic) = 1.195368171961735 " " y[1] (numeric) = 1.1953681719617244 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.9161994491707790000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9146378212718875 " " Order of pole = 2.38031816479633560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9139004637304554 " " y[1] (analytic) = 1.1972978554329454 " " y[1] (numeric) = 1.1972978554329345 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 9.087283997006940000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9139004637304594 " " Order of pole = 1.10134124042815530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9124257486476083 " " y[1] (analytic) = 1.201171266721671 " " y[1] (numeric) = 1.2011712667216599 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 9.2428370157010380000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9116883911061847 " " y[1] (analytic) = 1.2031150248456983 " " y[1] (numeric) = 1.2031150248456872 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 9.2279042460428470000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9116883911061863 " " Order of pole = 3.90798504668055100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9109510335647611 " " y[1] (analytic) = 1.2050635049294398 " " y[1] (numeric) = 1.2050635049294287 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 9.2129835488642020000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.910951033564765 " " Order of pole = 1.06581410364015030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.909476318481914 " " y[1] (analytic) = 1.2089746922665339 " " y[1] (numeric) = 1.2089746922665225 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 9.3668419393844650000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9094763184819225 " " Order of pole = 2.34479102800833060000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9087389609404904 " " y[1] (analytic) = 1.2109374303206135 " " y[1] (numeric) = 1.2109374303206022 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 9.351659770049661000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9087389609404932 " " Order of pole = 7.81597009336110200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9072642458576433 " " y[1] (analytic) = 1.2148772726713222 " " y[1] (numeric) = 1.2148772726713104 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 9.6868748191740360000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9072642458576509 " " Order of pole = 2.09610107049229550000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9065268883162197 " " y[1] (analytic) = 1.2168544081456953 " " y[1] (numeric) = 1.2168544081456834 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 9.8536099188918460000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9065268883162211 " " Order of pole = 3.90798504668055100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9057895307747962 " " y[1] (analytic) = 1.2188363740437125 " " y[1] (numeric) = 1.2188363740437005 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 9.8375868338842880000000000000E-13 "%" Correct digits = 15 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.904314815691949 " " y[1] (analytic) = 1.2228148601670759 " " y[1] (numeric) = 1.2228148601670634 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.0168749400136337000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9035774581505255 " " y[1] (analytic) = 1.2248114120815068 " " y[1] (numeric) = 1.2248114120814944 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.0152173431067184000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9035774581505281 " " Order of pole = 7.10542735760100200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9028401006091019 " " y[1] (analytic) = 1.2268128577983834 " " y[1] (numeric) = 1.2268128577983708 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 1.0316604036446106000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9028401006091056 " " Order of pole = 9.94759830064140300000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9013653855262548 " " y[1] (analytic) = 1.2308304947323836 " " y[1] (numeric) = 1.2308304947323707 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 1.0463331174169498000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.9013653855262628 " " Order of pole = 2.23820961764431560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9006280279848312 " " y[1] (analytic) = 1.2328467181600302 " " y[1] (numeric) = 1.2328467181600171 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 1.0626326450484426000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.900628027984834 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8998906704434076 " " y[1] (analytic) = 1.2348678998118139 " " y[1] (numeric) = 1.2348678998118006 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 1.078874614647621100000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8998906704434102 " " Order of pole = 7.10542735760100200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8984159553605605 " " y[1] (analytic) = 1.2389252029377305 " " y[1] (numeric) = 1.238925202937717 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 1.0932638119161485000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8984159553605633 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.897678597819137 " " y[1] (analytic) = 1.240961357154154 " " y[1] (numeric) = 1.2409613571541407 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 1.0735770472381372000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.897678597819139 " " Order of pole = 5.329070518200751000000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8969412402777134 " " y[1] (analytic) = 1.2430025350799576 " " y[1] (numeric) = 1.243002535079944 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 1.0896776569772344000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8954665251948662 " " y[1] (analytic) = 1.2471000282876572 " " y[1] (numeric) = 1.2471000282876434 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 1.1039022687101156000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8947291676534427 " " y[1] (analytic) = 1.249156376854182 " " y[1] (numeric) = 1.2491563768541682 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 1.102085035984168000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8939918101120191 " " y[1] (analytic) = 1.2512178157000196 " " y[1] (numeric) = 1.2512178157000058 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 1.1002693002456843000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.892517095029172 " " y[1] (analytic) = 1.2553560315570798 " " y[1] (numeric) = 1.2553560315570655 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.1320178784321115000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8917797374877484 " " y[1] (analytic) = 1.257432842406084 " " y[1] (numeric) = 1.25743284240607 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.1301482064051777000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8917797374877524 " " Order of pole = 1.13686837721616030000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8903050224049013 " " y[1] (analytic) = 1.2616019550653081 " " y[1] (numeric) = 1.2616019550652935 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 1.1616139200016884000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8903050224049062 " " Order of pole = 1.42108547152020040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8895676648634777 " " y[1] (analytic) = 1.2636942911354239 " " y[1] (numeric) = 1.263694291135409 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 1.1772616711443863000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8888303073220541 " " y[1] (analytic) = 1.265791836657621 " " y[1] (numeric) = 1.265791836657606 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.1928527817632154000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8888303073220553 " " Order of pole = 3.19744231092045100000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.887355592239207 " " y[1] (analytic) = 1.2700026253630083 " " y[1] (numeric) = 1.2700026253629932 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.1888977891353832000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8873555922392131 " " Order of pole = 1.70530256582424040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8866182346977834 " " y[1] (analytic) = 1.272115903378787 " " y[1] (numeric) = 1.272115903378772 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.1869227556072948000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8866182346977866 " " Order of pole = 9.23705556488130200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8858808771563599 " " y[1] (analytic) = 1.274234460512545 " " y[1] (numeric) = 1.2742344605125295 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 1.2198008158169071000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8844061620735127 " " y[1] (analytic) = 1.2784874825999206 " " y[1] (numeric) = 1.2784874825999049 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.2331107784972067000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8844061620735175 " " Order of pole = 1.31450406115618530000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8836688045320892 " " y[1] (analytic) = 1.2806219829703454 " " y[1] (numeric) = 1.2806219829703296 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.2310554683053795000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.883668804532094 " " Order of pole = 1.38555833473219540000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8829314469906656 " " y[1] (analytic) = 1.282761833293101 " " y[1] (numeric) = 1.2827618332930848 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.2636216434593278000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8829314469906683 " " Order of pole = 7.46069872548105200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8814567319078185 " " y[1] (analytic) = 1.2870576554461255 " " y[1] (numeric) = 1.2870576554461093 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.259404043862259200000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8814567319078287 " " Order of pole = 2.9487523534044160000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8807193743663949 " " y[1] (analytic) = 1.2892136632892182 " " y[1] (numeric) = 1.289213663289202 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.2572978879367455000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8807193743663977 " " Order of pole = 7.81597009336110200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8799820168249713 " " y[1] (analytic) = 1.2913750931110433 " " y[1] (numeric) = 1.291375093111027 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.2551934945932458000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Complex estimate of poles used" Radius of convergence = 0.8322782358569395 " " Order of pole = 7.52109485802066000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8785073017421242 " " y[1] (analytic) = 1.2957142915499893 " " y[1] (numeric) = 1.2957142915499729 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.2681268449077987000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8785073017421292 " " Order of pole = 1.42108547152020040000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8777699442007006 " " y[1] (analytic) = 1.2978920967880272 " " y[1] (numeric) = 1.2978920967880105 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.2831070788234553000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8777699442007089 " " Order of pole = 2.38031816479633560000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8762952291178535 " " y[1] (analytic) = 1.3022642114316874 " " y[1] (numeric) = 1.3022642114316703 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.3129005949131306000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8762952291178564 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.87555787157643 " " y[1] (analytic) = 1.3044585579223935 " " y[1] (numeric) = 1.3044585579223764 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.310692047316431000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8755578715764311 " " Order of pole = 2.486899575160350700000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8748205140350064 " " y[1] (analytic) = 1.3066584553793799 " " y[1] (numeric) = 1.3066584553793628 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.3084853588815817000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "Real estimate of pole used" Radius of convergence = 0.8748205140350093 " " Order of pole = 8.17124146124115200000000000000E-14 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8733457989521592 " " y[1] (analytic) = 1.311074978225715 " " y[1] (numeric) = 1.3110749782256974 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.3379497038999640000000000000E-12 "%" Correct digits = 14 h = 7.3735754142351670000E-4 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;" Iterations = 166 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 58 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 36 Minutes 59 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 36 Minutes 33 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 39 Minutes 34 Seconds "Time to Timeout " Unknown Percent Done = 7.536995066511053 "%" (%o57) true (%o57) diffeq.max