X-Git-Url: https://ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Finifcns_trans.cpp;h=d9dd4a2643ccff4b06b330eb92e11246bba0b05d;hb=e341c3c11f2e6ade3340a446be15705856370d5e;hp=10a36758f43001f6c02774531522c7fd2667c7c2;hpb=f9afb6aca6a971650dff63b11ca8c2ef18506690;p=ginac.git diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp index 10a36758..d9dd4a26 100644 --- a/ginac/inifcns_trans.cpp +++ b/ginac/inifcns_trans.cpp @@ -4,7 +4,7 @@ * functions. */ /* - * GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2023 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -24,6 +24,8 @@ #include "inifcns.h" #include "ex.h" #include "constant.h" +#include "add.h" +#include "mul.h" #include "numeric.h" #include "power.h" #include "operators.h" @@ -81,6 +83,27 @@ static ex exp_eval(const ex & x) return exp(x).hold(); } +static ex exp_expand(const ex & arg, unsigned options) +{ + ex exp_arg; + if (options & expand_options::expand_function_args) + exp_arg = arg.expand(options); + else + exp_arg=arg; + + if ((options & expand_options::expand_transcendental) + && is_exactly_a(exp_arg)) { + exvector prodseq; + prodseq.reserve(exp_arg.nops()); + for (const_iterator i = exp_arg.begin(); i != exp_arg.end(); ++i) + prodseq.push_back(exp(*i)); + + return dynallocate(prodseq).setflag(status_flags::expanded); + } + + return exp(exp_arg).hold(); +} + static ex exp_deriv(const ex & x, unsigned deriv_param) { GINAC_ASSERT(deriv_param==0); @@ -105,12 +128,48 @@ static ex exp_conjugate(const ex & x) return exp(x.conjugate()); } +static ex exp_power(const ex & x, const ex & a) +{ + /* + * The power law (e^x)^a=e^(x*a) is used in two cases: + * a) a is an integer and x may be complex; + * b) both x and a are reals. + * Negative a is excluded to keep automatic simplifications like exp(x)/exp(x)=1. + */ + if (a.info(info_flags::nonnegative) + && (a.info(info_flags::integer) || (x.info(info_flags::real) && a.info(info_flags::real)))) + return exp(x*a); + else if (a.info(info_flags::negative) + && (a.info(info_flags::integer) || (x.info(info_flags::real) && a.info(info_flags::real)))) + return power(exp(-x*a), _ex_1).hold(); + + return power(exp(x), a).hold(); +} + +static bool exp_info(const ex & x, unsigned inf) +{ + switch (inf) { + case info_flags::numeric: + case info_flags::expanded: + case info_flags::real: + return x.info(inf); + case info_flags::positive: + case info_flags::nonnegative: + return x.info(info_flags::real); + default: + return false; + } +} + REGISTER_FUNCTION(exp, eval_func(exp_eval). evalf_func(exp_evalf). + info_func(exp_info). + expand_func(exp_expand). derivative_func(exp_deriv). real_part_func(exp_real_part). imag_part_func(exp_imag_part). conjugate_func(exp_conjugate). + power_func(exp_power). latex_name("\\exp")); ////////// @@ -150,7 +209,7 @@ static ex log_eval(const ex & x) if (t.info(info_flags::real)) return t; } - + return log(x).hold(); } @@ -173,13 +232,17 @@ static ex log_series(const ex &arg, // maybe substitution of rel into arg fails because of a pole try { arg_pt = arg.subs(rel, subs_options::no_pattern); - } catch (pole_error) { + } catch (pole_error &) { must_expand_arg = true; } // or we are at the branch point anyways if (arg_pt.is_zero()) must_expand_arg = true; + if (arg.diff(ex_to(rel.lhs())).is_zero()) { + throw do_taylor(); + } + if (must_expand_arg) { // method: // This is the branch point: Series expand the argument first, then @@ -214,25 +277,19 @@ static ex log_series(const ex &arg, // in this case n more (or less) terms are needed // (sadly, to generate them, we have to start from the beginning) if (n == 0 && coeff == 1) { - epvector epv; - ex acc = (new pseries(rel, epv))->setflag(status_flags::dynallocated); - epv.reserve(2); - epv.push_back(expair(-1, _ex0)); - epv.push_back(expair(Order(_ex1), order)); - ex rest = pseries(rel, epv).add_series(argser); + ex rest = pseries(rel, epvector{expair(-1, _ex0), expair(Order(_ex1), order)}).add_series(argser); + ex acc = dynallocate(rel, epvector()); for (int i = order-1; i>0; --i) { - epvector cterm; - cterm.reserve(1); - cterm.push_back(expair(i%2 ? _ex1/i : _ex_1/i, _ex0)); - acc = pseries(rel, cterm).add_series(ex_to(acc)); + epvector cterm { expair(i%2 ? _ex1/i : _ex_1/i, _ex0) }; + acc = pseries(rel, std::move(cterm)).add_series(ex_to(acc)); acc = (ex_to(rest)).mul_series(ex_to(acc)); } return acc; } const ex newarg = ex_to((arg/coeff).series(rel, order+n, options)).shift_exponents(-n).convert_to_poly(true); - return pseries(rel, seq).add_series(ex_to(log(newarg).series(rel, order, options))); + return pseries(rel, std::move(seq)).add_series(ex_to(log(newarg).series(rel, order, options))); } else // it was a monomial - return pseries(rel, seq); + return pseries(rel, std::move(seq)); } if (!(options & series_options::suppress_branchcut) && arg_pt.info(info_flags::negative)) { @@ -244,9 +301,12 @@ static ex log_series(const ex &arg, const symbol foo; const ex replarg = series(log(arg), s==foo, order).subs(foo==point, subs_options::no_pattern); epvector seq; - seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0)); + if (order > 0) { + seq.reserve(2); + seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0)); + } seq.push_back(expair(Order(_ex1), order)); - return series(replarg - I*Pi + pseries(rel, seq), rel, order); + return series(replarg - I*Pi + pseries(rel, std::move(seq)), rel, order); } throw do_taylor(); // caught by function::series() } @@ -265,6 +325,53 @@ static ex log_imag_part(const ex & x) return atan2(GiNaC::imag_part(x), GiNaC::real_part(x)); } +static ex log_expand(const ex & arg, unsigned options) +{ + if ((options & expand_options::expand_transcendental) + && is_exactly_a(arg) && !arg.info(info_flags::indefinite)) { + exvector sumseq; + exvector prodseq; + sumseq.reserve(arg.nops()); + prodseq.reserve(arg.nops()); + bool possign=true; + + // searching for positive/negative factors + for (const_iterator i = arg.begin(); i != arg.end(); ++i) { + ex e; + if (options & expand_options::expand_function_args) + e=i->expand(options); + else + e=*i; + if (e.info(info_flags::positive)) + sumseq.push_back(log(e)); + else if (e.info(info_flags::negative)) { + sumseq.push_back(log(-e)); + possign = !possign; + } else + prodseq.push_back(e); + } + + if (sumseq.size() > 0) { + ex newarg; + if (options & expand_options::expand_function_args) + newarg=((possign?_ex1:_ex_1)*mul(prodseq)).expand(options); + else { + newarg=(possign?_ex1:_ex_1)*mul(prodseq); + ex_to(newarg).setflag(status_flags::purely_indefinite); + } + return add(sumseq)+log(newarg); + } else { + if (!(options & expand_options::expand_function_args)) + ex_to(arg).setflag(status_flags::purely_indefinite); + } + } + + if (options & expand_options::expand_function_args) + return log(arg.expand(options)).hold(); + else + return log(arg).hold(); +} + static ex log_conjugate(const ex & x) { // conjugate(log(x))==log(conjugate(x)) unless on the branch cut which @@ -279,8 +386,23 @@ static ex log_conjugate(const ex & x) return conjugate_function(log(x)).hold(); } +static bool log_info(const ex & x, unsigned inf) +{ + switch (inf) { + case info_flags::numeric: + case info_flags::expanded: + return x.info(inf); + case info_flags::real: + return x.info(info_flags::positive); + default: + return false; + } +} + REGISTER_FUNCTION(log, eval_func(log_eval). evalf_func(log_evalf). + info_func(log_info). + expand_func(log_expand). derivative_func(log_deriv). series_func(log_series). real_part_func(log_real_part). @@ -387,8 +509,21 @@ static ex sin_conjugate(const ex & x) return sin(x.conjugate()); } +static bool trig_info(const ex & x, unsigned inf) +{ + switch (inf) { + case info_flags::numeric: + case info_flags::expanded: + case info_flags::real: + return x.info(inf); + default: + return false; + } +} + REGISTER_FUNCTION(sin, eval_func(sin_eval). evalf_func(sin_evalf). + info_func(trig_info). derivative_func(sin_deriv). real_part_func(sin_real_part). imag_part_func(sin_imag_part). @@ -495,6 +630,7 @@ static ex cos_conjugate(const ex & x) } REGISTER_FUNCTION(cos, eval_func(cos_eval). + info_func(trig_info). evalf_func(cos_evalf). derivative_func(cos_deriv). real_part_func(cos_real_part). @@ -620,6 +756,7 @@ static ex tan_conjugate(const ex & x) REGISTER_FUNCTION(tan, eval_func(tan_eval). evalf_func(tan_evalf). + info_func(trig_info). derivative_func(tan_deriv). series_func(tan_series). real_part_func(tan_real_part). @@ -694,8 +831,20 @@ static ex asin_conjugate(const ex & x) return conjugate_function(asin(x)).hold(); } +static bool asin_info(const ex & x, unsigned inf) +{ + switch (inf) { + case info_flags::numeric: + case info_flags::expanded: + return x.info(inf); + default: + return false; + } +} + REGISTER_FUNCTION(asin, eval_func(asin_eval). evalf_func(asin_evalf). + info_func(asin_info). derivative_func(asin_deriv). conjugate_func(asin_conjugate). latex_name("\\arcsin")); @@ -769,6 +918,7 @@ static ex acos_conjugate(const ex & x) REGISTER_FUNCTION(acos, eval_func(acos_eval). evalf_func(acos_evalf). + info_func(asin_info). // Flags of acos are shared with asin functions derivative_func(acos_deriv). conjugate_func(acos_conjugate). latex_name("\\arccos")); @@ -860,9 +1010,12 @@ static ex atan_series(const ex &arg, else Order0correction += log((I*arg_pt+_ex1)/(I*arg_pt+_ex_1))*I*_ex1_2; epvector seq; - seq.push_back(expair(Order0correction, _ex0)); + if (order > 0) { + seq.reserve(2); + seq.push_back(expair(Order0correction, _ex0)); + } seq.push_back(expair(Order(_ex1), order)); - return series(replarg - pseries(rel, seq), rel, order); + return series(replarg - pseries(rel, std::move(seq)), rel, order); } throw do_taylor(); } @@ -883,8 +1036,25 @@ static ex atan_conjugate(const ex & x) return conjugate_function(atan(x)).hold(); } +static bool atan_info(const ex & x, unsigned inf) +{ + switch (inf) { + case info_flags::numeric: + case info_flags::expanded: + case info_flags::real: + return x.info(inf); + case info_flags::positive: + case info_flags::negative: + case info_flags::nonnegative: + return x.info(info_flags::real) && x.info(inf); + default: + return false; + } +} + REGISTER_FUNCTION(atan, eval_func(atan_eval). evalf_func(atan_evalf). + info_func(atan_info). derivative_func(atan_deriv). series_func(atan_series). conjugate_func(atan_conjugate). @@ -985,7 +1155,26 @@ static ex atan2_deriv(const ex & y, const ex & x, unsigned deriv_param) return -y*power(power(x,_ex2)+power(y,_ex2),_ex_1); } +static bool atan2_info(const ex & y, const ex & x, unsigned inf) +{ + switch (inf) { + case info_flags::numeric: + case info_flags::expanded: + case info_flags::real: + return y.info(inf) && x.info(inf); + case info_flags::positive: + case info_flags::negative: + case info_flags::nonnegative: + return y.info(info_flags::real) && x.info(info_flags::real) + && y.info(inf); + default: + return false; + } +} + REGISTER_FUNCTION(atan2, eval_func(atan2_eval). + evalf_func(atan2_evalf). + info_func(atan2_info). evalf_func(atan2_evalf). derivative_func(atan2_deriv)); @@ -1067,6 +1256,7 @@ static ex sinh_conjugate(const ex & x) REGISTER_FUNCTION(sinh, eval_func(sinh_eval). evalf_func(sinh_evalf). + info_func(atan_info). // Flags of sinh are shared with atan functions derivative_func(sinh_deriv). real_part_func(sinh_real_part). imag_part_func(sinh_imag_part). @@ -1151,6 +1341,7 @@ static ex cosh_conjugate(const ex & x) REGISTER_FUNCTION(cosh, eval_func(cosh_eval). evalf_func(cosh_evalf). + info_func(exp_info). // Flags of cosh are shared with exp functions derivative_func(cosh_deriv). real_part_func(cosh_real_part). imag_part_func(cosh_imag_part). @@ -1255,6 +1446,7 @@ static ex tanh_conjugate(const ex & x) REGISTER_FUNCTION(tanh, eval_func(tanh_eval). evalf_func(tanh_evalf). + info_func(atan_info). // Flags of tanh are shared with atan functions derivative_func(tanh_deriv). series_func(tanh_series). real_part_func(tanh_real_part). @@ -1320,6 +1512,7 @@ static ex asinh_conjugate(const ex & x) REGISTER_FUNCTION(asinh, eval_func(asinh_eval). evalf_func(asinh_evalf). + info_func(atan_info). // Flags of asinh are shared with atan functions derivative_func(asinh_deriv). conjugate_func(asinh_conjugate)); @@ -1384,6 +1577,7 @@ static ex acosh_conjugate(const ex & x) REGISTER_FUNCTION(acosh, eval_func(acosh_eval). evalf_func(acosh_evalf). + info_func(asin_info). // Flags of acosh are shared with asin functions derivative_func(acosh_deriv). conjugate_func(acosh_conjugate)); @@ -1454,22 +1648,25 @@ static ex atanh_series(const ex &arg, return ((log(_ex1+arg)-log(_ex1-arg))*_ex1_2).series(rel, order, options); // ...and the branch cuts (the discontinuity at the cut being just I*Pi) if (!(options & series_options::suppress_branchcut)) { - // method: - // This is the branch cut: assemble the primitive series manually and - // then add the corresponding complex step function. - const symbol &s = ex_to(rel.lhs()); - const ex &point = rel.rhs(); - const symbol foo; - const ex replarg = series(atanh(arg), s==foo, order).subs(foo==point, subs_options::no_pattern); + // method: + // This is the branch cut: assemble the primitive series manually and + // then add the corresponding complex step function. + const symbol &s = ex_to(rel.lhs()); + const ex &point = rel.rhs(); + const symbol foo; + const ex replarg = series(atanh(arg), s==foo, order).subs(foo==point, subs_options::no_pattern); ex Order0correction = replarg.op(0)+csgn(I*arg)*Pi*I*_ex1_2; if (arg_pt<_ex0) Order0correction += log((arg_pt+_ex_1)/(arg_pt+_ex1))*_ex1_2; else Order0correction += log((arg_pt+_ex1)/(arg_pt+_ex_1))*_ex_1_2; - epvector seq; - seq.push_back(expair(Order0correction, _ex0)); - seq.push_back(expair(Order(_ex1), order)); - return series(replarg - pseries(rel, seq), rel, order); + epvector seq; + if (order > 0) { + seq.reserve(2); + seq.push_back(expair(Order0correction, _ex0)); + } + seq.push_back(expair(Order(_ex1), order)); + return series(replarg - pseries(rel, std::move(seq)), rel, order); } throw do_taylor(); } @@ -1487,6 +1684,7 @@ static ex atanh_conjugate(const ex & x) REGISTER_FUNCTION(atanh, eval_func(atanh_eval). evalf_func(atanh_evalf). + info_func(asin_info). // Flags of atanh are shared with asin functions derivative_func(atanh_deriv). series_func(atanh_series). conjugate_func(atanh_conjugate));