X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns_trans.cpp;h=4f081f171df33bffb961a2fc91d5d94e672bd9f3;hp=c8a0a8214ca7f276da625096c36899cdd1be9d78;hb=e0a84a395ab1bf84813eea95fde9c8a361dae9bc;hpb=704fe31c78553ffe2058c72bc4d17e6a1ae31350 diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp index c8a0a821..4f081f17 100644 --- a/ginac/inifcns_trans.cpp +++ b/ginac/inifcns_trans.cpp @@ -4,7 +4,7 @@ * functions. */ /* - * GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2015 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 (new mul(prodseq))->setflag(status_flags::dynallocated | status_flags::expanded); + } + + return exp(exp_arg).hold(); +} + static ex exp_deriv(const ex & x, unsigned deriv_param) { GINAC_ASSERT(deriv_param==0); @@ -99,11 +122,19 @@ static ex exp_imag_part(const ex & x) return exp(GiNaC::real_part(x))*sin(GiNaC::imag_part(x)); } +static ex exp_conjugate(const ex & x) +{ + // conjugate(exp(x))==exp(conjugate(x)) + return exp(x.conjugate()); +} + REGISTER_FUNCTION(exp, eval_func(exp_eval). evalf_func(exp_evalf). + expand_func(exp_expand). derivative_func(exp_deriv). real_part_func(exp_real_part). imag_part_func(exp_imag_part). + conjugate_func(exp_conjugate). latex_name("\\exp")); ////////// @@ -143,7 +174,7 @@ static ex log_eval(const ex & x) if (t.info(info_flags::real)) return t; } - + return log(x).hold(); } @@ -173,6 +204,10 @@ static ex log_series(const ex &arg, 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 @@ -258,12 +293,75 @@ 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 + // runs along the negative real axis. + if (x.info(info_flags::positive)) { + return log(x); + } + if (is_exactly_a(x) && + !x.imag_part().is_zero()) { + return log(x.conjugate()); + } + return conjugate_function(log(x)).hold(); +} + REGISTER_FUNCTION(log, eval_func(log_eval). evalf_func(log_evalf). + expand_func(log_expand). derivative_func(log_deriv). series_func(log_series). real_part_func(log_real_part). imag_part_func(log_imag_part). + conjugate_func(log_conjugate). latex_name("\\ln")); ////////// @@ -359,11 +457,18 @@ static ex sin_imag_part(const ex & x) return sinh(GiNaC::imag_part(x))*cos(GiNaC::real_part(x)); } +static ex sin_conjugate(const ex & x) +{ + // conjugate(sin(x))==sin(conjugate(x)) + return sin(x.conjugate()); +} + REGISTER_FUNCTION(sin, eval_func(sin_eval). evalf_func(sin_evalf). derivative_func(sin_deriv). real_part_func(sin_real_part). imag_part_func(sin_imag_part). + conjugate_func(sin_conjugate). latex_name("\\sin")); ////////// @@ -459,11 +564,18 @@ static ex cos_imag_part(const ex & x) return -sinh(GiNaC::imag_part(x))*sin(GiNaC::real_part(x)); } +static ex cos_conjugate(const ex & x) +{ + // conjugate(cos(x))==cos(conjugate(x)) + return cos(x.conjugate()); +} + REGISTER_FUNCTION(cos, eval_func(cos_eval). evalf_func(cos_evalf). derivative_func(cos_deriv). real_part_func(cos_real_part). imag_part_func(cos_imag_part). + conjugate_func(cos_conjugate). latex_name("\\cos")); ////////// @@ -576,12 +688,19 @@ static ex tan_series(const ex &x, return (sin(x)/cos(x)).series(rel, order, options); } +static ex tan_conjugate(const ex & x) +{ + // conjugate(tan(x))==tan(conjugate(x)) + return tan(x.conjugate()); +} + REGISTER_FUNCTION(tan, eval_func(tan_eval). evalf_func(tan_evalf). derivative_func(tan_deriv). series_func(tan_series). real_part_func(tan_real_part). imag_part_func(tan_imag_part). + conjugate_func(tan_conjugate). latex_name("\\tan")); ////////// @@ -640,9 +759,21 @@ static ex asin_deriv(const ex & x, unsigned deriv_param) return power(1-power(x,_ex2),_ex_1_2); } +static ex asin_conjugate(const ex & x) +{ + // conjugate(asin(x))==asin(conjugate(x)) unless on the branch cuts which + // run along the real axis outside the interval [-1, +1]. + if (is_exactly_a(x) && + (!x.imag_part().is_zero() || (x > *_num_1_p && x < *_num1_p))) { + return asin(x.conjugate()); + } + return conjugate_function(asin(x)).hold(); +} + REGISTER_FUNCTION(asin, eval_func(asin_eval). evalf_func(asin_evalf). derivative_func(asin_deriv). + conjugate_func(asin_conjugate). latex_name("\\arcsin")); ////////// @@ -701,9 +832,21 @@ static ex acos_deriv(const ex & x, unsigned deriv_param) return -power(1-power(x,_ex2),_ex_1_2); } +static ex acos_conjugate(const ex & x) +{ + // conjugate(acos(x))==acos(conjugate(x)) unless on the branch cuts which + // run along the real axis outside the interval [-1, +1]. + if (is_exactly_a(x) && + (!x.imag_part().is_zero() || (x > *_num_1_p && x < *_num1_p))) { + return acos(x.conjugate()); + } + return conjugate_function(acos(x)).hold(); +} + REGISTER_FUNCTION(acos, eval_func(acos_eval). evalf_func(acos_evalf). derivative_func(acos_deriv). + conjugate_func(acos_conjugate). latex_name("\\arccos")); ////////// @@ -800,10 +943,27 @@ static ex atan_series(const ex &arg, throw do_taylor(); } +static ex atan_conjugate(const ex & x) +{ + // conjugate(atan(x))==atan(conjugate(x)) unless on the branch cuts which + // run along the imaginary axis outside the interval [-I, +I]. + if (x.info(info_flags::real)) + return atan(x); + if (is_exactly_a(x)) { + const numeric x_re = ex_to(x.real_part()); + const numeric x_im = ex_to(x.imag_part()); + if (!x_re.is_zero() || + (x_im > *_num_1_p && x_im < *_num1_p)) + return atan(x.conjugate()); + } + return conjugate_function(atan(x)).hold(); +} + REGISTER_FUNCTION(atan, eval_func(atan_eval). evalf_func(atan_evalf). derivative_func(atan_deriv). series_func(atan_series). + conjugate_func(atan_conjugate). latex_name("\\arctan")); ////////// @@ -975,11 +1135,18 @@ static ex sinh_imag_part(const ex & x) return cosh(GiNaC::real_part(x))*sin(GiNaC::imag_part(x)); } +static ex sinh_conjugate(const ex & x) +{ + // conjugate(sinh(x))==sinh(conjugate(x)) + return sinh(x.conjugate()); +} + REGISTER_FUNCTION(sinh, eval_func(sinh_eval). evalf_func(sinh_evalf). derivative_func(sinh_deriv). real_part_func(sinh_real_part). imag_part_func(sinh_imag_part). + conjugate_func(sinh_conjugate). latex_name("\\sinh")); ////////// @@ -1052,11 +1219,18 @@ static ex cosh_imag_part(const ex & x) return sinh(GiNaC::real_part(x))*sin(GiNaC::imag_part(x)); } +static ex cosh_conjugate(const ex & x) +{ + // conjugate(cosh(x))==cosh(conjugate(x)) + return cosh(x.conjugate()); +} + REGISTER_FUNCTION(cosh, eval_func(cosh_eval). evalf_func(cosh_evalf). derivative_func(cosh_deriv). real_part_func(cosh_real_part). imag_part_func(cosh_imag_part). + conjugate_func(cosh_conjugate). latex_name("\\cosh")); ////////// @@ -1149,12 +1323,19 @@ static ex tanh_imag_part(const ex & x) return tan(b)/(1+power(tanh(a),2)*power(tan(b),2)); } +static ex tanh_conjugate(const ex & x) +{ + // conjugate(tanh(x))==tanh(conjugate(x)) + return tanh(x.conjugate()); +} + REGISTER_FUNCTION(tanh, eval_func(tanh_eval). evalf_func(tanh_evalf). derivative_func(tanh_deriv). series_func(tanh_series). real_part_func(tanh_real_part). imag_part_func(tanh_imag_part). + conjugate_func(tanh_conjugate). latex_name("\\tanh")); ////////// @@ -1197,9 +1378,26 @@ static ex asinh_deriv(const ex & x, unsigned deriv_param) return power(_ex1+power(x,_ex2),_ex_1_2); } +static ex asinh_conjugate(const ex & x) +{ + // conjugate(asinh(x))==asinh(conjugate(x)) unless on the branch cuts which + // run along the imaginary axis outside the interval [-I, +I]. + if (x.info(info_flags::real)) + return asinh(x); + if (is_exactly_a(x)) { + const numeric x_re = ex_to(x.real_part()); + const numeric x_im = ex_to(x.imag_part()); + if (!x_re.is_zero() || + (x_im > *_num_1_p && x_im < *_num1_p)) + return asinh(x.conjugate()); + } + return conjugate_function(asinh(x)).hold(); +} + REGISTER_FUNCTION(asinh, eval_func(asinh_eval). evalf_func(asinh_evalf). - derivative_func(asinh_deriv)); + derivative_func(asinh_deriv). + conjugate_func(asinh_conjugate)); ////////// // inverse hyperbolic cosine (trigonometric function) @@ -1249,9 +1447,21 @@ static ex acosh_deriv(const ex & x, unsigned deriv_param) return power(x+_ex_1,_ex_1_2)*power(x+_ex1,_ex_1_2); } +static ex acosh_conjugate(const ex & x) +{ + // conjugate(acosh(x))==acosh(conjugate(x)) unless on the branch cut + // which runs along the real axis from +1 to -inf. + if (is_exactly_a(x) && + (!x.imag_part().is_zero() || x > *_num1_p)) { + return acosh(x.conjugate()); + } + return conjugate_function(acosh(x)).hold(); +} + REGISTER_FUNCTION(acosh, eval_func(acosh_eval). evalf_func(acosh_evalf). - derivative_func(acosh_deriv)); + derivative_func(acosh_deriv). + conjugate_func(acosh_conjugate)); ////////// // inverse hyperbolic tangent (trigonometric function) @@ -1320,30 +1530,42 @@ 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; + epvector seq; seq.push_back(expair(Order0correction, _ex0)); - seq.push_back(expair(Order(_ex1), order)); - return series(replarg - pseries(rel, seq), rel, order); + seq.push_back(expair(Order(_ex1), order)); + return series(replarg - pseries(rel, seq), rel, order); } throw do_taylor(); } +static ex atanh_conjugate(const ex & x) +{ + // conjugate(atanh(x))==atanh(conjugate(x)) unless on the branch cuts which + // run along the real axis outside the interval [-1, +1]. + if (is_exactly_a(x) && + (!x.imag_part().is_zero() || (x > *_num_1_p && x < *_num1_p))) { + return atanh(x.conjugate()); + } + return conjugate_function(atanh(x)).hold(); +} + REGISTER_FUNCTION(atanh, eval_func(atanh_eval). evalf_func(atanh_evalf). derivative_func(atanh_deriv). - series_func(atanh_series)); + series_func(atanh_series). + conjugate_func(atanh_conjugate)); } // namespace GiNaC