X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Finifcns.cpp;h=d68afbb50df6d6f965e8d6bbbd4573cd9bdf5115;hb=0b39999b706904d977d8d498e3b01796fb789371;hp=02c909f313180456e7598794500cad82c4a0370f;hpb=cca88b51436e4b654d16a4d60cd0d1c66fcf5dd6;p=ginac.git diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp index 02c909f3..d68afbb5 100644 --- a/ginac/inifcns.cpp +++ b/ginac/inifcns.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's initially known functions. */ /* - * GiNaC Copyright (C) 1999-2014 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2020 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 +24,7 @@ #include "ex.h" #include "constant.h" #include "lst.h" +#include "fderivative.h" #include "matrix.h" #include "mul.h" #include "power.h" @@ -66,6 +67,19 @@ static ex conjugate_conjugate(const ex & arg) return arg; } +// If x is real then U.diff(x)-I*V.diff(x) represents both conjugate(U+I*V).diff(x) +// and conjugate((U+I*V).diff(x)) +static ex conjugate_expl_derivative(const ex & arg, const symbol & s) +{ + if (s.info(info_flags::real)) + return conjugate(arg.diff(s)); + else { + exvector vec_arg; + vec_arg.push_back(arg); + return fderivative(ex_to(conjugate(arg)).get_serial(),0,vec_arg).hold()*arg.diff(s); + } +} + static ex conjugate_real_part(const ex & arg) { return arg.real_part(); @@ -95,7 +109,6 @@ static bool func_arg_info(const ex & arg, unsigned inf) case info_flags::prime: case info_flags::crational_polynomial: case info_flags::rational_function: - case info_flags::algebraic: case info_flags::positive: case info_flags::negative: case info_flags::nonnegative: @@ -115,6 +128,7 @@ static bool conjugate_info(const ex & arg, unsigned inf) REGISTER_FUNCTION(conjugate_function, eval_func(conjugate_eval). evalf_func(conjugate_evalf). + expl_derivative_func(conjugate_expl_derivative). info_func(conjugate_info). print_func(conjugate_print_latex). conjugate_func(conjugate_conjugate). @@ -159,8 +173,21 @@ static ex real_part_imag_part(const ex & arg) return 0; } +// If x is real then Re(e).diff(x) is equal to Re(e.diff(x)) +static ex real_part_expl_derivative(const ex & arg, const symbol & s) +{ + if (s.info(info_flags::real)) + return real_part_function(arg.diff(s)); + else { + exvector vec_arg; + vec_arg.push_back(arg); + return fderivative(ex_to(real_part(arg)).get_serial(),0,vec_arg).hold()*arg.diff(s); + } +} + REGISTER_FUNCTION(real_part_function, eval_func(real_part_eval). evalf_func(real_part_evalf). + expl_derivative_func(real_part_expl_derivative). print_func(real_part_print_latex). conjugate_func(real_part_conjugate). real_part_func(real_part_real_part). @@ -204,8 +231,21 @@ static ex imag_part_imag_part(const ex & arg) return 0; } +// If x is real then Im(e).diff(x) is equal to Im(e.diff(x)) +static ex imag_part_expl_derivative(const ex & arg, const symbol & s) +{ + if (s.info(info_flags::real)) + return imag_part_function(arg.diff(s)); + else { + exvector vec_arg; + vec_arg.push_back(arg); + return fderivative(ex_to(imag_part(arg)).get_serial(),0,vec_arg).hold()*arg.diff(s); + } +} + REGISTER_FUNCTION(imag_part_function, eval_func(imag_part_eval). evalf_func(imag_part_evalf). + expl_derivative_func(imag_part_expl_derivative). print_func(imag_part_print_latex). conjugate_func(imag_part_conjugate). real_part_func(imag_part_real_part). @@ -232,6 +272,9 @@ static ex abs_eval(const ex & arg) if (arg.info(info_flags::nonnegative)) return arg; + if (arg.info(info_flags::negative) || (-arg).info(info_flags::nonnegative)) + return -arg; + if (is_ex_the_function(arg, abs)) return arg; @@ -266,7 +309,7 @@ static ex abs_expand(const ex & arg, unsigned options) else prodseq.push_back(abs(*i)); } - return (new mul(prodseq))->setflag(status_flags::dynallocated | status_flags::expanded); + return dynallocate(prodseq).setflag(status_flags::expanded); } if (options & expand_options::expand_function_args) @@ -275,6 +318,12 @@ static ex abs_expand(const ex & arg, unsigned options) return abs(arg).hold(); } +static ex abs_expl_derivative(const ex & arg, const symbol & s) +{ + ex diff_arg = arg.diff(s); + return (diff_arg*arg.conjugate()+arg*diff_arg.conjugate())/2/abs(arg); +} + static void abs_print_latex(const ex & arg, const print_context & c) { c.s << "{|"; arg.print(c); c.s << "|}"; @@ -302,10 +351,12 @@ static ex abs_imag_part(const ex& arg) static ex abs_power(const ex & arg, const ex & exp) { - if (arg.is_equal(arg.conjugate()) && ((is_a(exp) && ex_to(exp).is_even()) - || exp.info(info_flags::even))) - return power(arg, exp); - else + if ((is_a(exp) && ex_to(exp).is_even()) || exp.info(info_flags::even)) { + if (arg.info(info_flags::real) || arg.is_equal(arg.conjugate())) + return pow(arg, exp); + else + return pow(arg, exp/2) * pow(arg.conjugate(), exp/2); + } else return power(abs(arg), exp).hold(); } @@ -339,6 +390,7 @@ bool abs_info(const ex & arg, unsigned inf) REGISTER_FUNCTION(abs, eval_func(abs_eval). evalf_func(abs_evalf). expand_func(abs_expand). + expl_derivative_func(abs_expl_derivative). info_func(abs_info). print_func(abs_print_latex). print_func(abs_print_csrc_float). @@ -400,9 +452,8 @@ static ex step_series(const ex & arg, && !(options & series_options::suppress_branchcut)) throw (std::domain_error("step_series(): on imaginary axis")); - epvector seq; - seq.push_back(expair(step(arg_pt), _ex0)); - return pseries(rel,seq); + epvector seq { expair(step(arg_pt), _ex0) }; + return pseries(rel, std::move(seq)); } static ex step_conjugate(const ex& arg) @@ -479,9 +530,8 @@ static ex csgn_series(const ex & arg, && !(options & series_options::suppress_branchcut)) throw (std::domain_error("csgn_series(): on imaginary axis")); - epvector seq; - seq.push_back(expair(csgn(arg_pt), _ex0)); - return pseries(rel,seq); + epvector seq { expair(csgn(arg_pt), _ex0) }; + return pseries(rel, std::move(seq)); } static ex csgn_conjugate(const ex& arg) @@ -587,9 +637,8 @@ static ex eta_series(const ex & x, const ex & y, (y_pt.info(info_flags::numeric) && y_pt.info(info_flags::negative)) || ((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative))) throw (std::domain_error("eta_series(): on discontinuity")); - epvector seq; - seq.push_back(expair(eta(x_pt,y_pt), _ex0)); - return pseries(rel,seq); + epvector seq { expair(eta(x_pt,y_pt), _ex0) }; + return pseries(rel, std::move(seq)); } static ex eta_conjugate(const ex & x, const ex & y) @@ -692,9 +741,8 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt // substitute the argument's series expansion ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern); // maybe that was terminating, so add a proper order term - epvector nseq; - nseq.push_back(expair(Order(_ex1), order)); - ser += pseries(rel, nseq); + epvector nseq { expair(Order(_ex1), order) }; + ser += pseries(rel, std::move(nseq)); // reexpanding it will collapse the series again return ser.series(rel, order); // NB: Of course, this still does not allow us to compute anything @@ -717,9 +765,8 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt // substitute the argument's series expansion ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern); // maybe that was terminating, so add a proper order term - epvector nseq; - nseq.push_back(expair(Order(_ex1), order)); - ser += pseries(rel, nseq); + epvector nseq { expair(Order(_ex1), order) }; + ser += pseries(rel, std::move(nseq)); // reexpanding it will collapse the series again return ser.series(rel, order); } @@ -741,7 +788,7 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt seq.push_back(expair((replarg.op(i)/power(s-foo,i)).series(foo==point,1,options).op(0).subs(foo==s, subs_options::no_pattern),i)); // append an order term: seq.push_back(expair(Order(_ex1), replarg.nops()-1)); - return pseries(rel, seq); + return pseries(rel, std::move(seq)); } } // all other cases should be safe, by now: @@ -903,7 +950,7 @@ static ex binomial_eval(const ex & x, const ex &y) return binomial(x, y).hold(); } -// At the moment the numeric evaluation of a binomail function always +// At the moment the numeric evaluation of a binomial function always // gives a real number, but if this would be implemented using the gamma // function, also complex conjugation should be changed (or rather, deleted). static ex binomial_conjugate(const ex & x, const ex & y) @@ -951,11 +998,10 @@ static ex Order_eval(const ex & x) static ex Order_series(const ex & x, const relational & r, int order, unsigned options) { // Just wrap the function into a pseries object - epvector new_seq; GINAC_ASSERT(is_a(r.lhs())); const symbol &s = ex_to(r.lhs()); - new_seq.push_back(expair(Order(_ex1), numeric(std::min(x.ldegree(s), order)))); - return pseries(r, new_seq); + epvector new_seq { expair(Order(_ex1), numeric(std::min(x.ldegree(s), order))) }; + return pseries(r, std::move(new_seq)); } static ex Order_conjugate(const ex & x) @@ -975,11 +1021,15 @@ static ex Order_imag_part(const ex & x) return Order(x).hold(); } -// Differentiation is handled in function::derivative because of its special requirements +static ex Order_expl_derivative(const ex & arg, const symbol & s) +{ + return Order(arg.diff(s)); +} REGISTER_FUNCTION(Order, eval_func(Order_eval). series_func(Order_series). latex_name("\\mathcal{O}"). + expl_derivative_func(Order_expl_derivative). conjugate_func(Order_conjugate). real_part_func(Order_real_part). imag_part_func(Order_imag_part)); @@ -988,13 +1038,36 @@ REGISTER_FUNCTION(Order, eval_func(Order_eval). // Solve linear system ////////// +class symbolset { + exset s; + void insert_symbols(const ex &e) + { + if (is_a(e)) { + s.insert(e); + } else { + for (const ex &sube : e) { + insert_symbols(sube); + } + } + } +public: + explicit symbolset(const ex &e) + { + insert_symbols(e); + } + bool has(const ex &e) const + { + return s.find(e) != s.end(); + } +}; + ex lsolve(const ex &eqns, const ex &symbols, unsigned options) { // solve a system of linear equations if (eqns.info(info_flags::relation_equal)) { if (!symbols.info(info_flags::symbol)) throw(std::invalid_argument("lsolve(): 2nd argument must be a symbol")); - const ex sol = lsolve(lst(eqns),lst(symbols)); + const ex sol = lsolve(lst{eqns}, lst{symbols}); GINAC_ASSERT(sol.nops()==1); GINAC_ASSERT(is_exactly_a(sol.op(0))); @@ -1003,20 +1076,20 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options) } // syntax checks - if (!eqns.info(info_flags::list)) { - throw(std::invalid_argument("lsolve(): 1st argument must be a list or an equation")); + if (!(eqns.info(info_flags::list) || eqns.info(info_flags::exprseq))) { + throw(std::invalid_argument("lsolve(): 1st argument must be a list, a sequence, or an equation")); } for (size_t i=0; i(symbols.op(c)),1); linpart -= co*symbols.op(c); sys(r,c) = co; @@ -1038,11 +1114,13 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options) } // test if system is linear and fill vars matrix + const symbolset sys_syms(sys); + const symbolset rhs_syms(rhs); for (size_t i=0; i