X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnormal.cpp;h=669a59f8de12d0a7cfb3d3eba694eaa9703d275d;hp=d59e42d58b7671d13ddcd1a0b6473d0da7ea1c78;hb=539de73dc25de63f2888f8696d73ac3fc83db45f;hpb=6d89c8f370b4f5f98319f340aa0da31cbdff0dc5 diff --git a/ginac/normal.cpp b/ginac/normal.cpp index d59e42d5..669a59f8 100644 --- a/ginac/normal.cpp +++ b/ginac/normal.cpp @@ -6,7 +6,7 @@ * computation, square-free factorization and rational function normalization. */ /* - * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2001 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 @@ -23,7 +23,6 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ -#include #include #include @@ -34,7 +33,6 @@ #include "constant.h" #include "expairseq.h" #include "fail.h" -#include "indexed.h" #include "inifcns.h" #include "lst.h" #include "mul.h" @@ -46,9 +44,7 @@ #include "symbol.h" #include "utils.h" -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_NAMESPACE_GINAC // If comparing expressions (ex::compare()) is fast, you can set this to 1. // Some routines like quo(), rem() and gcd() will then return a quick answer @@ -140,8 +136,17 @@ struct sym_desc { /** Maximum of deg_a and deg_b (Used for sorting) */ int max_deg; + /** Maximum number of terms of leading coefficient of symbol in both polynomials */ + int max_lcnops; + /** Commparison operator for sorting */ - bool operator<(const sym_desc &x) const {return max_deg < x.max_deg;} + bool operator<(const sym_desc &x) const + { + if (max_deg == x.max_deg) + return max_lcnops < x.max_lcnops; + else + return max_deg < x.max_deg; + } }; // Vector of sym_desc structures @@ -196,7 +201,8 @@ static void get_symbol_stats(const ex &a, const ex &b, sym_desc_vec &v) int deg_b = b.degree(*(it->sym)); it->deg_a = deg_a; it->deg_b = deg_b; - it->max_deg = std::max(deg_a,deg_b); + it->max_deg = std::max(deg_a, deg_b); + it->max_lcnops = std::max(a.lcoeff(*(it->sym)).nops(), b.lcoeff(*(it->sym)).nops()); it->ldeg_a = a.ldegree(*(it->sym)); it->ldeg_b = b.ldegree(*(it->sym)); it++; @@ -206,7 +212,7 @@ static void get_symbol_stats(const ex &a, const ex &b, sym_desc_vec &v) std::clog << "Symbols:\n"; it = v.begin(); itend = v.end(); while (it != itend) { - std::clog << " " << *it->sym << ": deg_a=" << it->deg_a << ", deg_b=" << it->deg_b << ", ldeg_a=" << it->ldeg_a << ", ldeg_b=" << it->ldeg_b << ", max_deg=" << it->max_deg << endl; + std::clog << " " << *it->sym << ": deg_a=" << it->deg_a << ", deg_b=" << it->deg_b << ", ldeg_a=" << it->ldeg_a << ", ldeg_b=" << it->ldeg_b << ", max_deg=" << it->max_deg << ", max_lcnops=" << it->max_lcnops << endl; std::clog << " lcoeff_a=" << a.lcoeff(*(it->sym)) << ", lcoeff_b=" << b.lcoeff(*(it->sym)) << endl; it++; } @@ -234,8 +240,12 @@ static numeric lcmcoeff(const ex &e, const numeric &l) for (unsigned i=0; i ex2; typedef std::pair exbool; struct ex2_less { - bool operator() (const ex2 p, const ex2 q) const + bool operator() (const ex2 &p, const ex2 &q) const { - return p.first.compare(q.first) < 0 || (!(q.first.compare(p.first) < 0) && p.second.compare(q.second) < 0); + int cmp = p.first.compare(q.first); + return ((cmp<0) || (!(cmp>0) && p.second.compare(q.second)<0)); } }; @@ -1174,6 +1188,8 @@ numeric ex::max_coefficient(void) const return bp->max_coefficient(); } +/** Implementation ex::max_coefficient(). + * @see heur_gcd */ numeric basic::max_coefficient(void) const { return _num1(); @@ -1236,11 +1252,7 @@ ex basic::smod(const numeric &xi) const ex numeric::smod(const numeric &xi) const { -#ifndef NO_NAMESPACE_GINAC return GiNaC::smod(*this, xi); -#else // ndef NO_NAMESPACE_GINAC - return ::smod(*this, xi); -#endif // ndef NO_NAMESPACE_GINAC } ex add::smod(const numeric &xi) const @@ -1251,21 +1263,13 @@ ex add::smod(const numeric &xi) const epvector::const_iterator itend = seq.end(); while (it != itend) { GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric)); -#ifndef NO_NAMESPACE_GINAC numeric coeff = GiNaC::smod(ex_to_numeric(it->coeff), xi); -#else // ndef NO_NAMESPACE_GINAC - numeric coeff = ::smod(ex_to_numeric(it->coeff), xi); -#endif // ndef NO_NAMESPACE_GINAC if (!coeff.is_zero()) newseq.push_back(expair(it->rest, coeff)); it++; } GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); -#ifndef NO_NAMESPACE_GINAC numeric coeff = GiNaC::smod(ex_to_numeric(overall_coeff), xi); -#else // ndef NO_NAMESPACE_GINAC - numeric coeff = ::smod(ex_to_numeric(overall_coeff), xi); -#endif // ndef NO_NAMESPACE_GINAC return (new add(newseq,coeff))->setflag(status_flags::dynallocated); } @@ -1281,11 +1285,7 @@ ex mul::smod(const numeric &xi) const #endif // def DO_GINAC_ASSERT mul * mulcopyp=new mul(*this); GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); -#ifndef NO_NAMESPACE_GINAC mulcopyp->overall_coeff = GiNaC::smod(ex_to_numeric(overall_coeff),xi); -#else // ndef NO_NAMESPACE_GINAC - mulcopyp->overall_coeff = ::smod(ex_to_numeric(overall_coeff),xi); -#endif // ndef NO_NAMESPACE_GINAC mulcopyp->clearflag(status_flags::evaluated); mulcopyp->clearflag(status_flags::hash_calculated); return mulcopyp->setflag(status_flags::dynallocated); @@ -1464,7 +1464,7 @@ ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args) } // Check arguments - if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)) { + if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial))) { throw(std::invalid_argument("gcd: arguments must be polynomials over the rationals")); } @@ -1678,7 +1678,7 @@ ex lcm(const ex &a, const ex &b, bool check_args) { if (is_ex_exactly_of_type(a, numeric) && is_ex_exactly_of_type(b, numeric)) return lcm(ex_to_numeric(a), ex_to_numeric(b)); - if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial)) + if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial))) throw(std::invalid_argument("lcm: arguments must be polynomials over the rationals")); ex ca, cb; @@ -1866,9 +1866,13 @@ static ex frac_cancel(const ex &n, const ex &d) //std::clog << "frac_cancel num = " << num << ", den = " << den << endl; + // Handle trivial case where denominator is 1 + if (den.is_equal(_ex1())) + return (new lst(num, den))->setflag(status_flags::dynallocated); + // Handle special cases where numerator or denominator is 0 if (num.is_zero()) - return (new lst(_ex0(), _ex1()))->setflag(status_flags::dynallocated); + return (new lst(num, _ex1()))->setflag(status_flags::dynallocated); if (den.expand().is_zero()) throw(std::overflow_error("frac_cancel: division by zero in frac_cancel")); @@ -1914,74 +1918,52 @@ ex add::normal(lst &sym_lst, lst &repl_lst, int level) const else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); - // Normalize and expand children, chop into summands - exvector o; - o.reserve(seq.size()+1); + // Normalize children and split each one into numerator and denominator + exvector nums, dens; + nums.reserve(seq.size()+1); + dens.reserve(seq.size()+1); epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - - // Normalize and expand child - ex n = recombine_pair_to_ex(*it).bp->normal(sym_lst, repl_lst, level-1).expand(); - - // If numerator is a sum, chop into summands - if (is_ex_exactly_of_type(n.op(0), add)) { - epvector::const_iterator bit = ex_to_add(n.op(0)).seq.begin(), bitend = ex_to_add(n.op(0)).seq.end(); - while (bit != bitend) { - o.push_back((new lst(recombine_pair_to_ex(*bit), n.op(1)))->setflag(status_flags::dynallocated)); - bit++; - } - - // The overall_coeff is already normalized (== rational), we just - // split it into numerator and denominator - GINAC_ASSERT(ex_to_numeric(ex_to_add(n.op(0)).overall_coeff).is_rational()); - numeric overall = ex_to_numeric(ex_to_add(n.op(0)).overall_coeff); - o.push_back((new lst(overall.numer(), overall.denom() * n.op(1)))->setflag(status_flags::dynallocated)); - } else - o.push_back(n); + ex n = recombine_pair_to_ex(*it).bp->normal(sym_lst, repl_lst, level-1); + nums.push_back(n.op(0)); + dens.push_back(n.op(1)); it++; } - o.push_back(overall_coeff.bp->normal(sym_lst, repl_lst, level-1)); - - // o is now a vector of {numerator, denominator} lists + ex n = overall_coeff.bp->normal(sym_lst, repl_lst, level-1); + nums.push_back(n.op(0)); + dens.push_back(n.op(1)); + GINAC_ASSERT(nums.size() == dens.size()); + + // Now, nums is a vector of all numerators and dens is a vector of + // all denominators +//std::clog << "add::normal uses " << nums.size() << " summands:\n"; + + // Add fractions sequentially + exvector::const_iterator num_it = nums.begin(), num_itend = nums.end(); + exvector::const_iterator den_it = dens.begin(), den_itend = dens.end(); +//std::clog << " num = " << *num_it << ", den = " << *den_it << endl; + ex num = *num_it++, den = *den_it++; + while (num_it != num_itend) { +//std::clog << " num = " << *num_it << ", den = " << *den_it << endl; + ex next_num = *num_it++, next_den = *den_it++; + + // Trivially add sequences of fractions with identical denominators + while ((den_it != den_itend) && next_den.is_equal(*den_it)) { + next_num += *num_it; + num_it++; den_it++; + } - // Determine common denominator - ex den = _ex1(); - exvector::const_iterator ait = o.begin(), aitend = o.end(); -//std::clog << "add::normal uses the following summands:\n"; - while (ait != aitend) { -//std::clog << " num = " << ait->op(0) << ", den = " << ait->op(1) << endl; - den = lcm(ait->op(1), den, false); - ait++; + // Additiion of two fractions, taking advantage of the fact that + // the heuristic GCD algorithm computes the cofactors at no extra cost + ex co_den1, co_den2; + ex g = gcd(den, next_den, &co_den1, &co_den2, false); + num = ((num * co_den2) + (next_num * co_den1)).expand(); + den *= co_den2; // this is the lcm(den, next_den) } //std::clog << " common denominator = " << den << endl; - // Add fractions - if (den.is_equal(_ex1())) { - - // Common denominator is 1, simply add all fractions - exvector num_seq; - for (ait=o.begin(); ait!=aitend; ait++) { - num_seq.push_back(ait->op(0) / ait->op(1)); - } - return (new lst((new add(num_seq))->setflag(status_flags::dynallocated), den))->setflag(status_flags::dynallocated); - - } else { - - // Perform fractional addition - exvector num_seq; - for (ait=o.begin(); ait!=aitend; ait++) { - ex q; - if (!divide(den, ait->op(1), q, false)) { - // should not happen - throw(std::runtime_error("invalid expression in add::normal, division failed")); - } - num_seq.push_back((ait->op(0) * q).expand()); - } - ex num = (new add(num_seq))->setflag(status_flags::dynallocated); - - // Cancel common factors from num/den - return frac_cancel(num, den); - } + // Cancel common factors from num/den + return frac_cancel(num, den); } @@ -2026,65 +2008,65 @@ ex power::normal(lst &sym_lst, lst &repl_lst, int level) const else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); - // Normalize basis - ex n = basis.bp->normal(sym_lst, repl_lst, level-1); + // Normalize basis and exponent (exponent gets reassembled) + ex n_basis = basis.bp->normal(sym_lst, repl_lst, level-1); + ex n_exponent = exponent.bp->normal(sym_lst, repl_lst, level-1); + n_exponent = n_exponent.op(0) / n_exponent.op(1); - if (exponent.info(info_flags::integer)) { + if (n_exponent.info(info_flags::integer)) { - if (exponent.info(info_flags::positive)) { + if (n_exponent.info(info_flags::positive)) { // (a/b)^n -> {a^n, b^n} - return (new lst(power(n.op(0), exponent), power(n.op(1), exponent)))->setflag(status_flags::dynallocated); + return (new lst(power(n_basis.op(0), n_exponent), power(n_basis.op(1), n_exponent)))->setflag(status_flags::dynallocated); - } else if (exponent.info(info_flags::negative)) { + } else if (n_exponent.info(info_flags::negative)) { // (a/b)^-n -> {b^n, a^n} - return (new lst(power(n.op(1), -exponent), power(n.op(0), -exponent)))->setflag(status_flags::dynallocated); + return (new lst(power(n_basis.op(1), -n_exponent), power(n_basis.op(0), -n_exponent)))->setflag(status_flags::dynallocated); } } else { - if (exponent.info(info_flags::positive)) { + if (n_exponent.info(info_flags::positive)) { // (a/b)^x -> {sym((a/b)^x), 1} - return (new lst(replace_with_symbol(power(n.op(0) / n.op(1), exponent), sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); - } else if (exponent.info(info_flags::negative)) { + } else if (n_exponent.info(info_flags::negative)) { - if (n.op(1).is_equal(_ex1())) { + if (n_basis.op(1).is_equal(_ex1())) { // a^-x -> {1, sym(a^x)} - return (new lst(_ex1(), replace_with_symbol(power(n.op(0), -exponent), sym_lst, repl_lst)))->setflag(status_flags::dynallocated); + return (new lst(_ex1(), replace_with_symbol(power(n_basis.op(0), -n_exponent), sym_lst, repl_lst)))->setflag(status_flags::dynallocated); } else { // (a/b)^-x -> {sym((b/a)^x), 1} - return (new lst(replace_with_symbol(power(n.op(1) / n.op(0), -exponent), sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); } - } else { // exponent not numeric + } else { // n_exponent not numeric // (a/b)^x -> {sym((a/b)^x, 1} - return (new lst(replace_with_symbol(power(n.op(0) / n.op(1), exponent), sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); } } } -/** Implementation of ex::normal() for pseries. It normalizes each coefficient and - * replaces the series by a temporary symbol. +/** Implementation of ex::normal() for pseries. It normalizes each coefficient + * and replaces the series by a temporary symbol. * @see ex::normal */ ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const { - epvector new_seq; - new_seq.reserve(seq.size()); - - epvector::const_iterator it = seq.begin(), itend = seq.end(); - while (it != itend) { - new_seq.push_back(expair(it->rest.normal(), it->coeff)); - it++; + epvector newseq; + for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + ex restexp = i->rest.normal(); + if (!restexp.is_zero()) + newseq.push_back(expair(restexp, i->coeff)); } - ex n = pseries(relational(var,point), new_seq); + ex n = pseries(relational(var,point), newseq); return (new lst(replace_with_symbol(n, sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); } @@ -2253,6 +2235,4 @@ ex ex::to_rational(lst &repl_lst) const } -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC