X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;ds=sidebyside;f=ginac%2Fmul.cpp;h=3d33c78a129eeaeaaf9074bc291e76624e403da8;hb=0f26d08929532724d24a60e9fa5e5e98c4b2fa55;hp=d2dd675cfa08b9af4265a599e8011b99c06e14d8;hpb=690cd58cc13ad5052eb5851c573984965d0c40c1;p=ginac.git diff --git a/ginac/mul.cpp b/ginac/mul.cpp index d2dd675c..3d33c78a 100644 --- a/ginac/mul.cpp +++ b/ginac/mul.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's products of expressions. */ /* - * GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2008 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 @@ -34,6 +34,8 @@ #include "lst.h" #include "archive.h" #include "utils.h" +#include "symbol.h" +#include "compiler.h" namespace GiNaC { @@ -84,20 +86,20 @@ mul::mul(const epvector & v) GINAC_ASSERT(is_canonical()); } -mul::mul(const epvector & v, const ex & oc) +mul::mul(const epvector & v, const ex & oc, bool do_index_renaming) { tinfo_key = &mul::tinfo_static; overall_coeff = oc; - construct_from_epvector(v); + construct_from_epvector(v, do_index_renaming); GINAC_ASSERT(is_canonical()); } -mul::mul(std::auto_ptr vp, const ex & oc) +mul::mul(std::auto_ptr vp, const ex & oc, bool do_index_renaming) { tinfo_key = &mul::tinfo_static; GINAC_ASSERT(vp.get()!=0); overall_coeff = oc; - construct_from_epvector(*vp); + construct_from_epvector(*vp, do_index_renaming); GINAC_ASSERT(is_canonical()); } @@ -218,8 +220,12 @@ void mul::do_print_csrc(const print_csrc & c, unsigned level) const c.s << "("; if (!overall_coeff.is_equal(_ex1)) { - overall_coeff.print(c, precedence()); - c.s << "*"; + if (overall_coeff.is_equal(_ex_1)) + c.s << "-"; + else { + overall_coeff.print(c, precedence()); + c.s << "*"; + } } // Print arguments, separated by "*" or "/" @@ -311,7 +317,11 @@ int mul::degree(const ex & s) const epvector::const_iterator i = seq.begin(), end = seq.end(); while (i != end) { if (ex_to(i->coeff).is_integer()) - deg_sum += i->rest.degree(s) * ex_to(i->coeff).to_int(); + deg_sum += recombine_pair_to_ex(*i).degree(s); + else { + if (i->rest.has(s)) + throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent"); + } ++i; } return deg_sum; @@ -324,7 +334,11 @@ int mul::ldegree(const ex & s) const epvector::const_iterator i = seq.begin(), end = seq.end(); while (i != end) { if (ex_to(i->coeff).is_integer()) - deg_sum += i->rest.ldegree(s) * ex_to(i->coeff).to_int(); + deg_sum += recombine_pair_to_ex(*i).ldegree(s); + else { + if (i->rest.has(s)) + throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent"); + } ++i; } return deg_sum; @@ -410,7 +424,7 @@ ex mul::eval(int level) const return *this; } - int seq_size = seq.size(); + size_t seq_size = seq.size(); if (overall_coeff.is_zero()) { // *(...,x;0) -> 0 return _ex0; @@ -434,9 +448,81 @@ ex mul::eval(int level) const } return (new add(distrseq, ex_to(addref.overall_coeff). - mul_dyn(ex_to(overall_coeff)))) - ->setflag(status_flags::dynallocated | status_flags::evaluated); + mul_dyn(ex_to(overall_coeff))) + )->setflag(status_flags::dynallocated | status_flags::evaluated); + } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) { + // Strip the content and the unit part from each term. Thus + // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)2 + + epvector::const_iterator last = seq.end(); + epvector::const_iterator i = seq.begin(); + epvector::const_iterator j = seq.begin(); + std::auto_ptr s(new epvector); + numeric oc = *_num1_p; + bool something_changed = false; + while (i!=last) { + if (likely(! (is_a(i->rest) && i->coeff.is_equal(_ex1)))) { + // power::eval has such a rule, no need to handle powers here + ++i; + continue; + } + + // XXX: What is the best way to check if the polynomial is a primitive? + numeric c = i->rest.integer_content(); + const numeric lead_coeff = + ex_to(ex_to(i->rest).seq.begin()->coeff).div(c); + const bool canonicalizable = lead_coeff.is_integer(); + + // XXX: The main variable is chosen in a random way, so this code + // does NOT transform the term into the canonical form (thus, in some + // very unlucky event it can even loop forever). Hopefully the main + // variable will be the same for all terms in *this + const bool unit_normal = lead_coeff.is_pos_integer(); + if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) { + ++i; + continue; + } + + if (! something_changed) { + s->reserve(seq_size); + something_changed = true; + } + + while ((j!=i) && (j!=last)) { + s->push_back(*j); + ++j; + } + + if (! unit_normal) + c = c.mul(*_num_1_p); + + oc = oc.mul(c); + + // divide add by the number in place to save at least 2 .eval() calls + const add& addref = ex_to(i->rest); + add* primitive = new add(addref); + primitive->setflag(status_flags::dynallocated); + primitive->clearflag(status_flags::hash_calculated); + primitive->overall_coeff = ex_to(primitive->overall_coeff).div_dyn(c); + for (epvector::iterator ai = primitive->seq.begin(); + ai != primitive->seq.end(); ++ai) + ai->coeff = ex_to(ai->coeff).div_dyn(c); + + s->push_back(expair(*primitive, _ex1)); + + ++i; + ++j; + } + if (something_changed) { + while (j!=last) { + s->push_back(*j); + ++j; + } + return (new mul(s, ex_to(overall_coeff).mul_dyn(oc)) + )->setflag(status_flags::dynallocated); + } } + return this->hold(); } @@ -594,7 +680,7 @@ bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatch return true; } -/** Checks wheter e matches to the pattern pat and the (possibly to be updated +/** Checks wheter e matches to the pattern pat and the (possibly to be updated) * list of replacements repls. This matching is in the sense of algebraic * substitutions. Matching starts with pat.op(factor) of the pattern because * the factors before this one have already been matched. The (possibly @@ -650,6 +736,8 @@ ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const { std::vector subsed(seq.size(), false); exvector subsresult(seq.size()); + ex divide_by = 1; + ex multiply_by = 1; for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) { @@ -657,36 +745,35 @@ ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const retry1: int nummatches = std::numeric_limits::max(); std::vector currsubsed(seq.size(), false); - bool succeed = true; lst repls; if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed)) continue; - bool foundfirstsubsedfactor = false; - for (size_t j=0; jsecond.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches); - } + for (size_t j=0; jfirst.subs(ex(repls), subs_options::no_pattern); + divide_by *= power(subsed_pattern, nummatches); + ex subsed_result + = it->second.subs(ex(repls), subs_options::no_pattern); + multiply_by *= power(subsed_result, nummatches); goto retry1; } else { -retry2: - int nummatches = std::numeric_limits::max(); - lst repls; for (size_t j=0; jnops(); j++) { - if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) { + int nummatches = std::numeric_limits::max(); + lst repls; + if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){ subsed[j] = true; - subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches); - goto retry2; + ex subsed_pattern + = it->first.subs(ex(repls), subs_options::no_pattern); + divide_by *= power(subsed_pattern, nummatches); + ex subsed_result + = it->second.subs(ex(repls), subs_options::no_pattern); + multiply_by *= power(subsed_result, nummatches); } } } @@ -702,15 +789,7 @@ retry2: if (!subsfound) return subs_one_level(m, options | subs_options::algebraic); - exvector ev; ev.reserve(nops()); - for (size_t i=0; isetflag(status_flags::dynallocated); + return ((*this)/divide_by)*multiply_by; } // protected @@ -792,14 +871,14 @@ tinfo_t mul::return_type_tinfo() const return this; } -ex mul::thisexpairseq(const epvector & v, const ex & oc) const +ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const { - return (new mul(v, oc))->setflag(status_flags::dynallocated); + return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated); } -ex mul::thisexpairseq(std::auto_ptr vp, const ex & oc) const +ex mul::thisexpairseq(std::auto_ptr vp, const ex & oc, bool do_index_renaming) const { - return (new mul(vp, oc))->setflag(status_flags::dynallocated); + return (new mul(vp, oc, do_index_renaming))->setflag(status_flags::dynallocated); } expair mul::split_ex_to_pair(const ex & e) const @@ -914,6 +993,24 @@ bool mul::can_be_further_expanded(const ex & e) ex mul::expand(unsigned options) const { + { + // trivial case: expanding the monomial (~ 30% of all calls) + epvector::const_iterator i = seq.begin(), seq_end = seq.end(); + while ((i != seq.end()) && is_a(i->rest) && i->coeff.info(info_flags::integer)) + ++i; + if (i == seq_end) { + setflag(status_flags::expanded); + return *this; + } + } + + // do not rename indices if the object has no indices at all + if ((!(options & expand_options::expand_rename_idx)) && + this->info(info_flags::has_indices)) + options |= expand_options::expand_rename_idx; + + const bool skip_idx_rename = !(options & expand_options::expand_rename_idx); + // First, expand the children std::auto_ptr expanded_seqp = expandchildren(options); const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq); @@ -969,28 +1066,34 @@ ex mul::expand(unsigned options) const ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated); exvector add1_dummy_indices, add2_dummy_indices, add_indices; + lst dummy_subs; - for (epvector::const_iterator i=add1begin; i!=add1end; ++i) { - add_indices = get_all_dummy_indices(i->rest); - add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end()); - } - for (epvector::const_iterator i=add2begin; i!=add2end; ++i) { - add_indices = get_all_dummy_indices(i->rest); - add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end()); - } + if (!skip_idx_rename) { + for (epvector::const_iterator i=add1begin; i!=add1end; ++i) { + add_indices = get_all_dummy_indices_safely(i->rest); + add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end()); + } + for (epvector::const_iterator i=add2begin; i!=add2end; ++i) { + add_indices = get_all_dummy_indices_safely(i->rest); + add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end()); + } - sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less()); - sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less()); - lst dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices); + sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less()); + sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less()); + dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices); + } // Multiply explicitly all non-numeric terms of add1 and add2: for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) { // We really have to combine terms here in order to compactify // the result. Otherwise it would become waayy tooo bigg. - numeric oc; - distrseq.clear(); - ex i2_new = (dummy_subs.op(0).nops()>0? - i2->rest.subs((lst)dummy_subs.op(0), (lst)dummy_subs.op(1), subs_options::no_pattern) : i2->rest); + numeric oc(*_num0_p); + epvector distrseq2; + distrseq2.reserve(add1.seq.size()); + const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ? + i2->rest : + i2->rest.subs(ex_to(dummy_subs.op(0)), + ex_to(dummy_subs.op(1)), subs_options::no_pattern)); for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) { // Don't push_back expairs which might have a rest that evaluates to a numeric, // since that would violate an invariant of expairseq: @@ -998,13 +1101,12 @@ ex mul::expand(unsigned options) const if (is_exactly_a(rest)) { oc += ex_to(rest).mul(ex_to(i1->coeff).mul(ex_to(i2->coeff))); } else { - distrseq.push_back(expair(rest, ex_to(i1->coeff).mul_dyn(ex_to(i2->coeff)))); + distrseq2.push_back(expair(rest, ex_to(i1->coeff).mul_dyn(ex_to(i2->coeff)))); } } - tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated); - } + tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated); + } last_expanded = tmp_accu; - } else { if (!last_expanded.is_equal(_ex1)) non_adds.push_back(split_ex_to_pair(last_expanded)); @@ -1022,12 +1124,18 @@ ex mul::expand(unsigned options) const size_t n = last_expanded.nops(); exvector distrseq; distrseq.reserve(n); - exvector va = get_all_dummy_indices(mul(non_adds)); - sort(va.begin(), va.end(), ex_is_less()); + exvector va; + if (! skip_idx_rename) { + va = get_all_dummy_indices_safely(mul(non_adds)); + sort(va.begin(), va.end(), ex_is_less()); + } for (size_t i=0; isetflag(status_flags::dynallocated); if (can_be_further_expanded(term)) { distrseq.push_back(term.expand());