X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=9ed27c6c4bf3f4c7435674de9138bb4aa16d76fc;hp=db68b275ffbbc788a476bad5b9b9f814b30229ff;hb=9e1051ad0a532338a6f995b9f41f17ac5cdc47a6;hpb=87d731b215909cc8ab8ecdb8c05fcd717bf63fd2 diff --git a/ginac/mul.cpp b/ginac/mul.cpp index db68b275..9ed27c6c 100644 --- a/ginac/mul.cpp +++ b/ginac/mul.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's products of expressions. */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2007 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 @@ -17,7 +17,7 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ #include @@ -30,9 +30,11 @@ #include "power.h" #include "operators.h" #include "matrix.h" +#include "indexed.h" #include "lst.h" #include "archive.h" #include "utils.h" +#include "compiler.h" namespace GiNaC { @@ -40,7 +42,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq, print_func(&mul::do_print). print_func(&mul::do_print_latex). print_func(&mul::do_print_csrc). - print_func(&inherited::do_print_tree). + print_func(&mul::do_print_tree). print_func(&mul::do_print_python_repr)) @@ -50,7 +52,7 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq, mul::mul() { - tinfo_key = TINFO_mul; + tinfo_key = &mul::tinfo_static; } ////////// @@ -61,7 +63,7 @@ mul::mul() mul::mul(const ex & lh, const ex & rh) { - tinfo_key = TINFO_mul; + tinfo_key = &mul::tinfo_static; overall_coeff = _ex1; construct_from_2_ex(lh,rh); GINAC_ASSERT(is_canonical()); @@ -69,7 +71,7 @@ mul::mul(const ex & lh, const ex & rh) mul::mul(const exvector & v) { - tinfo_key = TINFO_mul; + tinfo_key = &mul::tinfo_static; overall_coeff = _ex1; construct_from_exvector(v); GINAC_ASSERT(is_canonical()); @@ -77,32 +79,32 @@ mul::mul(const exvector & v) mul::mul(const epvector & v) { - tinfo_key = TINFO_mul; + tinfo_key = &mul::tinfo_static; overall_coeff = _ex1; construct_from_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 = TINFO_mul; + 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 = TINFO_mul; - GINAC_ASSERT(vp!=0); + 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()); } mul::mul(const ex & lh, const ex & mh, const ex & rh) { - tinfo_key = TINFO_mul; + tinfo_key = &mul::tinfo_static; exvector factors; factors.reserve(3); factors.push_back(lh); @@ -128,8 +130,8 @@ void mul::print_overall_coeff(const print_context & c, const char *mul_sym) cons const numeric &coeff = ex_to(overall_coeff); if (coeff.csgn() == -1) c.s << '-'; - if (!coeff.is_equal(_num1) && - !coeff.is_equal(_num_1)) { + if (!coeff.is_equal(*_num1_p) && + !coeff.is_equal(*_num_1_p)) { if (coeff.is_rational()) { if (coeff.is_negative()) (-coeff).print(c); @@ -217,8 +219,12 @@ 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 "/" @@ -310,7 +316,11 @@ 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; @@ -323,7 +333,11 @@ 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; @@ -409,7 +423,7 @@ 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; @@ -421,7 +435,7 @@ ex mul::eval(int level) const return recombine_pair_to_ex(*(seq.begin())); } else if ((seq_size==1) && is_exactly_a((*seq.begin()).rest) && - ex_to((*seq.begin()).coeff).is_equal(_num1)) { + ex_to((*seq.begin()).coeff).is_equal(*_num1_p)) { // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +()) const add & addref = ex_to((*seq.begin()).rest); std::auto_ptr distrseq(new epvector); @@ -433,9 +447,81 @@ 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_dyn(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(); } @@ -460,6 +546,41 @@ ex mul::evalf(int level) const return mul(s, overall_coeff.evalf(level)); } +void mul::find_real_imag(ex & rp, ex & ip) const +{ + rp = overall_coeff.real_part(); + ip = overall_coeff.imag_part(); + for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + ex factor = recombine_pair_to_ex(*i); + ex new_rp = factor.real_part(); + ex new_ip = factor.imag_part(); + if(new_ip.is_zero()) { + rp *= new_rp; + ip *= new_rp; + } else { + ex temp = rp*new_rp - ip*new_ip; + ip = ip*new_rp + rp*new_ip; + rp = temp; + } + } + rp = rp.expand(); + ip = ip.expand(); +} + +ex mul::real_part() const +{ + ex rp, ip; + find_real_imag(rp, ip); + return rp; +} + +ex mul::imag_part() const +{ + ex rp, ip; + find_real_imag(rp, ip); + return ip; +} + ex mul::evalm() const { // numeric*matrix @@ -558,61 +679,100 @@ 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) + * 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 + * updated) number of matches is in nummatches. subsed[i] is true for factors + * that already have been replaced by previous substitutions and matched[i] + * is true for factors that have been matched by the current match. + */ +bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, lst &repls, + int factor, int &nummatches, const std::vector &subsed, + std::vector &matched) +{ + if (factor == pat.nops()) + return true; + + for (size_t i=0; i(pattern)) { + lst repls; + int nummatches = std::numeric_limits::max(); + std::vector subsed(seq.size(), false); + std::vector matched(seq.size(), false); + if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches, + subsed, matched)) + return true; + } + return basic::has(pattern, options); +} + 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) { if (is_exactly_a(it->first)) { - +retry1: int nummatches = std::numeric_limits::max(); std::vector currsubsed(seq.size(), false); - bool succeed = true; lst repls; - - for (size_t j=0; jfirst.nops(); j++) { - bool found=false; - for (size_t k=0; kfirst.op(j), nummatches, repls)) { - currsubsed[k] = true; - found = true; - break; - } - } - if (!found) { - succeed = false; - break; - } - } - if (!succeed) + + 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 { - 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); + 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); } } } @@ -628,15 +788,7 @@ ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const 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 @@ -672,7 +824,7 @@ int mul::compare_same_type(const basic & other) const unsigned mul::return_type() const { if (seq.empty()) { - // mul without factors: should not happen, but commutes + // mul without factors: should not happen, but commutates return return_types::commutative; } @@ -692,8 +844,8 @@ unsigned mul::return_type() const if ((rt == return_types::noncommutative) && (!all_commutative)) { // another nc element found, compare type_infos if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) { - // diffent types -> mul is ncc - return return_types::noncommutative_composite; + // different types -> mul is ncc + return return_types::noncommutative_composite; } } ++i; @@ -702,10 +854,10 @@ unsigned mul::return_type() const return all_commutative ? return_types::commutative : return_types::noncommutative; } -unsigned mul::return_type_tinfo() const +tinfo_t mul::return_type_tinfo() const { if (seq.empty()) - return tinfo_key; // mul without factors: should not happen + return this; // mul without factors: should not happen // return type_info of first noncommutative element epvector::const_iterator i = seq.begin(), end = seq.end(); @@ -715,17 +867,17 @@ unsigned mul::return_type_tinfo() const ++i; } // no noncommutative element found, should not happen - return tinfo_key; + 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 @@ -766,7 +918,7 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p, ex mul::recombine_pair_to_ex(const expair & p) const { - if (ex_to(p.coeff).is_equal(_num1)) + if (ex_to(p.coeff).is_equal(*_num1_p)) return p.rest; else return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated); @@ -821,7 +973,21 @@ bool mul::can_make_flat(const expair & p) const // this assertion will probably fail somewhere // it would require a more careful make_flat, obeying the power laws // probably should return true only if p.coeff is integer - return ex_to(p.coeff).is_equal(_num1); + return ex_to(p.coeff).is_equal(*_num1_p); +} + +bool mul::can_be_further_expanded(const ex & e) +{ + if (is_exactly_a(e)) { + for (epvector::const_iterator cit = ex_to(e).seq.begin(); cit != ex_to(e).seq.end(); ++cit) { + if (is_exactly_a(cit->rest) && cit->coeff.info(info_flags::posint)) + return true; + } + } else if (is_exactly_a(e)) { + if (is_exactly_a(e.op(0)) && e.op(1).info(info_flags::posint)) + return true; + } + return false; } ex mul::expand(unsigned options) const @@ -833,18 +999,14 @@ ex mul::expand(unsigned options) const // Now, look for all the factors that are sums and multiply each one out // with the next one that is found while collecting the factors which are // not sums - int number_of_adds = 0; ex last_expanded = _ex1; epvector non_adds; non_adds.reserve(expanded_seq.size()); - bool non_adds_has_sums = false; // Look for sums or powers of sums in the non_adds (we need this later) - epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end(); - while (cit != last) { + for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) { if (is_exactly_a(cit->rest) && (cit->coeff.is_equal(_ex1))) { - ++number_of_adds; if (is_exactly_a(last_expanded)) { // Expand a product of two sums, aggressive version. @@ -862,6 +1024,7 @@ ex mul::expand(unsigned options) const const epvector::const_iterator add2end = add2.seq.end(); epvector distrseq; distrseq.reserve(add1.seq.size()+add2.seq.size()); + // Multiply add2 with the overall coefficient of add1 and append it to distrseq: if (!add1.overall_coeff.is_zero()) { if (add1.overall_coeff.is_equal(_ex1)) @@ -870,6 +1033,7 @@ ex mul::expand(unsigned options) const for (epvector::const_iterator i=add2begin; i!=add2end; ++i) distrseq.push_back(expair(i->rest, ex_to(i->coeff).mul_dyn(ex_to(add1.overall_coeff)))); } + // Multiply add1 with the overall coefficient of add2 and append it to distrseq: if (!add2.overall_coeff.is_zero()) { if (add2.overall_coeff.is_equal(_ex1)) @@ -878,69 +1042,93 @@ ex mul::expand(unsigned options) const for (epvector::const_iterator i=add1begin; i!=add1end; ++i) distrseq.push_back(expair(i->rest, ex_to(i->coeff).mul_dyn(ex_to(add2.overall_coeff)))); } + // Compute the new overall coefficient and put it together: 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; + + 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); + // Multiply explicitly all non-numeric terms of add1 and add2: - for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) { + 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(); - for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) { + 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); + 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: - const ex rest = ex((new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated)).expand(); - if (is_exactly_a(rest)) + const ex rest = (new mul(i1->rest, i2_new))->setflag(status_flags::dynallocated); + if (is_exactly_a(rest)) { oc += ex_to(rest).mul(ex_to(i1->coeff).mul(ex_to(i2->coeff))); - else + } else { distrseq.push_back(expair(rest, ex_to(i1->coeff).mul_dyn(ex_to(i2->coeff)))); + } } tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated); } last_expanded = tmp_accu; } else { - non_adds.push_back(split_ex_to_pair(last_expanded)); + if (!last_expanded.is_equal(_ex1)) + non_adds.push_back(split_ex_to_pair(last_expanded)); last_expanded = cit->rest; } + } else { - if (is_exactly_a(cit->rest)) - non_adds_has_sums = true; non_adds.push_back(*cit); } - ++cit; } // Now the only remaining thing to do is to multiply the factors which // were not sums into the "last_expanded" sum if (is_exactly_a(last_expanded)) { - const add & finaladd = ex_to(last_expanded); - - size_t n = finaladd.nops(); + size_t n = last_expanded.nops(); exvector distrseq; distrseq.reserve(n); + exvector va = get_all_dummy_indices_safely(mul(non_adds)); + sort(va.begin(), va.end(), ex_is_less()); for (size_t i=0; i((new mul(factors, overall_coeff))->setflag(status_flags::dynallocated)); - - // The new term may have sums in it if e.g. a sqrt() of a sum in - // the non_adds meets a sqrt() of a sum in the factor from - // last_expanded. In this case we should re-expand the term. - if (non_adds_has_sums || is_exactly_a(new_factor.rest)) - distrseq.push_back(ex(term).expand()); - else - distrseq.push_back(term.setflag(options == 0 ? status_flags::expanded : 0)); + factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i)))); + ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated); + if (can_be_further_expanded(term)) { + distrseq.push_back(term.expand()); + } else { + if (options == 0) + ex_to(term).setflag(status_flags::expanded); + distrseq.push_back(term); + } } + return ((new add(distrseq))-> setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0))); } + non_adds.push_back(split_ex_to_pair(last_expanded)); - return (new mul(non_adds, overall_coeff))-> - setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)); + ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated); + if (can_be_further_expanded(result)) { + return result.expand(); + } else { + if (options == 0) + ex_to(result).setflag(status_flags::expanded); + return result; + } }