* Implementation of GiNaC's products of expressions. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2010 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
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include <iostream>
-#include <vector>
-#include <stdexcept>
-#include <limits>
-
#include "mul.h"
#include "add.h"
#include "power.h"
#include "lst.h"
#include "archive.h"
#include "utils.h"
+#include "symbol.h"
+#include "compiler.h"
+
+#include <iostream>
+#include <limits>
+#include <stdexcept>
+#include <vector>
namespace GiNaC {
mul::mul()
{
- tinfo_key = TINFO_mul;
}
//////////
mul::mul(const ex & lh, const ex & rh)
{
- tinfo_key = TINFO_mul;
overall_coeff = _ex1;
construct_from_2_ex(lh,rh);
GINAC_ASSERT(is_canonical());
mul::mul(const exvector & v)
{
- tinfo_key = TINFO_mul;
overall_coeff = _ex1;
construct_from_exvector(v);
GINAC_ASSERT(is_canonical());
mul::mul(const epvector & v)
{
- tinfo_key = TINFO_mul;
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;
overall_coeff = oc;
- construct_from_epvector(v);
+ construct_from_epvector(v, do_index_renaming);
GINAC_ASSERT(is_canonical());
}
-mul::mul(std::auto_ptr<epvector> vp, const ex & oc)
+mul::mul(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming)
{
- tinfo_key = TINFO_mul;
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;
exvector factors;
factors.reserve(3);
factors.push_back(lh);
// archiving
//////////
-DEFAULT_ARCHIVING(mul)
-
//////////
// functions overriding virtual functions from base classes
//////////
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 "/"
case info_flags::integer_polynomial:
case info_flags::cinteger_polynomial:
case info_flags::rational_polynomial:
+ case info_flags::real:
+ case info_flags::rational:
+ case info_flags::integer:
+ case info_flags::crational:
+ case info_flags::cinteger:
+ case info_flags::positive:
+ case info_flags::nonnegative:
+ case info_flags::posint:
+ case info_flags::nonnegint:
+ case info_flags::even:
case info_flags::crational_polynomial:
case info_flags::rational_function: {
epvector::const_iterator i = seq.begin(), end = seq.end();
return false;
++i;
}
+ if (overall_coeff.is_equal(*_num1_p) && inf == info_flags::even)
+ return true;
return overall_coeff.info(inf);
}
case info_flags::algebraic: {
}
return false;
}
+ case info_flags::negative: {
+ bool neg = false;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ const ex& factor = recombine_pair_to_ex(*i++);
+ if (factor.info(info_flags::positive))
+ continue;
+ else if (factor.info(info_flags::negative))
+ neg = !neg;
+ else
+ return false;
+ }
+ if (overall_coeff.info(info_flags::negative))
+ neg = !neg;
+ return neg;
+ }
+ case info_flags::negint: {
+ bool neg = false;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ const ex& factor = recombine_pair_to_ex(*i++);
+ if (factor.info(info_flags::posint))
+ continue;
+ else if (factor.info(info_flags::negint))
+ neg = !neg;
+ else
+ return false;
+ }
+ if (overall_coeff.info(info_flags::negint))
+ neg = !neg;
+ else if (!overall_coeff.info(info_flags::posint))
+ return false;
+ return neg;
+ }
}
return inherited::info(inf);
}
epvector::const_iterator i = seq.begin(), end = seq.end();
while (i != end) {
if (ex_to<numeric>(i->coeff).is_integer())
- deg_sum += i->rest.degree(s) * ex_to<numeric>(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;
epvector::const_iterator i = seq.begin(), end = seq.end();
while (i != end) {
if (ex_to<numeric>(i->coeff).is_integer())
- deg_sum += i->rest.ldegree(s) * ex_to<numeric>(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;
return *this;
}
- int seq_size = seq.size();
+ size_t seq_size = seq.size();
if (overall_coeff.is_zero()) {
// *(...,x;0) -> 0
return _ex0;
}
return (new add(distrseq,
ex_to<numeric>(addref.overall_coeff).
- mul_dyn(ex_to<numeric>(overall_coeff))))
- ->setflag(status_flags::dynallocated | status_flags::evaluated);
+ mul_dyn(ex_to<numeric>(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<epvector> s(new epvector);
+ numeric oc = *_num1_p;
+ bool something_changed = false;
+ while (i!=last) {
+ if (likely(! (is_a<add>(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<numeric>(ex_to<add>(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<add>(i->rest);
+ add* primitive = new add(addref);
+ primitive->setflag(status_flags::dynallocated);
+ primitive->clearflag(status_flags::hash_calculated);
+ primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
+ for (epvector::iterator ai = primitive->seq.begin();
+ ai != primitive->seq.end(); ++ai)
+ ai->coeff = ex_to<numeric>(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<numeric>(overall_coeff).mul_dyn(oc))
+ )->setflag(status_flags::dynallocated);
+ }
}
+
return this->hold();
}
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
return inherited::eval_ncmul(v);
}
-bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls)
+bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& repls)
{
ex origbase;
int origexponent;
patternexpsign = 1;
}
- lst saverepls = repls;
+ exmap saverepls = repls;
if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
return false;
repls = saverepls;
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, exmap& repls,
+ int factor, int &nummatches, const std::vector<bool> &subsed,
+ std::vector<bool> &matched)
+{
+ GINAC_ASSERT(subsed.size() == e.nops());
+ GINAC_ASSERT(matched.size() == e.nops());
+
+ if (factor == (int)pat.nops())
+ return true;
+
+ for (size_t i=0; i<e.nops(); ++i) {
+ if(subsed[i] || matched[i])
+ continue;
+ exmap newrepls = repls;
+ int newnummatches = nummatches;
+ if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
+ matched[i] = true;
+ if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
+ newnummatches, subsed, matched)) {
+ repls = newrepls;
+ nummatches = newnummatches;
+ return true;
+ }
+ else
+ matched[i] = false;
+ }
+ }
+
+ return false;
+}
+
+bool mul::has(const ex & pattern, unsigned options) const
+{
+ if(!(options&has_options::algebraic))
+ return basic::has(pattern,options);
+ if(is_a<mul>(pattern)) {
+ exmap repls;
+ int nummatches = std::numeric_limits<int>::max();
+ std::vector<bool> subsed(nops(), false);
+ std::vector<bool> matched(nops(), 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<bool> subsed(seq.size(), false);
- exvector subsresult(seq.size());
+ std::vector<bool> subsed(nops(), false);
+ ex divide_by = 1;
+ ex multiply_by = 1;
for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
if (is_exactly_a<mul>(it->first)) {
-
+retry1:
int nummatches = std::numeric_limits<int>::max();
- std::vector<bool> currsubsed(seq.size(), false);
- bool succeed = true;
- lst repls;
-
- for (size_t j=0; j<it->first.nops(); j++) {
- bool found=false;
- for (size_t k=0; k<nops(); k++) {
- if (currsubsed[k] || subsed[k])
- continue;
- if (tryfactsubs(op(k), it->first.op(j), nummatches, repls)) {
- currsubsed[k] = true;
- found = true;
- break;
- }
- }
- if (!found) {
- succeed = false;
- break;
- }
- }
- if (!succeed)
+ std::vector<bool> currsubsed(nops(), false);
+ exmap repls;
+
+ if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
continue;
- bool foundfirstsubsedfactor = false;
- for (size_t j=0; j<subsed.size(); j++) {
- if (currsubsed[j]) {
- if (foundfirstsubsedfactor)
- subsresult[j] = op(j);
- else {
- foundfirstsubsedfactor = 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);
- }
+ for (size_t j=0; j<subsed.size(); j++)
+ if (currsubsed[j])
subsed[j] = true;
- }
- }
+ ex subsed_pattern
+ = it->first.subs(repls, subs_options::no_pattern);
+ divide_by *= power(subsed_pattern, nummatches);
+ ex subsed_result
+ = it->second.subs(repls, subs_options::no_pattern);
+ multiply_by *= power(subsed_result, nummatches);
+ goto retry1;
} else {
- int nummatches = std::numeric_limits<int>::max();
- lst repls;
-
for (size_t j=0; j<this->nops(); j++) {
- if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) {
+ int nummatches = std::numeric_limits<int>::max();
+ exmap 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(repls, subs_options::no_pattern);
+ divide_by *= power(subsed_pattern, nummatches);
+ ex subsed_result
+ = it->second.subs(repls, subs_options::no_pattern);
+ multiply_by *= power(subsed_result, nummatches);
}
}
}
if (!subsfound)
return subs_one_level(m, options | subs_options::algebraic);
- exvector ev; ev.reserve(nops());
- for (size_t i=0; i<nops(); i++) {
- if (subsed[i])
- ev.push_back(subsresult[i]);
- else
- ev.push_back(op(i));
- }
-
- return (new mul(ev))->setflag(status_flags::dynallocated);
+ return ((*this)/divide_by)*multiply_by;
}
// protected
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;
return all_commutative ? return_types::commutative : return_types::noncommutative;
}
-unsigned mul::return_type_tinfo() const
+return_type_t mul::return_type_tinfo() const
{
if (seq.empty())
- return tinfo_key; // mul without factors: should not happen
+ return make_return_type_t<mul>(); // mul without factors: should not happen
// return type_info of first noncommutative element
epvector::const_iterator i = seq.begin(), end = seq.end();
++i;
}
// no noncommutative element found, should not happen
- return tinfo_key;
+ return make_return_type_t<mul>();
}
-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<epvector> vp, const ex & oc) const
+ex mul::thisexpairseq(std::auto_ptr<epvector> 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
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<symbol>(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<epvector> expanded_seqp = expandchildren(options);
const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
// 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;
+ lst dummy_subs;
+
+ 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());
+ 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) {
+ 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<lst>(dummy_subs.op(0)),
+ ex_to<lst>(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:
- const ex rest = (new mul(i1->rest, rename_dummy_indices_uniquely(i1->rest, i2->rest)))->setflag(status_flags::dynallocated);
+ const ex rest = (new mul(i1->rest, i2_new))->setflag(status_flags::dynallocated);
if (is_exactly_a<numeric>(rest)) {
oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
} else {
- distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
+ distrseq2.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(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));
size_t n = last_expanded.nops();
exvector distrseq;
distrseq.reserve(n);
+ 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; i<n; ++i) {
epvector factors = non_adds;
- factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(mul(non_adds), last_expanded.op(i))));
+ if (skip_idx_rename)
+ factors.push_back(split_ex_to_pair(last_expanded.op(i)));
+ else
+ 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());
return std::auto_ptr<epvector>(0); // nothing has changed
}
+GINAC_BIND_UNARCHIVER(mul);
+
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff