* Implementation of GiNaC's products of expressions. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2006 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
*
* 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 <iostream>
#include "power.h"
#include "operators.h"
#include "matrix.h"
+#include "indexed.h"
#include "lst.h"
#include "archive.h"
#include "utils.h"
print_func<print_context>(&mul::do_print).
print_func<print_latex>(&mul::do_print_latex).
print_func<print_csrc>(&mul::do_print_csrc).
- print_func<print_tree>(&inherited::do_print_tree).
+ print_func<print_tree>(&mul::do_print_tree).
print_func<print_python_repr>(&mul::do_print_python_repr))
mul::mul()
{
- tinfo_key = TINFO_mul;
+ tinfo_key = &mul::tinfo_static;
}
//////////
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());
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());
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)
{
- tinfo_key = TINFO_mul;
+ tinfo_key = &mul::tinfo_static;
overall_coeff = oc;
construct_from_epvector(v);
GINAC_ASSERT(is_canonical());
mul::mul(std::auto_ptr<epvector> vp, const ex & oc)
{
- 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);
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);
const numeric &coeff = ex_to<numeric>(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);
return recombine_pair_to_ex(*(seq.begin()));
} else if ((seq_size==1) &&
is_exactly_a<add>((*seq.begin()).rest) &&
- ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
+ ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
// *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
const add & addref = ex_to<add>((*seq.begin()).rest);
std::auto_ptr<epvector> distrseq(new epvector);
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 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<bool> &subsed,
+ std::vector<bool> &matched)
+{
+ if (factor == pat.nops())
+ return true;
+
+ for (size_t i=0; i<e.nops(); ++i) {
+ if(subsed[i] || matched[i])
+ continue;
+ lst 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)) {
+ lst repls;
+ int nummatches = std::numeric_limits<int>::max();
+ std::vector<bool> subsed(seq.size(), false);
+ std::vector<bool> 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<bool> subsed(seq.size(), false);
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)
+
+ if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
continue;
bool foundfirstsubsedfactor = false;
subsed[j] = true;
}
}
+ goto retry1;
} else {
-
+retry2:
int nummatches = std::numeric_limits<int>::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;
}
}
}
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;
}
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
+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();
++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::recombine_pair_to_ex(const expair & p) const
{
- if (ex_to<numeric>(p.coeff).is_equal(_num1))
+ if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
return p.rest;
else
return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
// 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<numeric>(p.coeff).is_equal(_num1);
+ return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
+}
+
+bool mul::can_be_further_expanded(const ex & e)
+{
+ if (is_exactly_a<mul>(e)) {
+ for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
+ if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
+ return true;
+ }
+ } else if (is_exactly_a<power>(e)) {
+ if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
+ return true;
+ }
+ return false;
}
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<add>(cit->rest) &&
(cit->coeff.is_equal(_ex1))) {
- ++number_of_adds;
if (is_exactly_a<add>(last_expanded)) {
// Expand a product of two sums, aggressive version.
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))
for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(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))
for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(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(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());
+ }
+
+ 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<numeric>(rest))
+ 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
+ } else {
distrseq.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);
}
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<add>(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<add>(last_expanded)) {
- const add & finaladd = ex_to<add>(last_expanded);
-
- size_t n = finaladd.nops();
+ 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());
for (size_t i=0; i<n; ++i) {
epvector factors = non_adds;
- expair new_factor = split_ex_to_pair(finaladd.op(i).expand());
- factors.push_back(new_factor);
-
- const mul & term = static_cast<const mul &>((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<add>(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<basic>(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<basic>(result).setflag(status_flags::expanded);
+ return result;
+ }
}
git://www.ginac.de / ginac.git / blobdiff