* Implementation of GiNaC's products of expressions. */
/*
- * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2015 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 = &mul::tinfo_static;
}
//////////
mul::mul(const ex & lh, const ex & rh)
{
- 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 = &mul::tinfo_static;
overall_coeff = _ex1;
construct_from_exvector(v);
GINAC_ASSERT(is_canonical());
mul::mul(const epvector & v)
{
- tinfo_key = &mul::tinfo_static;
overall_coeff = _ex1;
construct_from_epvector(v);
GINAC_ASSERT(is_canonical());
mul::mul(const epvector & v, const ex & oc, bool do_index_renaming)
{
- tinfo_key = &mul::tinfo_static;
overall_coeff = oc;
construct_from_epvector(v, do_index_renaming);
GINAC_ASSERT(is_canonical());
mul::mul(std::auto_ptr<epvector> 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, do_index_renaming);
mul::mul(const ex & lh, const ex & mh, const ex & rh)
{
- tinfo_key = &mul::tinfo_static;
exvector factors;
factors.reserve(3);
factors.push_back(lh);
// archiving
//////////
-DEFAULT_ARCHIVING(mul)
-
//////////
// functions overriding virtual functions from base classes
//////////
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::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::positive:
+ case info_flags::negative: {
+ if ((inf==info_flags::positive) && (flags & status_flags::is_positive))
+ return true;
+ else if ((inf==info_flags::negative) && (flags & status_flags::is_negative))
+ return true;
+ if (flags & status_flags::purely_indefinite)
+ return false;
+
+ bool pos = true;
+ 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))
+ pos = !pos;
+ else
+ return false;
+ }
+ if (overall_coeff.info(info_flags::negative))
+ pos = !pos;
+ setflag(pos ? status_flags::is_positive : status_flags::is_negative);
+ return (inf == info_flags::positive? pos : !pos);
+ }
+ case info_flags::nonnegative: {
+ if (flags & status_flags::is_positive)
+ return true;
+ bool pos = true;
+ 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::nonnegative) || factor.info(info_flags::positive))
+ continue;
+ else if (factor.info(info_flags::negative))
+ pos = !pos;
+ else
+ return false;
+ }
+ return (overall_coeff.info(info_flags::negative)? !pos : pos);
+ }
+ case info_flags::posint:
+ case info_flags::negint: {
+ bool pos = true;
+ 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))
+ pos = !pos;
+ else
+ return false;
+ }
+ if (overall_coeff.info(info_flags::negint))
+ pos = !pos;
+ else if (!overall_coeff.info(info_flags::posint))
+ return false;
+ return (inf ==info_flags::posint? pos : !pos);
+ }
+ case info_flags::nonnegint: {
+ bool pos = true;
+ 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::nonnegint) || factor.info(info_flags::posint))
+ continue;
+ else if (factor.info(info_flags::negint))
+ pos = !pos;
+ else
+ return false;
+ }
+ if (overall_coeff.info(info_flags::negint))
+ pos = !pos;
+ else if (!overall_coeff.info(info_flags::posint))
+ return false;
+ return pos;
+ }
+ case info_flags::indefinite: {
+ if (flags & status_flags::purely_indefinite)
+ return true;
+ if (flags & (status_flags::is_positive | status_flags::is_negative))
+ return false;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ const ex& term = recombine_pair_to_ex(*i);
+ if (term.info(info_flags::positive) || term.info(info_flags::negative))
+ return false;
+ ++i;
+ }
+ setflag(status_flags::purely_indefinite);
+ return true;
+ }
}
return inherited::info(inf);
}
+bool mul::is_polynomial(const ex & var) const
+{
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ if (!i->rest.is_polynomial(var) ||
+ (i->rest.has(var) && !i->coeff.info(info_flags::nonnegint))) {
+ return false;
+ }
+ }
+ return true;
+}
+
int mul::degree(const ex & s) const
{
// Sum up degrees of factors
setflag(status_flags::dynallocated);
}
-#ifdef DO_GINAC_ASSERT
- epvector::const_iterator i = seq.begin(), end = seq.end();
- while (i != end) {
- GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
- (!(ex_to<numeric>(i->coeff).is_integer())));
- GINAC_ASSERT(!(i->is_canonical_numeric()));
- if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
- print(print_tree(std::cerr));
- GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
- /* for paranoia */
- expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
- GINAC_ASSERT(p.rest.is_equal(i->rest));
- GINAC_ASSERT(p.coeff.is_equal(i->coeff));
- /* end paranoia */
- ++i;
- }
-#endif // def DO_GINAC_ASSERT
-
if (flags & status_flags::evaluated) {
GINAC_ASSERT(seq.size()>0);
GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
return *this;
}
- int seq_size = seq.size();
+ size_t seq_size = seq.size();
if (overall_coeff.is_zero()) {
// *(...,x;0) -> 0
return _ex0;
ex_to<numeric>(addref.overall_coeff).
mul_dyn(ex_to<numeric>(overall_coeff)))
)->setflag(status_flags::dynallocated | status_flags::evaluated);
- } else if (seq_size >= 2) {
+ } 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
+ // 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 (! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1))) {
+ 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_dyn(c);
+ 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
// 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 ((c == *_num1_p) && ((! canonicalizable) || unit_normal)) {
+ if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
++i;
continue;
}
- std::auto_ptr<epvector> s(new epvector);
- s->reserve(seq.size());
+ if (! something_changed) {
+ s->reserve(seq_size);
+ something_changed = true;
+ }
- epvector::const_iterator j=seq.begin();
- while (j!=i) {
+ while ((j!=i) && (j!=last)) {
s->push_back(*j);
++j;
}
- if (! unit_normal) {
+ if (! unit_normal)
c = c.mul(*_num_1_p);
- }
- const ex primitive = (i->rest)/c;
- s->push_back(expair(primitive, _ex1));
- ++j;
+ 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(c))
+ return (new mul(s, ex_to<numeric>(overall_coeff).mul_dyn(oc))
)->setflag(status_flags::dynallocated);
}
}
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)
+/** Checks whether 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
* 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)
+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)
{
- if (factor == pat.nops())
+ 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;
- lst newrepls = repls;
+ exmap newrepls = repls;
int newnummatches = nummatches;
if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
matched[i] = true;
if(!(options&has_options::algebraic))
return basic::has(pattern,options);
if(is_a<mul>(pattern)) {
- lst repls;
+ exmap repls;
int nummatches = std::numeric_limits<int>::max();
- std::vector<bool> subsed(seq.size(), false);
- std::vector<bool> matched(seq.size(), false);
+ 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;
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;
if (is_exactly_a<mul>(it->first)) {
retry1:
int nummatches = std::numeric_limits<int>::max();
- std::vector<bool> currsubsed(seq.size(), false);
- lst repls;
+ std::vector<bool> currsubsed(nops(), false);
+ exmap repls;
if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
continue;
if (currsubsed[j])
subsed[j] = true;
ex subsed_pattern
- = it->first.subs(ex(repls), subs_options::no_pattern);
+ = it->first.subs(repls, subs_options::no_pattern);
divide_by *= power(subsed_pattern, nummatches);
ex subsed_result
- = it->second.subs(ex(repls), subs_options::no_pattern);
+ = it->second.subs(repls, subs_options::no_pattern);
multiply_by *= power(subsed_result, nummatches);
goto retry1;
for (size_t j=0; j<this->nops(); j++) {
int nummatches = std::numeric_limits<int>::max();
- lst repls;
+ exmap repls;
if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
subsed[j] = true;
ex subsed_pattern
- = it->first.subs(ex(repls), subs_options::no_pattern);
+ = it->first.subs(repls, subs_options::no_pattern);
divide_by *= power(subsed_pattern, nummatches);
ex subsed_result
- = it->second.subs(ex(repls), subs_options::no_pattern);
+ = it->second.subs(repls, subs_options::no_pattern);
multiply_by *= power(subsed_result, nummatches);
}
}
return ((*this)/divide_by)*multiply_by;
}
+ex mul::conjugate() const
+{
+ // The base class' method is wrong here because we have to be careful at
+ // branch cuts. power::conjugate takes care of that already, so use it.
+ epvector *newepv = 0;
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ if (newepv) {
+ newepv->push_back(split_ex_to_pair(recombine_pair_to_ex(*i).conjugate()));
+ continue;
+ }
+ ex x = recombine_pair_to_ex(*i);
+ ex c = x.conjugate();
+ if (c.is_equal(x)) {
+ continue;
+ }
+ newepv = new epvector;
+ newepv->reserve(seq.size());
+ for (epvector::const_iterator j=seq.begin(); j!=i; ++j) {
+ newepv->push_back(*j);
+ }
+ newepv->push_back(split_ex_to_pair(c));
+ }
+ ex x = overall_coeff.conjugate();
+ if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
+ return *this;
+ }
+ ex result = thisexpairseq(newepv ? *newepv : seq, x);
+ delete newepv;
+ return result;
+}
+
+
// protected
/** Implementation of ex::diff() for a product. It applies the product rule.
// all factors checked
return all_commutative ? return_types::commutative : return_types::noncommutative;
}
-
-tinfo_t mul::return_type_tinfo() const
+
+return_type_t mul::return_type_tinfo() const
{
if (seq.empty())
- return this; // 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 this;
+ return make_return_type_t<mul>();
}
ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
}
return expair(e,_ex1);
}
-
+
expair mul::combine_ex_with_coeff_to_pair(const ex & e,
const ex & c) const
{
return split_ex_to_pair(power(e,c));
}
-
+
expair mul::combine_pair_with_coeff_to_pair(const expair & p,
const ex & c) const
{
return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
}
-
+
ex mul::recombine_pair_to_ex(const expair & p) const
{
if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
bool mul::expair_needs_further_processing(epp it)
{
if (is_exactly_a<mul>(it->rest) &&
- ex_to<numeric>(it->coeff).is_integer()) {
+ ex_to<numeric>(it->coeff).is_integer()) {
// combined pair is product with integer power -> expand it
*it = split_ex_to_pair(recombine_pair_to_ex(*it));
return true;
}
if (is_exactly_a<numeric>(it->rest)) {
+ if (it->coeff.is_equal(_ex1)) {
+ // pair has coeff 1 and must be moved to the end
+ return true;
+ }
expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
if (!ep.is_equal(*it)) {
// combined pair is a numeric power which can be simplified
*it = ep;
return true;
}
- if (it->coeff.is_equal(_ex1)) {
- // combined pair has coeff 1 and must be moved to the end
- return true;
- }
}
return false;
}
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);
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_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());
- }
+ 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<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:
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 = get_all_dummy_indices_safely(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; i<n; ++i) {
epvector factors = non_adds;
- factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, 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());
/** Member-wise expand the expairs representing this sequence. This must be
* overridden from expairseq::expandchildren() and done iteratively in order
- * to allow for early cancallations and thus safe memory.
+ * to allow for early cancellations and thus safe memory.
*
* @see mul::expand()
* @return pointer to epvector containing expanded representation or zero
return std::auto_ptr<epvector>(0); // nothing has changed
}
+GINAC_BIND_UNARCHIVER(mul);
+
} // namespace GiNaC