#include "lst.h"
#include "archive.h"
#include "utils.h"
+#include "symbol.h"
+#include "compiler.h"
namespace GiNaC {
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_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<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();
}
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)
+ return (new mul(*this))->setflag(status_flags::dynallocated | status_flags::expanded);
+ }
+
+ // 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());
git://www.ginac.de / ginac.git / blobdiff