ex mul::expand(unsigned options) const
{
- if (options == 0 && (flags & status_flags::expanded))
- return *this;
-
- exvector sub_expanded_seq;
-
+ // First, expand the children
epvector * expanded_seqp = expandchildren(options);
-
- const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
-
+ const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
+
+ // 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());
- epvector::const_iterator cit = expanded_seq.begin();
- epvector::const_iterator last = expanded_seq.end();
- ex last_expanded = _ex1();
- while (cit!=last) {
- if (is_ex_exactly_of_type((*cit).rest,add) &&
- ((*cit).coeff.is_equal(_ex1()))) {
+ epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
+ while (cit != last) {
+ if (is_ex_exactly_of_type(cit->rest, add) &&
+ (cit->coeff.is_equal(_ex1()))) {
++number_of_adds;
- if (is_ex_exactly_of_type(last_expanded,add)) {
- // expand adds
+ if (is_ex_exactly_of_type(last_expanded, add)) {
const add & add1 = ex_to<add>(last_expanded);
- const add & add2 = ex_to<add>((*cit).rest);
+ const add & add2 = ex_to<add>(cit->rest);
int n1 = add1.nops();
int n2 = add2.nops();
exvector distrseq;
distrseq.reserve(n1*n2);
for (int i1=0; i1<n1; ++i1) {
for (int i2=0; i2<n2; ++i2) {
- distrseq.push_back(add1.op(i1)*add2.op(i2));
+ distrseq.push_back(add1.op(i1) * add2.op(i2));
}
}
- last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+ last_expanded = (new add(distrseq))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
} else {
non_adds.push_back(split_ex_to_pair(last_expanded));
- last_expanded = (*cit).rest;
+ last_expanded = cit->rest;
}
} else {
non_adds.push_back(*cit);
if (expanded_seqp)
delete expanded_seqp;
- if (is_ex_exactly_of_type(last_expanded,add)) {
+ // Now the only remaining thing to do is to multiply the factors which
+ // were not sums into the "last_expanded" sum
+ if (is_ex_exactly_of_type(last_expanded, add)) {
add const & finaladd = ex_to<add>(last_expanded);
exvector distrseq;
int n = finaladd.nops();
for (int i=0; i<n; ++i) {
epvector factors = non_adds;
factors.push_back(split_ex_to_pair(finaladd.op(i)));
- distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
+ distrseq.push_back((new mul(factors, overall_coeff))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
}
return ((new add(distrseq))->
setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
ex ncmul::expand(unsigned options) const
{
- exvector sub_expanded_seq;
- intvector positions_of_adds;
- intvector number_of_add_operands;
-
- exvector expanded_seq=expandchildren(options);
-
- positions_of_adds.resize(expanded_seq.size());
- number_of_add_operands.resize(expanded_seq.size());
-
- int number_of_adds=0;
- int number_of_expanded_terms=1;
-
- unsigned current_position=0;
- exvector::const_iterator last=expanded_seq.end();
+ // First, expand the children
+ exvector expanded_seq = expandchildren(options);
+
+ // Now, look for all the factors that are sums and remember their
+ // position and number of terms. One remark is in order here: we do not
+ // take into account the overall_coeff of the add objects. This is
+ // because in GiNaC, all terms of a sum must be of the same type, so
+ // a non-zero overall_coeff (which can only be numeric) would imply that
+ // the sum only has commutative terms. But then it would never appear
+ // as a factor of an ncmul.
+ intvector positions_of_adds(expanded_seq.size());
+ intvector number_of_add_operands(expanded_seq.size());
+
+ int number_of_adds = 0;
+ int number_of_expanded_terms = 1;
+
+ unsigned current_position = 0;
+ exvector::const_iterator last = expanded_seq.end();
for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
- if (is_ex_exactly_of_type((*cit),add)) {
- positions_of_adds[number_of_adds]=current_position;
- const add & expanded_addref=ex_to<add>(*cit);
- number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
+ if (is_ex_exactly_of_type(*cit, add)) {
+ positions_of_adds[number_of_adds] = current_position;
+ const add & expanded_addref = ex_to<add>(*cit);
+ number_of_add_operands[number_of_adds] = expanded_addref.seq.size();
number_of_expanded_terms *= expanded_addref.seq.size();
number_of_adds++;
}
current_position++;
}
- if (number_of_adds==0) {
- return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
- (options == 0 ? status_flags::expanded : 0));
- }
+ // If there are no sums, we are done
+ if (number_of_adds == 0)
+ return (new ncmul(expanded_seq, true))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+ // Now, form all possible products of the terms of the sums with the
+ // remaining factors, and add them together
exvector distrseq;
distrseq.reserve(number_of_expanded_terms);
- intvector k;
- k.resize(number_of_adds);
-
- int l;
- for (l=0; l<number_of_adds; l++) {
- k[l]=0;
- }
+ intvector k(number_of_adds);
- while (1) {
- exvector term;
- term=expanded_seq;
- for (l=0; l<number_of_adds; l++) {
- GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
- const add & addref=ex_to<add>(expanded_seq[positions_of_adds[l]]);
- term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
+ while (true) {
+ exvector term = expanded_seq;
+ for (int i=0; i<number_of_adds; i++) {
+ GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[i]], add));
+ const add & addref = ex_to<add>(expanded_seq[positions_of_adds[i]]);
+ term[positions_of_adds[i]] = addref.recombine_pair_to_ex(addref.seq[k[i]]);
}
- distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
- (options == 0 ? status_flags::expanded : 0)));
+ distrseq.push_back((new ncmul(term, true))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
// increment k[]
- l=number_of_adds-1;
- while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
- k[l]=0;
+ int l = number_of_adds-1;
+ while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
+ k[l] = 0;
l--;
}
- if (l<0) break;
+ if (l<0)
+ break;
}
- return (new add(distrseq))->setflag(status_flags::dynallocated |
- (options == 0 ? status_flags::expanded : 0));
+ return (new add(distrseq))->
+ setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}
int ncmul::degree(const ex & s) const