DEFAULT_ARCHIVING(ncmul)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
// public
bool ncmul::info(unsigned inf) const
{
- throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
+ return inherited::info(inf);
}
typedef std::vector<int> intvector;
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());
+ // 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.
+ 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;
+ int number_of_adds = 0;
+ int number_of_expanded_terms = 1;
- unsigned current_position=0;
- exvector::const_iterator last=expanded_seq.end();
+ 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();
- number_of_expanded_terms *= expanded_addref.seq.size();
+ if (is_exactly_a<add>(*cit)) {
+ positions_of_adds[number_of_adds] = current_position;
+ unsigned num_ops = cit->nops();
+ number_of_add_operands[number_of_adds] = num_ops;
+ number_of_expanded_terms *= num_ops;
number_of_adds++;
}
- current_position++;
+ ++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]]);
- }
- distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
- (options == 0 ? status_flags::expanded : 0)));
+ while (true) {
+ exvector term = expanded_seq;
+ for (int i=0; i<number_of_adds; i++)
+ term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
+ 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
typedef std::vector<unsigned> unsignedvector;
typedef std::vector<exvector> exvectorvector;
+/** Perform automatic term rewriting rules in this class. In the following
+ * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ * stand for such expressions that contain a plain number.
+ * - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...) (associativity)
+ * - ncmul(x) -> x
+ * - ncmul() -> 1
+ * - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...)) (pull out commutative elements)
+ * - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2)) (collect elements of same type)
+ * - ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
+ *
+ * @param level cut-off in recursive evaluation */
ex ncmul::eval(int level) const
{
- // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
- // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
- // ncmul(x) -> x
- // ncmul() -> 1
- // ncmul(...,c1,...,c2,...)
- // *(c1,c2,ncmul(...)) (pull out commutative elements)
- // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
- // (collect elements of same type)
- // ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
- // the following rule would be nice, but produces a recursion,
+ // The following additional rule would be nice, but produces a recursion,
// which must be trapped by introducing a flag that the sub-ncmuls()
// are already evaluated (maybe later...)
// ncmul(x1,x2,...,X,y1,y2,...) ->
exvector evaledseq=evalchildren(level);
// ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
- // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
+ // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
unsigned factors = 0;
exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
while (cit != citend)
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