return f * thiscontainer(v);
}
+ if(this->tinfo()==TINFO_indexed && seq.size()==1)
+ return base;
+
// Canonicalize indices according to the symmetry properties
if (seq.size() > 2) {
exvector v = seq;
return f.get_free_indices();
}
+template<class T> size_t number_of_type(const exvector&v)
+{
+ size_t number = 0;
+ for(exvector::const_iterator i=v.begin(); i!=v.end(); ++i)
+ if(is_exactly_a<T>(*i))
+ ++number;
+ return number;
+}
+
/** Rename dummy indices in an expression.
*
* @param e Expression to work on
* @param global_dummy_indices The set of dummy indices that have appeared
* before and which we would like to use in "e", too. This gets updated
* by the function */
-static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
+template<class T> static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
{
- size_t global_size = global_dummy_indices.size(),
- local_size = local_dummy_indices.size();
+ size_t global_size = number_of_type<T>(global_dummy_indices),
+ local_size = number_of_type<T>(local_dummy_indices);
// Any local dummy indices at all?
if (local_size == 0)
int remaining = local_size - global_size;
exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end();
while (it != itend && remaining > 0) {
- if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(op0_is_equal(), *it)) == global_dummy_indices.end()) {
+ if (is_exactly_a<T>(*it) && find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(idx_is_equal_ignore_dim(), *it)) == global_dummy_indices.end()) {
global_dummy_indices.push_back(*it);
global_size++;
remaining--;
exvector local_syms, global_syms;
local_syms.reserve(local_size);
global_syms.reserve(local_size);
- for (size_t i=0; i<local_size; i++)
- local_syms.push_back(local_dummy_indices[i].op(0));
+ for (size_t i=0; local_syms.size()!=local_size; i++)
+ if(is_exactly_a<T>(local_dummy_indices[i]))
+ local_syms.push_back(local_dummy_indices[i].op(0));
shaker_sort(local_syms.begin(), local_syms.end(), ex_is_less(), ex_swap());
- for (size_t i=0; i<local_size; i++) // don't use more global symbols than necessary
- global_syms.push_back(global_dummy_indices[i].op(0));
+ for (size_t i=0; global_syms.size()!=local_size; i++) // don't use more global symbols than necessary
+ if(is_exactly_a<T>(global_dummy_indices[i]))
+ global_syms.push_back(global_dummy_indices[i].op(0));
shaker_sort(global_syms.begin(), global_syms.end(), ex_is_less(), ex_swap());
// Remove common indices
// Forward declaration needed in absence of friend injection, C.f. [namespace.memdef]:
ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
+template<class T> ex idx_symmetrization(const ex& r,const exvector& local_dummy_indices)
+{ exvector dummy_syms;
+ dummy_syms.reserve(r.nops());
+ for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
+ if(is_exactly_a<T>(*it))
+ dummy_syms.push_back(it->op(0));
+ if(dummy_syms.size() < 2)
+ return r;
+ ex q=symmetrize(r, dummy_syms);
+ return q;
+}
+
+// Forward declaration needed in absence of friend injection, C.f. [namespace.memdef]:
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
+
/** Simplify product of indexed expressions (commutative, noncommutative and
* simple squares), return list of free indices. */
ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
// At least one dummy index, is it a defined scalar product?
bool contracted = false;
- if (free.empty()) {
-
- // Find minimal dimension of all indices of both factors
- exvector::const_iterator dit = ex_to<indexed>(*it1).seq.begin() + 1, ditend = ex_to<indexed>(*it1).seq.end();
- ex dim = ex_to<idx>(*dit).get_dim();
- ++dit;
- for (; dit != ditend; ++dit) {
- dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
- }
- dit = ex_to<indexed>(*it2).seq.begin() + 1;
- ditend = ex_to<indexed>(*it2).seq.end();
- for (; dit != ditend; ++dit) {
- dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
- }
+ if (free.empty() && it1->nops()==2 && it2->nops()==2) {
+
+ ex dim = minimal_dim(
+ ex_to<idx>(it1->op(1)).get_dim(),
+ ex_to<idx>(it2->op(1)).get_dim()
+ );
// User-defined scalar product?
if (sp.is_defined(*it1, *it2, dim)) {
// The result should be symmetric with respect to exchange of dummy
// indices, so if the symmetrization vanishes, the whole expression is
// zero. This detects things like eps.i.j.k * p.j * p.k = 0.
- if (local_dummy_indices.size() >= 2) {
- exvector dummy_syms;
- dummy_syms.reserve(local_dummy_indices.size());
- for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
- dummy_syms.push_back(it->op(0));
- if (symmetrize(r, dummy_syms).is_zero()) {
- free_indices.clear();
- return _ex0;
- }
+ ex q = idx_symmetrization<idx>(r, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ q = idx_symmetrization<varidx>(q, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ q = idx_symmetrization<spinidx>(q, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
}
// Dummy index renaming
- r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<idx>(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<varidx>(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<spinidx>(r, dummy_indices, local_dummy_indices);
// Product of indexed object with a scalar?
if (is_exactly_a<mul>(r) && r.nops() == 2
}
};
+bool hasindex(const ex &x, const ex &sym)
+{
+ if(is_a<idx>(x) && x.op(0)==sym)
+ return true;
+ else
+ for(size_t i=0; i<x.nops(); ++i)
+ if(hasindex(x.op(i), sym))
+ return true;
+ return false;
+}
+
/** Simplify indexed expression, return list of free indices. */
ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
{
}
// Rename the dummy indices
- return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<idx>(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<varidx>(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<spinidx>(e_expanded, dummy_indices, local_dummy_indices);
+ return e_expanded;
}
// Simplification of sum = sum of simplifications, check consistency of
if (num_terms_orig < 2 || dummy_indices.size() < 2)
return sum;
- // Yes, construct vector of all dummy index symbols
- exvector dummy_syms;
- dummy_syms.reserve(dummy_indices.size());
- for (exvector::const_iterator it = dummy_indices.begin(); it != dummy_indices.end(); ++it)
- dummy_syms.push_back(it->op(0));
-
// Chop the sum into terms and symmetrize each one over the dummy
// indices
std::vector<terminfo> terms;
for (size_t i=0; i<sum.nops(); i++) {
const ex & term = sum.op(i);
- ex term_symm = symmetrize(term, dummy_syms);
+ exvector dummy_indices_of_term;
+ dummy_indices_of_term.reserve(dummy_indices.size());
+ for(exvector::iterator i=dummy_indices.begin(); i!=dummy_indices.end(); ++i)
+ if(hasindex(term,i->op(0)))
+ dummy_indices_of_term.push_back(*i);
+ ex term_symm = idx_symmetrization<idx>(term, dummy_indices_of_term);
+ term_symm = idx_symmetrization<varidx>(term_symm, dummy_indices_of_term);
+ term_symm = idx_symmetrization<spinidx>(term_symm, dummy_indices_of_term);
if (term_symm.is_zero())
continue;
terms.push_back(terminfo(term, term_symm));
git://www.ginac.de / ginac.git / commitdiff