* Implementation of GiNaC's special tensors. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2002 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <iostream>
#include <stdexcept>
#include <vector>
return i.hold();
}
-/** Contraction of an indexed delta tensor with something else. */
-bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+bool tensor::replace_contr_index(exvector::iterator self, exvector::iterator other) const
{
- GINAC_ASSERT(is_a<indexed>(*self));
- GINAC_ASSERT(is_a<indexed>(*other));
- GINAC_ASSERT(self->nops() == 3);
- GINAC_ASSERT(is_a<tensdelta>(self->op(0)));
-
- // Try to contract first index
+ // Try to contract the first index
const idx *self_idx = &ex_to<idx>(self->op(1));
const idx *free_idx = &ex_to<idx>(self->op(2));
bool first_index_tried = false;
const idx &other_idx = ex_to<idx>(other->op(i));
if (is_dummy_pair(*self_idx, other_idx)) {
- // Contraction found, remove delta tensor and substitute
- // index in second object
+ // Contraction found, remove this tensor and substitute the
+ // index in the second object
*self = _ex1;
*other = other->subs(other_idx == *free_idx);
return true;
if (!first_index_tried) {
- // No contraction with first index found, try second index
+ // No contraction with the first index found, try the second index
self_idx = &ex_to<idx>(self->op(2));
free_idx = &ex_to<idx>(self->op(1));
first_index_tried = true;
return false;
}
+/** Contraction of an indexed delta tensor with something else. */
+bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 3);
+ GINAC_ASSERT(is_a<tensdelta>(self->op(0)));
+
+ // Replace the dummy index with this tensor's other index and remove
+ // the tensor (this is valid for contractions with all other tensors)
+ return replace_contr_index(self, other);
+}
+
/** Contraction of an indexed metric tensor with something else. */
bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
if (is_ex_of_type(other->op(0), tensdelta))
return false;
- // Try to contract first index
- const idx *self_idx = &ex_to<idx>(self->op(1));
- const idx *free_idx = &ex_to<idx>(self->op(2));
- bool first_index_tried = false;
-
-again:
- if (self_idx->is_symbolic()) {
- for (unsigned i=1; i<other->nops(); i++) {
- const idx &other_idx = ex_to<idx>(other->op(i));
- if (is_dummy_pair(*self_idx, other_idx)) {
-
- // Contraction found, remove metric tensor and substitute
- // index in second object
- *self = _ex1;
- *other = other->subs(other_idx == *free_idx);
- return true;
- }
- }
- }
-
- if (!first_index_tried) {
-
- // No contraction with first index found, try second index
- self_idx = &ex_to<idx>(self->op(2));
- free_idx = &ex_to<idx>(self->op(1));
- first_index_tried = true;
- goto again;
- }
-
- return false;
+ // Replace the dummy index with this tensor's other index and remove
+ // the tensor (this is valid for contractions with all other tensors)
+ return replace_contr_index(self, other);
}
/** Contraction of an indexed spinor metric with something else. */
*self = sign * M.determinant().simplify_indexed();
*other = _ex1;
return true;
-
- } else if (other->return_type() == return_types::commutative) {
-
-#if 0
- // This handles eps.i.j.k * p.j * p.k = 0
- // Maybe something like this should go to simplify_indexed() because
- // such relations are true for any antisymmetric tensors...
- exvector c;
-
- // Handle all indices of the epsilon tensor
- for (int i=0; i<num; i++) {
- ex idx = self->op(i+1);
-
- // Look whether there's a contraction with this index
- exvector::const_iterator ait, aitend = v.end();
- for (ait = v.begin(); ait != aitend; ait++) {
- if (ait == self)
- continue;
- if (is_a<indexed>(*ait) && ait->return_type() == return_types::commutative && ex_to<indexed>(*ait).has_dummy_index_for(idx) && ait->nops() == 2) {
-
- // Yes, did we already have another contraction with the same base expression?
- ex base = ait->op(0);
- if (std::find_if(c.begin(), c.end(), bind2nd(ex_is_equal(), base)) == c.end()) {
-
- // No, add the base expression to the list
- c.push_back(base);
-
- } else {
-
- // Yes, the contraction is zero
- *self = _ex0;
- *other = _ex0;
- return true;
- }
- }
- }
- }
-#endif
}
return false;
{
if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
+ ex dim = ex_to<idx>(i1).get_dim();
+ if (!dim.is_equal(ex_to<idx>(i2).get_dim()))
+ throw(std::invalid_argument("all indices of metric tensor must have the same dimension"));
return indexed(tensmetric(), sy_symm(), i1, i2);
}
{
if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
+ ex dim = ex_to<idx>(i1).get_dim();
+ if (!dim.is_equal(ex_to<idx>(i2).get_dim()))
+ throw(std::invalid_argument("all indices of metric tensor must have the same dimension"));
return indexed(minkmetric(pos_sig), sy_symm(), i1, i2);
}
git://www.ginac.de / ginac.git / blobdiff