* Implementation of GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2006 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
#include "utils.h"
#include "integral.h"
#include "matrix.h"
+#include "inifcns.h"
namespace GiNaC {
indexed::indexed() : symtree(not_symmetric())
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
}
//////////
indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric())
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(not_symmetric())
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(not_symmetric())
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(not_symmetric())
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(not_symmetric())
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(symm)
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(not_symmetric())
{
seq.insert(seq.end(), v.begin(), v.end());
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
{
seq.insert(seq.end(), v.begin(), v.end());
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
validate();
}
indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
}
indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
}
indexed::indexed(const symmetry & symm, std::auto_ptr<exvector> vp) : inherited(vp), symtree(symm)
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
}
//////////
return f * thiscontainer(v);
}
- if(this->tinfo()==TINFO_indexed && seq.size()==1)
+ if(this->tinfo()==&indexed::tinfo_static && seq.size()==1)
return base;
// Canonicalize indices according to the symmetry properties
return ex_to<basic>(base).eval_indexed(*this);
}
+ex indexed::real_part() const
+{
+ if(op(0).info(info_flags::real))
+ return *this;
+ return real_part_function(*this).hold();
+}
+
+ex indexed::imag_part() const
+{
+ if(op(0).info(info_flags::real))
+ return 0;
+ return imag_part_function(*this).hold();
+}
+
ex indexed::thiscontainer(const exvector & v) const
{
return indexed(ex_to<symmetry>(symtree), v);
}
};
-exvector power::get_free_indices() const
-{
- // Get free indices of basis
- exvector basis_indices = basis.get_free_indices();
-
- if (exponent.info(info_flags::even)) {
- // If the exponent is an even number, then any "free" index that
- // forms a dummy pair with itself is actually a summation index
- exvector really_free;
- std::remove_copy_if(basis_indices.begin(), basis_indices.end(),
- std::back_inserter(really_free), is_summation_idx());
- return really_free;
- } else
- return basis_indices;
-}
-
exvector integral::get_free_indices() const
{
if (a.get_free_indices().size() || b.get_free_indices().size())
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)) {
}
}
+exvector get_all_dummy_indices_safely(const ex & e)
+{
+ if (is_a<indexed>(e))
+ return ex_to<indexed>(e).get_dummy_indices();
+ else if (is_a<power>(e) && e.op(1)==2) {
+ return e.op(0).get_free_indices();
+ }
+ else if (is_a<mul>(e) || is_a<ncmul>(e)) {
+ exvector dummies;
+ exvector free_indices;
+ for (int i=0; i<e.nops(); ++i) {
+ exvector dummies_of_factor = get_all_dummy_indices_safely(e.op(i));
+ dummies.insert(dummies.end(), dummies_of_factor.begin(),
+ dummies_of_factor.end());
+ exvector free_of_factor = e.op(i).get_free_indices();
+ free_indices.insert(free_indices.begin(), free_of_factor.begin(),
+ free_of_factor.end());
+ }
+ exvector free_out, dummy_out;
+ find_free_and_dummy(free_indices.begin(), free_indices.end(), free_out,
+ dummy_out);
+ dummies.insert(dummies.end(), dummy_out.begin(), dummy_out.end());
+ return dummies;
+ }
+ else if(is_a<add>(e)) {
+ exvector result;
+ for(int i=0; i<e.nops(); ++i) {
+ exvector dummies_of_term = get_all_dummy_indices_safely(e.op(i));
+ sort(dummies_of_term.begin(), dummies_of_term.end());
+ exvector new_vec;
+ set_union(result.begin(), result.end(), dummies_of_term.begin(),
+ dummies_of_term.end(), std::back_inserter<exvector>(new_vec),
+ ex_is_less());
+ result.swap(new_vec);
+ }
+ return result;
+ }
+ return exvector();
+}
+
/** Returns all dummy indices from the exvector */
exvector get_all_dummy_indices(const ex & e)
{
ex rename_dummy_indices_uniquely(const exvector & va, const exvector & vb, const ex & b)
{
lst indices_subs = rename_dummy_indices_uniquely(va, vb);
- return (indices_subs.op(0).nops()>0 ? b.subs((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern) : b);
+ return (indices_subs.op(0).nops()>0 ? b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming) : b);
}
ex rename_dummy_indices_uniquely(const ex & a, const ex & b)
{
- exvector va = get_all_dummy_indices(a);
+ exvector va = get_all_dummy_indices_safely(a);
if (va.size() > 0) {
- exvector vb = get_all_dummy_indices(b);
+ exvector vb = get_all_dummy_indices_safely(b);
if (vb.size() > 0) {
sort(va.begin(), va.end(), ex_is_less());
sort(vb.begin(), vb.end(), ex_is_less());
lst indices_subs = rename_dummy_indices_uniquely(va, vb);
if (indices_subs.op(0).nops() > 0)
- return b.subs((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern);
+ return b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming);
}
}
return b;
ex rename_dummy_indices_uniquely(exvector & va, const ex & b, bool modify_va)
{
if (va.size() > 0) {
- exvector vb = get_all_dummy_indices(b);
+ exvector vb = get_all_dummy_indices_safely(b);
if (vb.size() > 0) {
sort(vb.begin(), vb.end(), ex_is_less());
lst indices_subs = rename_dummy_indices_uniquely(va, vb);
}
sort(va.begin(), va.end(), ex_is_less());
}
- return b.subs((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern);
+ return b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming);
}
}
}
pointer_to_map_function_1arg<bool> fcn(expand_dummy_sum, subs_idx);
if (is_a<add>(e_expanded) || is_a<lst>(e_expanded) || is_a<matrix>(e_expanded)) {
return e_expanded.map(fcn);
- } else if (is_a<ncmul>(e_expanded) || is_a<mul>(e_expanded) || is_a<power>(e_expanded)) {
- exvector v = get_all_dummy_indices(e_expanded);
- exvector::const_iterator it = v.begin(), itend = v.end();
- while (it != itend) {
- varidx nu = ex_to<varidx>(*it);
- if (nu.is_dim_numeric()) {
- ex en = 0;
- for (int i=0; i < ex_to<numeric>(nu.get_dim()).to_int(); i++) {
- if (is_a<varidx>(nu) && !subs_idx) {
- en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim())));
- } else {
- en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim())));
- }
- }
- return expand_dummy_sum(en, subs_idx);
- }
- ++it;
- }
- return e;
- } else if (is_a<indexed>(e_expanded)) {
- exvector v = ex_to<indexed>(e_expanded).get_dummy_indices();
- exvector::const_iterator it = v.begin(), itend = v.end();
- while (it != itend) {
- varidx nu = ex_to<varidx>(*it);
- if (nu.is_dim_numeric()) {
+ } else if (is_a<ncmul>(e_expanded) || is_a<mul>(e_expanded) || is_a<power>(e_expanded) || is_a<indexed>(e_expanded)) {
+ exvector v;
+ if (is_a<indexed>(e_expanded))
+ v = ex_to<indexed>(e_expanded).get_dummy_indices();
+ else
+ v = get_all_dummy_indices(e_expanded);
+ ex result = e_expanded;
+ for(exvector::const_iterator it=v.begin(); it!=v.end(); ++it) {
+ ex nu = *it;
+ if (ex_to<idx>(nu).get_dim().info(info_flags::nonnegint)) {
+ int idim = ex_to<numeric>(ex_to<idx>(nu).get_dim()).to_int();
ex en = 0;
- for (int i=0; i < ex_to<numeric>(nu.get_dim()).to_int(); i++) {
- if (is_a<varidx>(nu) && !subs_idx) {
- en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim())));
+ for (int i=0; i < idim; i++) {
+ if (subs_idx && is_a<varidx>(nu)) {
+ ex other = ex_to<varidx>(nu).toggle_variance();
+ en += result.subs(lst(
+ nu == idx(i, idim),
+ other == idx(i, idim)
+ ));
} else {
- en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim())));
+ en += result.subs( nu.op(0) == i );
}
}
- return expand_dummy_sum(en, subs_idx);
- }
- ++it;
+ result = en;
+ }
}
- return e;
+ return result;
} else {
return e;
}
git://www.ginac.de / ginac.git / blobdiff