* Implementation of GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2008 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <iostream>
#include <sstream>
#include <stdexcept>
+#include <limits>
#include "indexed.h"
#include "idx.h"
#include "symmetry.h"
#include "operators.h"
#include "lst.h"
-#include "print.h"
#include "archive.h"
+#include "symbol.h"
#include "utils.h"
+#include "integral.h"
+#include "matrix.h"
+#include "inifcns.h"
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(indexed, exprseq,
+ print_func<print_context>(&indexed::do_print).
+ print_func<print_latex>(&indexed::do_print_latex).
+ print_func<print_tree>(&indexed::do_print_tree))
//////////
// default constructor
//////////
-indexed::indexed() : symtree(sy_none())
+indexed::indexed() : symtree(not_symmetric())
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
}
//////////
// other constructors
//////////
-indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
+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(sy_none())
+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(sy_none())
+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(sy_none())
+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(sy_none())
+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(sy_none())
+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, exvector * vp) : inherited(vp), symtree(symm)
+indexed::indexed(const symmetry & symm, std::auto_ptr<exvector> vp) : inherited(vp), symtree(symm)
{
- tinfo_key = TINFO_indexed;
+ tinfo_key = &indexed::tinfo_static;
}
//////////
symtree = sy_anti();
break;
default:
- symtree = sy_none();
+ symtree = not_symmetric();
break;
}
const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
// functions overriding virtual functions from base classes
//////////
-void indexed::print(const print_context & c, unsigned level) const
+void indexed::printindices(const print_context & c, unsigned level) const
{
- GINAC_ASSERT(seq.size() > 0);
-
- if (is_a<print_tree>(c)) {
+ if (seq.size() > 1) {
- c.s << std::string(level, ' ') << class_name()
- << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
- << ", " << seq.size()-1 << " indices"
- << ", symmetry=" << symtree << std::endl;
- unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
- seq[0].print(c, level + delta_indent);
- printindices(c, level + delta_indent);
+ exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
- } else {
+ if (is_a<print_latex>(c)) {
- bool is_tex = is_a<print_latex>(c);
- const ex & base = seq[0];
+ // TeX output: group by variance
+ bool first = true;
+ bool covariant = true;
- if (precedence() <= level)
- c.s << (is_tex ? "{(" : "(");
- if (is_tex)
- c.s << "{";
- base.print(c, precedence());
- if (is_tex)
+ while (it != itend) {
+ bool cur_covariant = (is_a<varidx>(*it) ? ex_to<varidx>(*it).is_covariant() : true);
+ if (first || cur_covariant != covariant) { // Variance changed
+ // The empty {} prevents indices from ending up on top of each other
+ if (!first)
+ c.s << "}{}";
+ covariant = cur_covariant;
+ if (covariant)
+ c.s << "_{";
+ else
+ c.s << "^{";
+ }
+ it->print(c, level);
+ c.s << " ";
+ first = false;
+ it++;
+ }
c.s << "}";
- printindices(c, level);
- if (precedence() <= level)
- c.s << (is_tex ? ")}" : ")");
+
+ } else {
+
+ // Ordinary output
+ while (it != itend) {
+ it->print(c, level);
+ it++;
+ }
+ }
}
}
+void indexed::print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const
+{
+ if (precedence() <= level)
+ c.s << openbrace << '(';
+ c.s << openbrace;
+ seq[0].print(c, precedence());
+ c.s << closebrace;
+ printindices(c, level);
+ if (precedence() <= level)
+ c.s << ')' << closebrace;
+}
+
+void indexed::do_print(const print_context & c, unsigned level) const
+{
+ print_indexed(c, "", "", level);
+}
+
+void indexed::do_print_latex(const print_latex & c, unsigned level) const
+{
+ print_indexed(c, "{", "}", level);
+}
+
+void indexed::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << class_name() << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << ", " << seq.size()-1 << " indices"
+ << ", symmetry=" << symtree << std::endl;
+ seq[0].print(c, level + c.delta_indent);
+ printindices(c, level + c.delta_indent);
+}
+
bool indexed::info(unsigned inf) const
{
if (inf == info_flags::indexed) return true;
return f * thiscontainer(v);
}
+ if(this->tinfo()==&indexed::tinfo_static && seq.size()==1)
+ return base;
+
// Canonicalize indices according to the symmetry properties
if (seq.size() > 2) {
exvector v = seq;
GINAC_ASSERT(is_exactly_a<symmetry>(symtree));
int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
- if (sig != INT_MAX) {
+ if (sig != std::numeric_limits<int>::max()) {
// Something has changed while sorting indices, more evaluations later
if (sig == 0)
return _ex0;
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);
}
-ex indexed::thiscontainer(exvector * vp) const
+ex indexed::thiscontainer(std::auto_ptr<exvector> vp) const
{
return indexed(ex_to<symmetry>(symtree), vp);
}
+unsigned indexed::return_type() const
+{
+ if(is_a<matrix>(op(0)))
+ return return_types::commutative;
+ else
+ return op(0).return_type();
+}
+
ex indexed::expand(unsigned options) const
{
GINAC_ASSERT(seq.size() > 0);
- if ((options & expand_options::expand_indexed) && is_exactly_a<add>(seq[0])) {
-
- // expand_indexed expands (a+b).i -> a.i + b.i
- const ex & base = seq[0];
- ex sum = _ex0;
- for (size_t i=0; i<base.nops(); i++) {
+ if (options & expand_options::expand_indexed) {
+ ex newbase = seq[0].expand(options);
+ if (is_exactly_a<add>(newbase)) {
+ ex sum = _ex0;
+ for (size_t i=0; i<newbase.nops(); i++) {
+ exvector s = seq;
+ s[0] = newbase.op(i);
+ sum += thiscontainer(s).expand(options);
+ }
+ return sum;
+ }
+ if (!are_ex_trivially_equal(newbase, seq[0])) {
exvector s = seq;
- s[0] = base.op(i);
- sum += thiscontainer(s).expand();
+ s[0] = newbase;
+ return ex_to<indexed>(thiscontainer(s)).inherited::expand(options);
}
- return sum;
-
- } else
- return inherited::expand(options);
+ }
+ return inherited::expand(options);
}
//////////
// non-virtual functions in this class
//////////
-void indexed::printindices(const print_context & c, unsigned level) const
-{
- if (seq.size() > 1) {
-
- exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
-
- if (is_a<print_latex>(c)) {
-
- // TeX output: group by variance
- bool first = true;
- bool covariant = true;
-
- while (it != itend) {
- bool cur_covariant = (is_a<varidx>(*it) ? ex_to<varidx>(*it).is_covariant() : true);
- if (first || cur_covariant != covariant) { // Variance changed
- // The empty {} prevents indices from ending up on top of each other
- if (!first)
- c.s << "}{}";
- covariant = cur_covariant;
- if (covariant)
- c.s << "_{";
- else
- c.s << "^{";
- }
- it->print(c, level);
- c.s << " ";
- first = false;
- it++;
- }
- c.s << "}";
-
- } else {
-
- // Ordinary output
- while (it != itend) {
- it->print(c, level);
- it++;
- }
- }
- }
-}
-
/** Check whether all indices are of class idx and validate the symmetry
* tree. This function is used internally to make sure that all constructed
* indexed objects really carry indices and not some other classes. */
return free_indices;
}
-exvector power::get_free_indices() const
+struct is_summation_idx : public std::unary_function<ex, bool> {
+ bool operator()(const ex & e)
+ {
+ return is_dummy_pair(e, e);
+ }
+};
+
+exvector integral::get_free_indices() const
+{
+ if (a.get_free_indices().size() || b.get_free_indices().size())
+ throw (std::runtime_error("integral::get_free_indices: boundary values should not have free indices"));
+ return f.get_free_indices();
+}
+
+template<class T> size_t number_of_type(const exvector&v)
{
- // Return free indices of basis
- return basis.get_free_indices();
+ 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 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
else {
while (global_uniq.size() > local_uniq.size())
global_uniq.pop_back();
- return e.subs(lst(local_uniq.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()));
+ return e.subs(lst(local_uniq.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()), subs_options::no_pattern);
}
}
{
bool something_changed = false;
+ // Find dummy symbols that occur twice in the same indexed object.
+ exvector local_var_dummies;
+ local_var_dummies.reserve(e.nops()/2);
+ for (size_t i=1; i<e.nops(); ++i) {
+ if (!is_a<varidx>(e.op(i)))
+ continue;
+ for (size_t j=i+1; j<e.nops(); ++j) {
+ if (is_dummy_pair(e.op(i), e.op(j))) {
+ local_var_dummies.push_back(e.op(i));
+ for (exvector::iterator k = variant_dummy_indices.begin();
+ k!=variant_dummy_indices.end(); ++k) {
+ if (e.op(i).op(0) == k->op(0)) {
+ variant_dummy_indices.erase(k);
+ break;
+ }
+ }
+ break;
+ }
+ }
+ }
+
+ // In the case where a dummy symbol occurs twice in the same indexed object
+ // we try all posibilities of raising/lowering and keep the least one in
+ // the sense of ex_is_less.
+ ex optimal_e = e;
+ size_t numpossibs = 1 << local_var_dummies.size();
+ for (size_t i=0; i<numpossibs; ++i) {
+ ex try_e = e;
+ for (size_t j=0; j<local_var_dummies.size(); ++j) {
+ exmap m;
+ if (1<<j & i) {
+ ex curr_idx = local_var_dummies[j];
+ ex curr_toggle = ex_to<varidx>(curr_idx).toggle_variance();
+ m[curr_idx] = curr_toggle;
+ m[curr_toggle] = curr_idx;
+ }
+ try_e = e.subs(m, subs_options::no_pattern);
+ }
+ if(ex_is_less()(try_e, optimal_e))
+ { optimal_e = try_e;
+ something_changed = true;
+ }
+ }
+ e = optimal_e;
+
+ if (!is_a<indexed>(e))
+ return true;
+
+ exvector seq = ex_to<indexed>(e).seq;
+
// If a dummy index is encountered for the first time in the
// product, pull it up, otherwise, pull it down
- exvector::const_iterator it2, it2start, it2end;
- for (it2start = ex_to<indexed>(e).seq.begin(), it2end = ex_to<indexed>(e).seq.end(), it2 = it2start + 1; it2 != it2end; ++it2) {
+ for (exvector::iterator it2 = seq.begin()+1, it2end = seq.end();
+ it2 != it2end; ++it2) {
if (!is_exactly_a<varidx>(*it2))
continue;
for (vit = variant_dummy_indices.begin(), vitend = variant_dummy_indices.end(); vit != vitend; ++vit) {
if (it2->op(0).is_equal(vit->op(0))) {
if (ex_to<varidx>(*it2).is_covariant()) {
- e = e.subs(lst(
- *it2 == ex_to<varidx>(*it2).toggle_variance(),
- ex_to<varidx>(*it2).toggle_variance() == *it2
- ));
+ /*
+ * N.B. we don't want to use
+ *
+ * e = e.subs(lst(
+ * *it2 == ex_to<varidx>(*it2).toggle_variance(),
+ * ex_to<varidx>(*it2).toggle_variance() == *it2
+ * ), subs_options::no_pattern);
+ *
+ * since this can trigger non-trivial repositioning of indices,
+ * e.g. due to non-trivial symmetry properties of e, thus
+ * invalidating iterators
+ */
+ *it2 = ex_to<varidx>(*it2).toggle_variance();
something_changed = true;
- it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
- it2start = ex_to<indexed>(e).seq.begin();
- it2end = ex_to<indexed>(e).seq.end();
}
moved_indices.push_back(*vit);
variant_dummy_indices.erase(vit);
for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) {
if (it2->op(0).is_equal(vit->op(0))) {
if (ex_to<varidx>(*it2).is_contravariant()) {
- e = e.subs(*it2 == ex_to<varidx>(*it2).toggle_variance());
+ *it2 = ex_to<varidx>(*it2).toggle_variance();
something_changed = true;
- it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
- it2start = ex_to<indexed>(e).seq.begin();
- it2end = ex_to<indexed>(e).seq.end();
}
goto next_index;
}
next_index: ;
}
+ if (something_changed)
+ e = ex_to<indexed>(e).thiscontainer(seq);
+
return something_changed;
}
}
};
-/** 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)
+/* An auxiliary function used by simplify_indexed() and expand_dummy_sum()
+ * It returns an exvector of factors from the supplied product */
+static void product_to_exvector(const ex & e, exvector & v, bool & non_commutative)
{
// Remember whether the product was commutative or noncommutative
// (because we chop it into factors and need to reassemble later)
- bool non_commutative = is_exactly_a<ncmul>(e);
+ non_commutative = is_exactly_a<ncmul>(e);
// Collect factors in an exvector, store squares twice
- exvector v;
v.reserve(e.nops() * 2);
if (is_exactly_a<power>(e)) {
ex f = e.op(i);
if (is_exactly_a<power>(f) && f.op(1).is_equal(_ex2)) {
v.push_back(f.op(0));
- v.push_back(f.op(0));
+ v.push_back(f.op(0));
} else if (is_exactly_a<ncmul>(f)) {
// Noncommutative factor found, split it as well
non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
v.push_back(f);
}
}
+}
+
+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)
+{
+ // Collect factors in an exvector
+ exvector v;
+
+ // Remember whether the product was commutative or noncommutative
+ // (because we chop it into factors and need to reassemble later)
+ bool non_commutative;
+ product_to_exvector(e, v, non_commutative);
// Perform contractions
bool something_changed = false;
// 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));
* performs contraction of dummy indices where possible and checks whether
* the free indices in sums are consistent.
*
+ * @param options Simplification options (currently unused)
* @return simplified expression */
-ex ex::simplify_indexed() const
+ex ex::simplify_indexed(unsigned options) const
{
exvector free_indices, dummy_indices;
scalar_products sp;
* scalar products by known values if desired.
*
* @param sp Scalar products to be replaced automatically
+ * @param options Simplification options (currently unused)
* @return simplified expression */
-ex ex::simplify_indexed(const scalar_products & sp) const
+ex ex::simplify_indexed(const scalar_products & sp, unsigned options) const
{
exvector free_indices, dummy_indices;
return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
}
}
+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)
+{
+ exvector p;
+ bool nc;
+ product_to_exvector(e, p, nc);
+ exvector::const_iterator ip = p.begin(), ipend = p.end();
+ exvector v, v1;
+ while (ip != ipend) {
+ if (is_a<indexed>(*ip)) {
+ v1 = ex_to<indexed>(*ip).get_dummy_indices();
+ v.insert(v.end(), v1.begin(), v1.end());
+ exvector::const_iterator ip1 = ip+1;
+ while (ip1 != ipend) {
+ if (is_a<indexed>(*ip1)) {
+ v1 = ex_to<indexed>(*ip).get_dummy_indices(ex_to<indexed>(*ip1));
+ v.insert(v.end(), v1.begin(), v1.end());
+ }
+ ++ip1;
+ }
+ }
+ ++ip;
+ }
+ return v;
+}
+
+lst rename_dummy_indices_uniquely(const exvector & va, const exvector & vb)
+{
+ exvector common_indices;
+ set_intersection(va.begin(), va.end(), vb.begin(), vb.end(), std::back_insert_iterator<exvector>(common_indices), ex_is_less());
+ if (common_indices.empty()) {
+ return lst(lst(), lst());
+ } else {
+ exvector new_indices, old_indices;
+ old_indices.reserve(2*common_indices.size());
+ new_indices.reserve(2*common_indices.size());
+ exvector::const_iterator ip = common_indices.begin(), ipend = common_indices.end();
+ while (ip != ipend) {
+ ex newsym=(new symbol)->setflag(status_flags::dynallocated);
+ ex newidx;
+ if(is_exactly_a<spinidx>(*ip))
+ newidx = (new spinidx(newsym, ex_to<spinidx>(*ip).get_dim(),
+ ex_to<spinidx>(*ip).is_covariant(),
+ ex_to<spinidx>(*ip).is_dotted()))
+ -> setflag(status_flags::dynallocated);
+ else if (is_exactly_a<varidx>(*ip))
+ newidx = (new varidx(newsym, ex_to<varidx>(*ip).get_dim(),
+ ex_to<varidx>(*ip).is_covariant()))
+ -> setflag(status_flags::dynallocated);
+ else
+ newidx = (new idx(newsym, ex_to<idx>(*ip).get_dim()))
+ -> setflag(status_flags::dynallocated);
+ old_indices.push_back(*ip);
+ new_indices.push_back(newidx);
+ if(is_a<varidx>(*ip)) {
+ old_indices.push_back(ex_to<varidx>(*ip).toggle_variance());
+ new_indices.push_back(ex_to<varidx>(newidx).toggle_variance());
+ }
+ ++ip;
+ }
+ return lst(lst(old_indices.begin(), old_indices.end()), lst(new_indices.begin(), new_indices.end()));
+ }
+}
+
+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(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_safely(a);
+ if (va.size() > 0) {
+ 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(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_safely(b);
+ if (vb.size() > 0) {
+ sort(vb.begin(), vb.end(), ex_is_less());
+ lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+ if (indices_subs.op(0).nops() > 0) {
+ if (modify_va) {
+ for (lst::const_iterator i = ex_to<lst>(indices_subs.op(1)).begin(); i != ex_to<lst>(indices_subs.op(1)).end(); ++i)
+ va.push_back(*i);
+ exvector uncommon_indices;
+ set_difference(vb.begin(), vb.end(), indices_subs.op(0).begin(), indices_subs.op(0).end(), std::back_insert_iterator<exvector>(uncommon_indices), ex_is_less());
+ exvector::const_iterator ip = uncommon_indices.begin(), ipend = uncommon_indices.end();
+ while (ip != ipend) {
+ va.push_back(*ip);
+ ++ip;
+ }
+ sort(va.begin(), va.end(), ex_is_less());
+ }
+ 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 expand_dummy_sum(const ex & e, bool subs_idx)
+{
+ ex e_expanded = e.expand();
+ 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) || 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 < 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 += result.subs( nu.op(0) == i );
+ }
+ }
+ result = en;
+ }
+ }
+ return result;
+ } else {
+ return e;
+ }
+}
+
} // namespace GiNaC