* Implementation of GiNaC's indexed expressions. */
/*
- * 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 "indexed.h"
#include "mul.h"
#include "ncmul.h"
#include "power.h"
+#include "relational.h"
+#include "symmetry.h"
+#include "lst.h"
+#include "print.h"
#include "archive.h"
#include "utils.h"
-#include "debugmsg.h"
namespace GiNaC {
GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
//////////
-indexed::indexed() : symmetry(unknown)
+indexed::indexed() : symtree(sy_none())
{
- debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
}
void indexed::copy(const indexed & other)
{
inherited::copy(other);
- symmetry = other.symmetry;
+ symtree = other.symtree;
}
DEFAULT_DESTROY(indexed)
// other constructors
//////////
-indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
+indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
{
- debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(unknown)
+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())
{
- debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
{
- debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
{
- debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(symm)
+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)
{
- debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
+indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
seq.insert(seq.end(), v.begin(), v.end());
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
{
- debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
seq.insert(seq.end(), v.begin(), v.end());
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
+ validate();
}
-indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
+indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
{
- debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
}
-indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
+indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
{
- debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
}
-indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
+indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm)
{
- debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
- assert_all_indices_of_type_idx();
}
//////////
indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
- unsigned int symm;
- if (!(n.find_unsigned("symmetry", symm)))
- throw (std::runtime_error("unknown indexed symmetry type in archive"));
+ if (!n.find_ex("symmetry", symtree, sym_lst)) {
+ // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property
+ unsigned symm = 0;
+ n.find_unsigned("symmetry", symm);
+ switch (symm) {
+ case 1:
+ symtree = sy_symm();
+ break;
+ case 2:
+ symtree = sy_anti();
+ break;
+ default:
+ symtree = sy_none();
+ break;
+ }
+ const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
+ }
}
void indexed::archive(archive_node &n) const
{
inherited::archive(n);
- n.add_unsigned("symmetry", symmetry);
+ n.add_ex("symmetry", symtree);
}
DEFAULT_UNARCHIVE(indexed)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
-void indexed::printraw(std::ostream & os) const
+void indexed::print(const print_context & c, unsigned level) const
{
- debugmsg("indexed printraw", LOGLEVEL_PRINT);
GINAC_ASSERT(seq.size() > 0);
- os << class_name() << "(";
- seq[0].printraw(os);
- os << ",indices=";
- printrawindices(os);
- os << ",hash=" << hashvalue << ",flags=" << flags << ")";
-}
+ if (is_a<print_tree>(c)) {
-void indexed::printtree(std::ostream & os, unsigned indent) const
-{
- debugmsg("indexed printtree", LOGLEVEL_PRINT);
- GINAC_ASSERT(seq.size() > 0);
+ 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);
- os << std::string(indent, ' ') << class_name() << ", " << seq.size()-1 << " indices";
- os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
- printtreeindices(os, indent);
-}
+ } else {
-void indexed::print(std::ostream & os, unsigned upper_precedence) const
-{
- debugmsg("indexed print", LOGLEVEL_PRINT);
- GINAC_ASSERT(seq.size() > 0);
+ bool is_tex = is_a<print_latex>(c);
+ const ex & base = seq[0];
- const ex & base = seq[0];
- bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul)
- || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power);
- if (need_parens)
- os << "(";
- os << base;
- if (need_parens)
- os << ")";
- printindices(os);
+ if (precedence() <= level)
+ c.s << (is_tex ? "{(" : "(");
+ if (is_tex)
+ c.s << "{";
+ base.print(c, precedence());
+ if (is_tex)
+ c.s << "}";
+ printindices(c, level);
+ if (precedence() <= level)
+ c.s << (is_tex ? ")}" : ")");
+ }
}
bool indexed::info(unsigned inf) const
return inherited::info(inf);
}
+struct idx_is_not : public std::binary_function<ex, unsigned, bool> {
+ bool operator() (const ex & e, unsigned inf) const {
+ return !(ex_to<idx>(e).get_value().info(inf));
+ }
+};
+
bool indexed::all_index_values_are(unsigned inf) const
{
// No indices? Then no property can be fulfilled
return false;
// Check all indices
- exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
- while (it != itend) {
- GINAC_ASSERT(is_ex_of_type(*it, idx));
- if (!ex_to_idx(*it).get_value().info(inf))
- return false;
- it++;
- }
- return true;
+ return find_if(seq.begin() + 1, seq.end(), bind2nd(idx_is_not(), inf)) == seq.end();
}
int indexed::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other, indexed));
+ GINAC_ASSERT(is_a<indexed>(other));
return inherited::compare_same_type(other);
}
-// The main difference between sort_index_vector() and canonicalize_indices()
-// is that the latter takes the symmetry of the object into account. Once we
-// implement mixed symmetries, canonicalize_indices() will only be able to
-// reorder index pairs with known symmetry properties, while sort_index_vector()
-// always sorts the whole vector.
-
-/** Bring a vector of indices into a canonic order (don't care about the
- * symmetry of the objects carrying the indices). Dummy indices will lie
- * next to each other after the sorting.
- *
- * @param v Index vector to be sorted */
-static void sort_index_vector(exvector &v)
-{
- // Nothing to sort if less than 2 elements
- if (v.size() < 2)
- return;
-
- // Simple bubble sort algorithm should be sufficient for the small
- // number of indices expected
- exvector::iterator it1 = v.begin(), itend = v.end(), next_to_last_idx = itend - 1;
- while (it1 != next_to_last_idx) {
- exvector::iterator it2 = it1 + 1;
- while (it2 != itend) {
- if (it1->compare(*it2) > 0)
- it1->swap(*it2);
- it2++;
- }
- it1++;
- }
-}
-
-/** Bring a vector of indices into a canonic order. This operation only makes
- * sense if the object carrying these indices is either symmetric or totally
- * antisymmetric with respect to the indices.
- *
- * @param itbegin Start of index vector
- * @param itend End of index vector
- * @param antisymm Whether the object is antisymmetric
- * @return the sign introduced by the reordering of the indices if the object
- * is antisymmetric (or 0 if two equal indices are encountered). For
- * symmetric objects, this is always +1. If the index vector was
- * already in a canonic order this function returns INT_MAX. */
-static int canonicalize_indices(exvector::iterator itbegin, exvector::iterator itend, bool antisymm)
-{
- bool something_changed = false;
- int sig = 1;
-
- // Simple bubble sort algorithm should be sufficient for the small
- // number of indices expected
- exvector::iterator it1 = itbegin, next_to_last_idx = itend - 1;
- while (it1 != next_to_last_idx) {
- exvector::iterator it2 = it1 + 1;
- while (it2 != itend) {
- int cmpval = it1->compare(*it2);
- if (cmpval == 1) {
- it1->swap(*it2);
- something_changed = true;
- if (antisymm)
- sig = -sig;
- } else if (cmpval == 0 && antisymm) {
- something_changed = true;
- sig = 0;
- }
- it2++;
- }
- it1++;
- }
-
- return something_changed ? sig : INT_MAX;
-}
-
ex indexed::eval(int level) const
{
// First evaluate children, then we will end up here again
if (level > 1)
- return indexed(symmetry, evalchildren(level));
+ return indexed(ex_to<symmetry>(symtree), evalchildren(level));
const ex &base = seq[0];
// If the base object is 0, the whole object is 0
if (base.is_zero())
- return _ex0();
+ return _ex0;
// If the base object is a product, pull out the numeric factor
if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) {
- exvector v = seq;
- ex f = ex_to_numeric(base.op(base.nops() - 1));
+ exvector v(seq);
+ ex f = ex_to<numeric>(base.op(base.nops() - 1));
v[0] = seq[0] / f;
return f * thisexprseq(v);
}
// Canonicalize indices according to the symmetry properties
- if (seq.size() > 2 && (symmetry != unknown && symmetry != mixed)) {
+ if (seq.size() > 2) {
exvector v = seq;
- int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
+ GINAC_ASSERT(is_exactly_a<symmetry>(symtree));
+ int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
if (sig != INT_MAX) {
// Something has changed while sorting indices, more evaluations later
if (sig == 0)
- return _ex0();
+ return _ex0;
return ex(sig) * thisexprseq(v);
}
}
// Let the class of the base object perform additional evaluations
- return base.bp->eval_indexed(*this);
+ return ex_to<basic>(base).eval_indexed(*this);
}
ex indexed::thisexprseq(const exvector & v) const
{
- return indexed(symmetry, v);
+ return indexed(ex_to<symmetry>(symtree), v);
}
ex indexed::thisexprseq(exvector * vp) const
{
- return indexed(symmetry, vp);
+ return indexed(ex_to<symmetry>(symtree), vp);
}
ex indexed::expand(unsigned options) const
// expand_indexed expands (a+b).i -> a.i + b.i
const ex & base = seq[0];
- ex sum = _ex0();
+ ex sum = _ex0;
for (unsigned i=0; i<base.nops(); i++) {
exvector s = seq;
s[0] = base.op(i);
// non-virtual functions in this class
//////////
-void indexed::printrawindices(std::ostream & os) const
+void indexed::printindices(const print_context & c, unsigned level) const
{
if (seq.size() > 1) {
- exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
- while (it != itend) {
- it->printraw(os);
- it++;
- if (it != itend)
- os << ",";
- }
- }
-}
-void indexed::printtreeindices(std::ostream & os, unsigned indent) const
-{
- if (seq.size() > 1) {
exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
- while (it != itend) {
- os << std::string(indent + delta_indent, ' ');
- it->printraw(os);
- os << std::endl;
- it++;
- }
- }
-}
-void indexed::printindices(std::ostream & os) const
-{
- if (seq.size() > 1) {
- exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
- while (it != itend) {
- it->print(os);
- it++;
+ if (is_a<print_latex>(c)) {
+
+ // TeX output: group by variance
+ bool first = true;
+ bool covariant = true;
+
+ while (it != itend) {
+ bool cur_covariant = (is_ex_of_type(*it, varidx) ? 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. This function is used
- * internally to make sure that all constructed indexed objects really
- * carry indices and not some other classes. */
-void indexed::assert_all_indices_of_type_idx(void) const
+/** 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. */
+void indexed::validate(void) const
{
GINAC_ASSERT(seq.size() > 0);
exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
throw(std::invalid_argument("indices of indexed object must be of type idx"));
it++;
}
+
+ if (!symtree.is_zero()) {
+ if (!is_ex_exactly_of_type(symtree, symmetry))
+ throw(std::invalid_argument("symmetry of indexed object must be of type symmetry"));
+ const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
+ }
+}
+
+/** Implementation of ex::diff() for an indexed object always returns 0.
+ *
+ * @see ex::diff */
+ex indexed::derivative(const symbol & s) const
+{
+ return _ex0;
}
//////////
if (v1.size() != v2.size())
return false;
- // And also the indices themselves
- exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
- bit = v2.begin(), bitend = v2.end();
- while (ait != aitend) {
- if (!ait->is_equal(*bit))
- return false;
- ait++; bit++;
- }
- return true;
+ return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal());
}
exvector indexed::get_indices(void) const
return dummy_indices;
}
+bool indexed::has_dummy_index_for(const ex & i) const
+{
+ exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
+ while (it != itend) {
+ if (is_dummy_pair(*it, i))
+ return true;
+ it++;
+ }
+ return false;
+}
+
exvector indexed::get_free_indices(void) const
{
exvector free_indices, dummy_indices;
return basis.get_free_indices();
}
+/** Rename dummy indices in an expression.
+ *
+ * @param e Expression to work on
+ * @param local_dummy_indices The set of dummy indices that appear in the
+ * expression "e"
+ * @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)
+{
+ unsigned global_size = global_dummy_indices.size(),
+ local_size = local_dummy_indices.size();
+
+ // Any local dummy indices at all?
+ if (local_size == 0)
+ return e;
+
+ if (global_size < local_size) {
+
+ // More local indices than we encountered before, add the new ones
+ // to the global set
+ int old_global_size = global_size;
+ 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(ex_is_equal(), *it)) == global_dummy_indices.end()) {
+ global_dummy_indices.push_back(*it);
+ global_size++;
+ remaining--;
+ }
+ it++;
+ }
+
+ // If this is the first set of local indices, do nothing
+ if (old_global_size == 0)
+ return e;
+ }
+ GINAC_ASSERT(local_size <= global_size);
+
+ // Construct lists of index symbols
+ exlist local_syms, global_syms;
+ for (unsigned i=0; i<local_size; 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 (unsigned i=0; i<global_size; 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
+ exlist local_uniq, global_uniq;
+ set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator<exlist>(local_uniq), ex_is_less());
+ set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator<exlist>(global_uniq), ex_is_less());
+
+ // Replace remaining non-common local index symbols by global ones
+ if (local_uniq.empty())
+ return e;
+ else {
+ while (global_uniq.size() > local_uniq.size())
+ global_uniq.pop_back();
+ return e.subs(lst(local_uniq), lst(global_uniq));
+ }
+}
+
+/** Given a set of indices, extract those of class varidx. */
+static void find_variant_indices(const exvector & v, exvector & variant_indices)
+{
+ exvector::const_iterator it1, itend;
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ if (is_exactly_a<varidx>(*it1))
+ variant_indices.push_back(*it1);
+ }
+}
+
+/** Raise/lower dummy indices in a single indexed objects to canonicalize their
+ * variance.
+ *
+ * @param e Object to work on
+ * @param variant_dummy_indices The set of indices that might need repositioning (will be changed by this function)
+ * @param moved_indices The set of indices that have been repositioned (will be changed by this function)
+ * @return true if 'e' was changed */
+bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices)
+{
+ bool something_changed = false;
+
+ // 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) {
+ if (!is_exactly_a<varidx>(*it2))
+ continue;
+
+ exvector::iterator vit, vitend;
+ 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
+ ));
+ 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);
+ goto next_index;
+ }
+ }
+
+ 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());
+ 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: ;
+ }
+
+ return something_changed;
+}
+
+/* Ordering that only compares the base expressions of indexed objects. */
+struct ex_base_is_less : public std::binary_function<ex, ex, bool> {
+ bool operator() (const ex &lh, const ex &rh) const
+ {
+ return (is_a<indexed>(lh) ? lh.op(0) : lh).compare(is_a<indexed>(rh) ? rh.op(0) : rh) < 0;
+ }
+};
+
/** 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, const scalar_products & sp)
+ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
{
// Remember whether the product was commutative or noncommutative
// (because we chop it into factors and need to reassemble later)
if (is_ex_exactly_of_type(e, power)) {
// We only get called for simple squares, split a^2 -> a*a
- GINAC_ASSERT(e.op(1).is_equal(_ex2()));
+ GINAC_ASSERT(e.op(1).is_equal(_ex2));
v.push_back(e.op(0));
v.push_back(e.op(0));
} else {
- for (int i=0; i<e.nops(); i++) {
+ for (unsigned i=0; i<e.nops(); i++) {
ex f = e.op(i);
- if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
+ if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2)) {
v.push_back(f.op(0));
v.push_back(f.op(0));
} else if (is_ex_exactly_of_type(f, ncmul)) {
// Noncommutative factor found, split it as well
non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
- for (int j=0; j<f.nops(); j++)
+ for (unsigned j=0; j<f.nops(); j++)
v.push_back(f.op(j));
} else
v.push_back(f);
if (!is_ex_of_type(*it1, indexed))
continue;
+ bool first_noncommutative = (it1->return_type() != return_types::commutative);
+
// Indexed factor found, get free indices and look for contraction
// candidates
exvector free1, dummy1;
- find_free_and_dummy(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end(), free1, dummy1);
+ find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free1, dummy1);
exvector::iterator it2;
for (it2 = it1 + 1; it2 != itend; it2++) {
if (!is_ex_of_type(*it2, indexed))
continue;
+ bool second_noncommutative = (it2->return_type() != return_types::commutative);
+
// Find free indices of second factor and merge them with free
// indices of first factor
exvector un;
- find_free_and_dummy(ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end(), un, dummy1);
+ find_free_and_dummy(ex_to<indexed>(*it2).seq.begin() + 1, ex_to<indexed>(*it2).seq.end(), un, dummy1);
un.insert(un.end(), free1.begin(), free1.end());
// Check whether the two factors share dummy indices
exvector free, dummy;
find_free_and_dummy(un, free, dummy);
- if (dummy.size() == 0)
+ unsigned num_dummies = dummy.size();
+ if (num_dummies == 0)
continue;
// At least one dummy index, is it a defined scalar product?
- if (free.size() == 0) {
+ bool contracted = false;
+ if (free.empty()) {
if (sp.is_defined(*it1, *it2)) {
*it1 = sp.evaluate(*it1, *it2);
- *it2 = _ex1();
- something_changed = true;
- goto try_again;
+ *it2 = _ex1;
+ goto contraction_done;
}
}
- // Contraction of symmetric with antisymmetric object is zero
- if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
- ex_to_indexed(*it2).symmetry == indexed::antisymmetric
- || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
- ex_to_indexed(*it2).symmetry == indexed::symmetric)
- && dummy.size() > 1) {
- free_indices.clear();
- return _ex0();
- }
-
// Try to contract the first one with the second one
- bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
+ contracted = ex_to<basic>(it1->op(0)).contract_with(it1, it2, v);
if (!contracted) {
// That didn't work; maybe the second object knows how to
// contract itself with the first one
- contracted = it2->op(0).bp->contract_with(it2, it1, v);
+ contracted = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
}
if (contracted) {
- something_changed = true;
+contraction_done:
+ if (first_noncommutative || second_noncommutative
+ || is_ex_exactly_of_type(*it1, add) || is_ex_exactly_of_type(*it2, add)
+ || is_ex_exactly_of_type(*it1, mul) || is_ex_exactly_of_type(*it2, mul)
+ || is_ex_exactly_of_type(*it1, ncmul) || is_ex_exactly_of_type(*it2, ncmul)) {
+
+ // One of the factors became a sum or product:
+ // re-expand expression and run again
+ // Non-commutative products are always re-expanded to give
+ // simplify_ncmul() the chance to re-order and canonicalize
+ // the product
+ ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v)));
+ return simplify_indexed(r, free_indices, dummy_indices, sp);
+ }
// Both objects may have new indices now or they might
// even not be indexed objects any more, so we have to
// start over
+ something_changed = true;
goto try_again;
}
}
}
// Find free indices (concatenate them all and call find_free_and_dummy())
- exvector un, dummy_indices;
- it1 = v.begin(); itend = v.end();
- while (it1 != itend) {
- exvector free_indices_of_factor = it1->get_free_indices();
+ // and all dummy indices that appear
+ exvector un, individual_dummy_indices;
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ exvector free_indices_of_factor;
+ if (is_ex_of_type(*it1, indexed)) {
+ exvector dummy_indices_of_factor;
+ find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free_indices_of_factor, dummy_indices_of_factor);
+ individual_dummy_indices.insert(individual_dummy_indices.end(), dummy_indices_of_factor.begin(), dummy_indices_of_factor.end());
+ } else
+ free_indices_of_factor = it1->get_free_indices();
un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
- it1++;
}
- find_free_and_dummy(un, free_indices, dummy_indices);
+ exvector local_dummy_indices;
+ find_free_and_dummy(un, free_indices, local_dummy_indices);
+ local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end());
+
+ // Filter out the dummy indices with variance
+ exvector variant_dummy_indices;
+ find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+ // Any indices with variance present at all?
+ if (!variant_dummy_indices.empty()) {
+
+ // Yes, bring the product into a canonical order that only depends on
+ // the base expressions of indexed objects
+ if (!non_commutative)
+ std::sort(v.begin(), v.end(), ex_base_is_less());
+
+ exvector moved_indices;
+
+ // Iterate over all indexed objects in the product
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ if (!is_ex_of_type(*it1, indexed))
+ continue;
+
+ if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices))
+ something_changed = true;
+ }
+ }
ex r;
- if (something_changed) {
- if (non_commutative)
- r = ncmul(v);
- else
- r = mul(v);
- } else
+ if (something_changed)
+ r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
+ else
r = e;
+ // 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) {
+ lst dummy_syms;
+ for (int i=0; i<local_dummy_indices.size(); i++)
+ dummy_syms.append(local_dummy_indices[i].op(0));
+ if (r.symmetrize(dummy_syms).is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ }
+
+ // Dummy index renaming
+ r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
+
// Product of indexed object with a scalar?
if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
&& is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
- return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
+ return ex_to<basic>(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
else
return r;
}
+/** This structure stores the original and symmetrized versions of terms
+ * obtained during the simplification of sums. */
+class symminfo {
+public:
+ symminfo() {}
+ ~symminfo() {}
+
+ symminfo(const ex & symmterm_, const ex & orig_)
+ {
+ if (is_a<mul>(orig_)) {
+ ex tmp = orig_.op(orig_.nops()-1);
+ orig = orig_ / tmp;
+ } else
+ orig = orig_;
+
+ if (is_a<mul>(symmterm_)) {
+ coeff = symmterm_.op(symmterm_.nops()-1);
+ symmterm = symmterm_ / coeff;
+ } else {
+ coeff = 1;
+ symmterm = symmterm_;
+ }
+ }
+
+ symminfo(const symminfo & other)
+ {
+ symmterm = other.symmterm;
+ coeff = other.coeff;
+ orig = other.orig;
+ }
+
+ const symminfo & operator=(const symminfo & other)
+ {
+ if (this != &other) {
+ symmterm = other.symmterm;
+ coeff = other.coeff;
+ orig = other.orig;
+ }
+ return *this;
+ }
+
+ ex symmterm;
+ ex coeff;
+ ex orig;
+};
+
+class symminfo_is_less {
+public:
+ bool operator() (const symminfo & si1, const symminfo & si2)
+ {
+ int comp = si1.symmterm.compare(si2.symmterm);
+ if (comp < 0) return true;
+ if (comp > 0) return false;
+ comp = si1.orig.compare(si2.orig);
+ if (comp < 0) return true;
+ if (comp > 0) return false;
+ comp = si1.coeff.compare(si2.coeff);
+ if (comp < 0) return true;
+ return false;
+ }
+};
+
/** Simplify indexed expression, return list of free indices. */
-ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
{
// Expand the expression
ex e_expanded = e.expand();
// Simplification of single indexed object: just find the free indices
+ // and perform dummy index renaming/repositioning
if (is_ex_of_type(e_expanded, indexed)) {
- const indexed &i = ex_to_indexed(e_expanded);
- exvector dummy_indices;
- find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
- return e_expanded;
+
+ // Find the dummy indices
+ const indexed &i = ex_to<indexed>(e_expanded);
+ exvector local_dummy_indices;
+ find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
+
+ // Filter out the dummy indices with variance
+ exvector variant_dummy_indices;
+ find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+ // Any indices with variance present at all?
+ if (!variant_dummy_indices.empty()) {
+
+ // Yes, reposition them
+ exvector moved_indices;
+ reposition_dummy_indices(e_expanded, variant_dummy_indices, moved_indices);
+ }
+
+ // Rename the dummy indices
+ return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
}
// Simplification of sum = sum of simplifications, check consistency of
// free indices in each term
if (is_ex_exactly_of_type(e_expanded, add)) {
bool first = true;
- ex sum = _ex0();
+ ex sum = _ex0;
free_indices.clear();
for (unsigned i=0; i<e_expanded.nops(); i++) {
exvector free_indices_of_term;
- ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
+ ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, dummy_indices, sp);
if (!term.is_zero()) {
if (first) {
free_indices = free_indices_of_term;
if (!indices_consistent(free_indices, free_indices_of_term))
throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
- sum = sum.op(0).bp->add_indexed(sum, term);
+ sum = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
else
sum += term;
}
}
}
+ // If the sum turns out to be zero, we are finished
+ if (sum.is_zero()) {
+ free_indices.clear();
+ return sum;
+ }
+
+ // Symmetrizing over the dummy indices may cancel terms
+ int num_terms_orig = (is_a<add>(sum) ? sum.nops() : 1);
+ if (num_terms_orig > 1 && dummy_indices.size() >= 2) {
+
+ // Construct list of all dummy index symbols
+ lst dummy_syms;
+ for (int i=0; i<dummy_indices.size(); i++)
+ dummy_syms.append(dummy_indices[i].op(0));
+
+ // Symmetrize each term separately and store the resulting
+ // terms in a list of symminfo structures
+ std::vector<symminfo> v;
+ for (int i=0; i<sum.nops(); i++) {
+ ex sum_symm = sum.op(i).symmetrize(dummy_syms);
+ if (is_a<add>(sum_symm))
+ for (int j=0; j<sum_symm.nops(); j++)
+ v.push_back(symminfo(sum_symm.op(j), sum.op(i)));
+ else
+ v.push_back(symminfo(sum_symm, sum.op(i)));
+ }
+
+ // Now add up all the unsymmetrized versions of the terms that
+ // did not cancel out in the symmetrization
+ exvector result;
+ std::sort(v.begin(), v.end(), symminfo_is_less());
+ for (std::vector<symminfo>::iterator i=v.begin(); i!=v.end(); ) {
+ std::vector<symminfo>::iterator j = i;
+ for (j++; j!=v.end() && i->symmterm == j->symmterm; j++) ;
+ for (std::vector<symminfo>::iterator k=i; k!=j; k++)
+ result.push_back((k->coeff)*(i->orig));
+ i = j;
+ }
+ ex sum_symm = (new add(result))->setflag(status_flags::dynallocated);
+ if (sum_symm.is_zero())
+ free_indices.clear();
+ return sum_symm;
+ }
+
return sum;
}
// Simplification of products
if (is_ex_exactly_of_type(e_expanded, mul)
|| is_ex_exactly_of_type(e_expanded, ncmul)
- || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
- return simplify_indexed_product(e_expanded, free_indices, sp);
+ || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2)))
+ return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
// Cannot do anything
free_indices.clear();
return e_expanded;
}
-ex simplify_indexed(const ex & e)
+/** Simplify/canonicalize expression containing indexed objects. This
+ * performs contraction of dummy indices where possible and checks whether
+ * the free indices in sums are consistent.
+ *
+ * @return simplified expression */
+ex ex::simplify_indexed(void) const
{
- exvector free_indices;
+ exvector free_indices, dummy_indices;
scalar_products sp;
- return simplify_indexed(e, free_indices, sp);
+ return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
}
-ex simplify_indexed(const ex & e, const scalar_products & sp)
+/** Simplify/canonicalize expression containing indexed objects. This
+ * performs contraction of dummy indices where possible, checks whether
+ * the free indices in sums are consistent, and automatically replaces
+ * scalar products by known values if desired.
+ *
+ * @param sp Scalar products to be replaced automatically
+ * @return simplified expression */
+ex ex::simplify_indexed(const scalar_products & sp) const
{
- exvector free_indices;
- return simplify_indexed(e, free_indices, sp);
+ exvector free_indices, dummy_indices;
+ return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
+}
+
+/** Symmetrize expression over its free indices. */
+ex ex::symmetrize(void) const
+{
+ return GiNaC::symmetrize(*this, get_free_indices());
+}
+
+/** Antisymmetrize expression over its free indices. */
+ex ex::antisymmetrize(void) const
+{
+ return GiNaC::antisymmetrize(*this, get_free_indices());
+}
+
+/** Symmetrize expression by cyclic permutation over its free indices. */
+ex ex::symmetrize_cyclic(void) const
+{
+ return GiNaC::symmetrize_cyclic(*this, get_free_indices());
}
//////////
spm[make_key(v1, v2)] = sp;
}
+void scalar_products::add_vectors(const lst & l)
+{
+ // Add all possible pairs of products
+ unsigned num = l.nops();
+ for (unsigned i=0; i<num; i++) {
+ ex a = l.op(i);
+ for (unsigned j=0; j<num; j++) {
+ ex b = l.op(j);
+ add(a, b, a*b);
+ }
+ }
+}
+
void scalar_products::clear(void)
{
spm.clear();
void scalar_products::debugprint(void) const
{
std::cerr << "map size=" << spm.size() << std::endl;
- for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
- const spmapkey & k = cit->first;
+ spmap::const_iterator i = spm.begin(), end = spm.end();
+ while (i != end) {
+ const spmapkey & k = i->first;
std::cerr << "item key=(" << k.first << "," << k.second;
- std::cerr << "), value=" << cit->second << std::endl;
+ std::cerr << "), value=" << i->second << std::endl;
+ ++i;
}
}
git://www.ginac.de / ginac.git / blobdiff