/** @file indexed.cpp
*
- * Implementation of GiNaC's index carrying objects. */
+ * Implementation of GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2000 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 <string>
+#include <iostream>
+#include <stdexcept>
#include "indexed.h"
-#include "ex.h"
#include "idx.h"
-#include "debugmsg.h"
+#include "add.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"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_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
//////////
-// public
-
-indexed::indexed()
+indexed::indexed() : symtree(sy_none())
{
- debugmsg("indexed default constructor",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
+ tinfo_key = TINFO_indexed;
}
-indexed::~indexed()
+void indexed::copy(const indexed & other)
{
- debugmsg("indexed destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
+ inherited::copy(other);
+ symtree = other.symtree;
}
-indexed::indexed(const indexed & other)
+DEFAULT_DESTROY(indexed)
+
+//////////
+// other constructors
+//////////
+
+indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
{
- debugmsg("indexed copy constructor",LOGLEVEL_CONSTRUCT);
- copy (other);
+ tinfo_key = TINFO_indexed;
+ validate();
}
-const indexed & indexed::operator=(const indexed & other)
+indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none())
{
- debugmsg("indexed operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ tinfo_key = TINFO_indexed;
+ validate();
}
-// protected
+indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none())
+{
+ tinfo_key = TINFO_indexed;
+ validate();
+}
-void indexed::copy(const indexed & other)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none())
{
- inherited::copy(other);
+ tinfo_key = TINFO_indexed;
+ validate();
}
-void indexed::destroy(bool call_parent)
+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())
{
- if (call_parent) {
- inherited::destroy(call_parent);
- }
+ tinfo_key = TINFO_indexed;
+ validate();
}
-//////////
-// other constructors
-//////////
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
+{
+ tinfo_key = TINFO_indexed;
+ validate();
+}
-// public
+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;
+ validate();
+}
-indexed::indexed(const ex & i1) : inherited(i1)
+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",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ tinfo_key = TINFO_indexed;
+ validate();
}
-indexed::indexed(const ex & i1, const ex & i2) : inherited(i1,i2)
+indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ seq.insert(seq.end(), v.begin(), v.end());
+ tinfo_key = TINFO_indexed;
+ validate();
}
-indexed::indexed(const ex & i1, const ex & i2, const ex & i3)
- : inherited(i1,i2,i3)
+indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
{
- debugmsg("indexed constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ seq.insert(seq.end(), v.begin(), v.end());
+ tinfo_key = TINFO_indexed;
+ validate();
}
-indexed::indexed(const ex & i1, const ex & i2, const ex & i3, const ex & i4)
- : inherited(i1,i2,i3,i4)
+indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
{
- debugmsg("indexed constructor from ex,ex,ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ tinfo_key = TINFO_indexed;
}
-indexed::indexed(const exvector & iv) : inherited(iv)
+indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
{
- debugmsg("indexed constructor from exvector",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ tinfo_key = TINFO_indexed;
}
-indexed::indexed(exvector * ivp) : inherited(ivp)
+indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm)
{
- debugmsg("indexed constructor from exvector *",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ tinfo_key = TINFO_indexed;
}
//////////
// archiving
//////////
-/** Construct object from archive_node. */
indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_indexed;
-}
-
-/** Unarchive the object. */
-ex indexed::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new indexed(n, sym_lst))->setflag(status_flags::dynallocated);
+ 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);
+ }
}
-/** Archive the object. */
void indexed::archive(archive_node &n) const
{
inherited::archive(n);
+ n.add_ex("symmetry", symtree);
}
+DEFAULT_UNARCHIVE(indexed)
+
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
-// public
+void indexed::print(const print_context & c, unsigned level) const
+{
+ GINAC_ASSERT(seq.size() > 0);
+
+ if (is_of_type(c, print_tree)) {
+
+ 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);
+
+ } else {
+
+ bool is_tex = is_of_type(c, print_latex);
+ 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)
+ || is_ex_of_type(base, indexed);
+ if (is_tex)
+ c.s << "{";
+ if (need_parens)
+ c.s << "(";
+ base.print(c);
+ if (need_parens)
+ c.s << ")";
+ if (is_tex)
+ c.s << "}";
+ printindices(c, level);
+ }
+}
-basic * indexed::duplicate() const
+bool indexed::info(unsigned inf) const
{
- debugmsg("indexed duplicate",LOGLEVEL_DUPLICATE);
- return new indexed(*this);
+ if (inf == info_flags::indexed) return true;
+ if (inf == info_flags::has_indices) return seq.size() > 1;
+ return inherited::info(inf);
}
-void indexed::printraw(std::ostream & os) const
+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
{
- debugmsg("indexed printraw",LOGLEVEL_PRINT);
- os << "indexed(indices=";
- printrawindices(os);
- os << ",hash=" << hashvalue << ",flags=" << flags << ")";
+ // No indices? Then no property can be fulfilled
+ if (seq.size() < 2)
+ return false;
+
+ // Check all indices
+ return find_if(seq.begin() + 1, seq.end(), bind2nd(idx_is_not(), inf)) == seq.end();
}
-void indexed::printtree(std::ostream & os, unsigned indent) const
+int indexed::compare_same_type(const basic & other) const
{
- debugmsg("indexed printtree",LOGLEVEL_PRINT);
- os << std::string(indent,' ') << "indexed: " << seq.size() << " indices";
- os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
- printtreeindices(os,indent);
+ GINAC_ASSERT(is_a<indexed>(other));
+ return inherited::compare_same_type(other);
}
-void indexed::print(std::ostream & os, unsigned upper_precedence) const
+ex indexed::eval(int level) const
{
- debugmsg("indexed print",LOGLEVEL_PRINT);
- os << "UNNAMEDINDEX";
- printindices(os);
+ // First evaluate children, then we will end up here again
+ if (level > 1)
+ 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;
+
+ // 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));
+ v[0] = seq[0] / f;
+ return f * thisexprseq(v);
+ }
+
+ // 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) {
+ // Something has changed while sorting indices, more evaluations later
+ if (sig == 0)
+ return _ex0;
+ return ex(sig) * thisexprseq(v);
+ }
+ }
+
+ // Let the class of the base object perform additional evaluations
+ return ex_to<basic>(base).eval_indexed(*this);
}
-void indexed::printcsrc(std::ostream & os, unsigned type,
- unsigned upper_precedence) const
+ex indexed::thisexprseq(const exvector & v) const
{
- debugmsg("indexed print csrc",LOGLEVEL_PRINT);
- print(os,upper_precedence);
+ return indexed(ex_to<symmetry>(symtree), v);
}
-bool indexed::info(unsigned inf) const
+ex indexed::thisexprseq(exvector * vp) const
{
- if (inf==info_flags::indexed) return true;
- if (inf==info_flags::has_indices) return seq.size()!=0;
- return inherited::info(inf);
+ return indexed(ex_to<symmetry>(symtree), vp);
}
-exvector indexed::get_indices(void) const
+ex indexed::expand(unsigned options) const
{
- return seq;
+ GINAC_ASSERT(seq.size() > 0);
- /*
- idxvector filtered_indices;
- filtered_indices.reserve(indices.size());
- for (idxvector::const_iterator cit=indices.begin(); cit!=indices.end(); ++cit) {
- if ((*cit).get_type()==t) {
- filtered_indices.push_back(*cit);
+ if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) {
+
+ // expand_indexed expands (a+b).i -> a.i + b.i
+ const ex & base = seq[0];
+ ex sum = _ex0;
+ for (unsigned i=0; i<base.nops(); i++) {
+ exvector s = seq;
+ s[0] = base.op(i);
+ sum += thisexprseq(s).expand();
+ }
+ return sum;
+
+ } else
+ return inherited::expand(options);
+}
+
+//////////
+// virtual functions which can be overridden by derived classes
+//////////
+
+// none
+
+//////////
+// 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_of_type(c, print_latex)) {
+
+ // 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++;
+ }
}
}
- return filtered_indices;
- */
}
-// protected
+/** 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();
+ while (it != itend) {
+ if (!is_ex_of_type(*it, idx))
+ 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. It always returns 0.
+/** Implementation of ex::diff() for an indexed object always returns 0.
+ *
* @see ex::diff */
ex indexed::derivative(const symbol & s) const
{
- return _ex0();
+ return _ex0;
}
-int indexed::compare_same_type(const basic & other) const
+//////////
+// global functions
+//////////
+
+/** Check whether two sorted index vectors are consistent (i.e. equal). */
+static bool indices_consistent(const exvector & v1, const exvector & v2)
{
- GINAC_ASSERT(is_of_type(other,indexed));
- return inherited::compare_same_type(other);
+ // Number of indices must be the same
+ if (v1.size() != v2.size())
+ return false;
+
+ return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal());
}
-bool indexed::is_equal_same_type(const basic & other) const
+exvector indexed::get_indices(void) const
{
- GINAC_ASSERT(is_of_type(other,indexed));
- return inherited::is_equal_same_type(other);
+ GINAC_ASSERT(seq.size() >= 1);
+ return exvector(seq.begin() + 1, seq.end());
}
-unsigned indexed::return_type(void) const
+exvector indexed::get_dummy_indices(void) const
{
- return return_types::noncommutative;
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+ return dummy_indices;
}
-
-unsigned indexed::return_type_tinfo(void) const
+
+exvector indexed::get_dummy_indices(const indexed & other) const
{
- return tinfo_key;
+ exvector indices = get_free_indices();
+ exvector other_indices = other.get_free_indices();
+ indices.insert(indices.end(), other_indices.begin(), other_indices.end());
+ exvector dummy_indices;
+ find_dummy_indices(indices, dummy_indices);
+ return dummy_indices;
}
-ex indexed::thisexprseq(const exvector & v) const
+bool indexed::has_dummy_index_for(const ex & i) const
{
- return indexed(v);
+ exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
+ while (it != itend) {
+ if (is_dummy_pair(*it, i))
+ return true;
+ it++;
+ }
+ return false;
}
-ex indexed::thisexprseq(exvector * vp) const
+exvector indexed::get_free_indices(void) const
{
- return indexed(vp);
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+ return free_indices;
}
-//////////
-// virtual functions which can be overridden by derived classes
-//////////
-
-// none
+exvector add::get_free_indices(void) const
+{
+ exvector free_indices;
+ for (unsigned i=0; i<nops(); i++) {
+ if (i == 0)
+ free_indices = op(i).get_free_indices();
+ else {
+ exvector free_indices_of_term = op(i).get_free_indices();
+ if (!indices_consistent(free_indices, free_indices_of_term))
+ throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
+ }
+ }
+ return free_indices;
+}
-//////////
-// non-virtual functions in this class
-//////////
+exvector mul::get_free_indices(void) const
+{
+ // Concatenate free indices of all factors
+ exvector un;
+ for (unsigned i=0; i<nops(); i++) {
+ exvector free_indices_of_factor = op(i).get_free_indices();
+ un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
+ }
-// protected
+ // And remove the dummy indices
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(un, free_indices, dummy_indices);
+ return free_indices;
+}
-void indexed::printrawindices(std::ostream & os) const
+exvector ncmul::get_free_indices(void) const
{
- if (seq.size()!=0) {
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- (*cit).printraw(os);
- os << ",";
- }
+ // Concatenate free indices of all factors
+ exvector un;
+ for (unsigned i=0; i<nops(); i++) {
+ exvector free_indices_of_factor = op(i).get_free_indices();
+ un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
}
+
+ // And remove the dummy indices
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(un, free_indices, dummy_indices);
+ return free_indices;
}
-void indexed::printtreeindices(std::ostream & os, unsigned indent) const
+exvector power::get_free_indices(void) const
{
- if (seq.size()!=0) {
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- os << std::string(indent+delta_indent,' ');
- (*cit).printraw(os);
- os << std::endl;
+ // Return free indices of basis
+ return basis.get_free_indices();
+}
+
+/** Rename dummy indices in an expression.
+ *
+ * @param e Expression to be worked 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));
}
}
-void indexed::printindices(std::ostream & os) const
-{
- if (seq.size()!=0) {
- if (seq.size()>1) {
- os << "{";
+/* 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, 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)
+ bool non_commutative = is_ex_exactly_of_type(e, ncmul);
+
+ // Collect factors in an exvector, store squares twice
+ exvector v;
+ v.reserve(e.nops() * 2);
+
+ 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));
+ v.push_back(e.op(0));
+ v.push_back(e.op(0));
+ } else {
+ 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)) {
+ 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 (unsigned j=0; j<f.nops(); j++)
+ v.push_back(f.op(j));
+ } else
+ v.push_back(f);
}
- exvector::const_iterator last=seq.end()-1;
- exvector::const_iterator cit=seq.begin();
- for (; cit!=last; ++cit) {
- (*cit).print(os);
- os << ",";
+ }
+
+ // Perform contractions
+ bool something_changed = false;
+ GINAC_ASSERT(v.size() > 1);
+ exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
+ for (it1 = v.begin(); it1 != next_to_last; it1++) {
+
+try_again:
+ 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);
+
+ 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);
+ 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);
+ unsigned num_dummies = dummy.size();
+ if (num_dummies == 0)
+ continue;
+
+ // At least one dummy index, is it a defined scalar product?
+ bool contracted = false;
+ if (free.empty()) {
+ if (sp.is_defined(*it1, *it2)) {
+ *it1 = sp.evaluate(*it1, *it2);
+ *it2 = _ex1;
+ goto contraction_done;
+ }
+ }
+
+ // Try to contract the first one with the second one
+ 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 = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
+ }
+ if (contracted) {
+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())
+ // 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());
+ }
+ 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;
+ for (it1 = local_dummy_indices.begin(), itend = local_dummy_indices.end(); it1 != itend; ++it1) {
+ if (is_exactly_a<varidx>(*it1))
+ variant_dummy_indices.push_back(*it1);
+ }
+
+ // 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;
+
+ ex new_it1;
+ bool it1_dirty = false; // It this is true, then new_it1 holds a new value for *it1
+
+ // If a dummy index is encountered for the first time in the
+ // product, pull it up, otherwise, pull it down
+ exvector::iterator it2, it2end;
+ for (it2 = const_cast<indexed &>(ex_to<indexed>(*it1)).seq.begin(), it2end = const_cast<indexed &>(ex_to<indexed>(*it1)).seq.end(); 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()) {
+ new_it1 = (it1_dirty ? new_it1 : *it1).subs(*it2 == ex_to<varidx>(*it2).toggle_variance());
+ it1_dirty = true;
+ something_changed = true;
+ }
+ 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()) {
+ new_it1 = (it1_dirty ? new_it1 : *it1).subs(*it2 == ex_to<varidx>(*it2).toggle_variance());
+ it1_dirty = true;
+ something_changed = true;
+ }
+ goto next_index;
+ }
+ }
+
+next_index: ;
+ }
+
+ if (it1_dirty)
+ *it1 = new_it1;
}
- (*cit).print(os);
- if (seq.size()>1) {
- os << "}";
+ }
+
+ ex r;
+ 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 ex_to<basic>(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
+ else
+ return r;
}
-bool indexed::all_of_type_idx(void) const
+/** Simplify indexed expression, return list of free indices. */
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
{
- // used only inside of ASSERTs
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if (!is_ex_of_type(*cit,idx)) return false;
+ // Expand the expression
+ ex e_expanded = e.expand();
+
+ // Simplification of single indexed object: just find the free indices
+ // and perform dummy index renaming
+ if (is_ex_of_type(e_expanded, indexed)) {
+ 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);
+ 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;
+ 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, dummy_indices, sp);
+ if (!term.is_zero()) {
+ if (first) {
+ free_indices = free_indices_of_term;
+ sum = term;
+ first = false;
+ } else {
+ 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 = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
+ else
+ sum += term;
+ }
+ }
+ }
+
+ return sum;
}
- return true;
+
+ // 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, dummy_indices, sp);
+
+ // Cannot do anything
+ free_indices.clear();
+ return e_expanded;
}
-//////////
-// static member variables
-//////////
+/** 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, dummy_indices;
+ scalar_products sp;
+ return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
+}
-// none
+/** 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, 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());
+}
//////////
-// global constants
+// helper classes
//////////
-const indexed some_indexed;
-const type_info & typeid_indexed=typeid(some_indexed);
+void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
+{
+ 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();
+}
+
+/** Check whether scalar product pair is defined. */
+bool scalar_products::is_defined(const ex & v1, const ex & v2) const
+{
+ return spm.find(make_key(v1, v2)) != spm.end();
+}
+
+/** Return value of defined scalar product pair. */
+ex scalar_products::evaluate(const ex & v1, const ex & v2) const
+{
+ return spm.find(make_key(v1, v2))->second;
+}
+
+void scalar_products::debugprint(void) const
+{
+ std::cerr << "map size=" << spm.size() << std::endl;
+ 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=" << i->second << std::endl;
+ ++i;
+ }
+}
+
+/** Make key from object pair. */
+spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
+{
+ // If indexed, extract base objects
+ ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
+ ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
+
+ // Enforce canonical order in pair
+ if (s1.compare(s2) > 0)
+ return spmapkey(s2, s1);
+ else
+ return spmapkey(s1, s2);
+}
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff