X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=d9b2f474fc8266e7e96a87ee483c1f5eace86352;hp=3f2cb717b2b5e5577c5ef4ed01b82e39bfb94505;hb=34704348ad3e512010cbf85b6a9dee9fff22cd66;hpb=c5ca06e3a25226684028dec4bd8cba0833998be6;ds=sidebyside diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index 3f2cb717..d9b2f474 100644 --- a/ginac/indexed.cpp +++ b/ginac/indexed.cpp @@ -3,7 +3,7 @@ * 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 @@ -20,8 +20,8 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include -#include #include "indexed.h" #include "idx.h" @@ -29,31 +29,30 @@ #include "mul.h" #include "ncmul.h" #include "power.h" +#include "relational.h" +#include "symmetry.h" #include "lst.h" -#include "inifcns.h" // for symmetrize() #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) @@ -62,97 +61,81 @@ 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(); } ////////// @@ -161,61 +144,66 @@ indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(sy 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(ex_to(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::print(const print_context & c, unsigned level) const { - debugmsg("indexed print", LOGLEVEL_PRINT); GINAC_ASSERT(seq.size() > 0); - if (is_of_type(c, print_tree)) { + if (is_a(c)) { c.s << std::string(level, ' ') << class_name() << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec - << ", " << seq.size()-1 << " indices"; - switch (symmetry) { - case symmetric: c.s << ", symmetric"; break; - case antisymmetric: c.s << ", antisymmetric"; break; - default: break; - } - c.s << std::endl; + << ", " << seq.size()-1 << " indices" + << ", symmetry=" << symtree << std::endl; unsigned delta_indent = static_cast(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); + bool is_tex = is_a(c); 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 (precedence() <= level) + c.s << (is_tex ? "{(" : "("); if (is_tex) c.s << "{"; - if (need_parens) - c.s << "("; - base.print(c); - if (need_parens) - c.s << ")"; + base.print(c, precedence()); if (is_tex) c.s << "}"; printindices(c, level); + if (precedence() <= level) + c.s << (is_tex ? ")}" : ")"); } } @@ -228,7 +216,7 @@ bool indexed::info(unsigned inf) const struct idx_is_not : public std::binary_function { bool operator() (const ex & e, unsigned inf) const { - return !(ex_to_idx(e).get_value().info(inf)); + return !(ex_to(e).get_value().info(inf)); } }; @@ -244,118 +232,55 @@ bool indexed::all_index_values_are(unsigned inf) const int indexed::compare_same_type(const basic & other) const { - GINAC_ASSERT(is_of_type(other, indexed)); + GINAC_ASSERT(is_a(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. 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(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)); + ex f = ex_to(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 == symmetric || symmetry == antisymmetric)) { - exvector v(seq); - int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric); + if (seq.size() > 2) { + exvector v = seq; + GINAC_ASSERT(is_exactly_a(symtree)); + int sig = canonicalize(v.begin() + 1, ex_to(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); -} - -int indexed::degree(const ex & s) const -{ - return is_equal(*s.bp) ? 1 : 0; -} - -int indexed::ldegree(const ex & s) const -{ - return is_equal(*s.bp) ? 1 : 0; -} - -ex indexed::coeff(const ex & s, int n) const -{ - if (is_equal(*s.bp)) - return n==1 ? _ex1() : _ex0(); - else - return n==0 ? ex(*this) : _ex0(); + return ex_to(base).eval_indexed(*this); } ex indexed::thisexprseq(const exvector & v) const { - return indexed(symmetry, v); + return indexed(ex_to(symtree), v); } ex indexed::thisexprseq(exvector * vp) const { - return indexed(symmetry, vp); + return indexed(ex_to(symtree), vp); } ex indexed::expand(unsigned options) const @@ -366,7 +291,7 @@ 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(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) { + bool cur_covariant = (is_ex_of_type(*it, varidx) ? ex_to(*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 << "}"; + c.s << "}{}"; covariant = cur_covariant; if (covariant) c.s << "_{"; @@ -429,10 +355,10 @@ void indexed::printindices(const print_context & c, unsigned level) const } } -/** 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(); @@ -441,6 +367,20 @@ void indexed::assert_all_indices_of_type_idx(void) const 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(ex_to(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; } ////////// @@ -551,7 +491,7 @@ exvector power::get_free_indices(void) const /** Rename dummy indices in an expression. * - * @param e Expression to be worked on + * @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 @@ -559,8 +499,8 @@ exvector power::get_free_indices(void) const * by the function */ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices) { - int global_size = global_dummy_indices.size(), - local_size = local_dummy_indices.size(); + unsigned global_size = global_dummy_indices.size(), + local_size = local_dummy_indices.size(); // Any local dummy indices at all? if (local_size == 0) @@ -570,6 +510,7 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex // 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) { @@ -580,27 +521,111 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex } it++; } - } - // Replace index symbols in expression + // If this is the first set of local indices, do nothing + if (old_global_size == 0) + return e; + } GINAC_ASSERT(local_size <= global_size); - bool all_equal = true; - lst local_syms, global_syms; - for (unsigned i=0; i(local_uniq), ex_is_less()); + set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator(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(*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(e).seq.begin(), it2end = ex_to(e).seq.end(), it2 = it2start + 1; it2 != it2end; ++it2) { + if (!is_exactly_a(*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(*it2).is_covariant()) { + e = e.subs(lst( + *it2 == ex_to(*it2).toggle_variance(), + ex_to(*it2).toggle_variance() == *it2 + )); + something_changed = true; + it2 = ex_to(e).seq.begin() + (it2 - it2start); + it2start = ex_to(e).seq.begin(); + it2end = ex_to(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(*it2).is_contravariant()) { + e = e.subs(*it2 == ex_to(*it2).toggle_variance()); + something_changed = true; + it2 = ex_to(e).seq.begin() + (it2 - it2start); + it2start = ex_to(e).seq.begin(); + it2end = ex_to(e).seq.end(); + } + goto next_index; + } + } + +next_index: ; } - if (all_equal) - return e; - else - return e.subs(local_syms, global_syms); + + return something_changed; } +/* Ordering that only compares the base expressions of indexed objects. */ +struct ex_base_is_less : public std::binary_function { + bool operator() (const ex &lh, const ex &rh) const + { + return (is_a(lh) ? lh.op(0) : lh).compare(is_a(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) @@ -615,19 +640,19 @@ ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & du 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(*it1).seq.begin() + 1, ex_to(*it1).seq.end(), free1, dummy1); exvector::iterator it2; for (it2 = it1 + 1; it2 != itend; it2++) { @@ -662,42 +687,33 @@ try_again: // 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(*it2).seq.begin() + 1, ex_to(*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? bool contracted = false; - if (free.size() == 0) { + if (free.empty()) { if (sp.is_defined(*it1, *it2)) { *it1 = sp.evaluate(*it1, *it2); - *it2 = _ex1(); + *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 - contracted = it1->op(0).bp->contract_with(it1, it2, v); + contracted = ex_to(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(it2->op(0)).contract_with(it2, it1, v); } if (contracted) { contraction_done: @@ -727,35 +743,70 @@ contraction_done: // Find free indices (concatenate them all and call find_free_and_dummy()) // and all dummy indices that appear exvector un, individual_dummy_indices; - it1 = v.begin(); itend = v.end(); - while (it1 != itend) { + 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); + find_free_and_dummy(ex_to(*it1).seq.begin() + 1, ex_to(*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++; } 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) 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; iscalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1))); + return ex_to(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to(r.op(1))); else return r; } @@ -767,11 +818,27 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi ex e_expanded = e.expand(); // Simplification of single indexed object: just find the free indices - // and perform dummy index renaming + // and perform dummy index renaming/repositioning if (is_ex_of_type(e_expanded, indexed)) { - const indexed &i = ex_to_indexed(e_expanded); + + // Find the dummy indices + const indexed &i = ex_to(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); } @@ -779,7 +846,7 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi // 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; iadd_indexed(sum, term); + sum = ex_to(sum.op(0)).add_indexed(sum, term); else sum += term; } } } + if (sum.is_zero()) { + free_indices.clear(); + return sum; + } + + // Symmetrizing over the dummy indices may cancel terms + int num_terms_orig = (is_a(sum) ? sum.nops() : 1); + if (num_terms_orig > 1 && dummy_indices.size() >= 2) { + lst dummy_syms; + for (int i=0; i(sum_symm) ? sum_symm.nops() : 1); + if (num_terms < num_terms_orig) + 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()))) + || (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 @@ -900,10 +988,12 @@ ex scalar_products::evaluate(const ex & v1, const ex & v2) const 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; } }