X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=dcd6d9510d6d0ac688802373f30f7d93e0f07362;hp=0ab989e801baccc8a94d60a7df7306da1822a78f;hb=9f015041142625abf6645b3ea39c62b59a5f442c;hpb=61b8ecb02c8212efbc15f59face8a9c620dc823c diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index 0ab989e8..dcd6d951 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 @@ -20,6 +20,7 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include #include #include "indexed.h" @@ -28,28 +29,30 @@ #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) @@ -58,97 +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(); } ////////// @@ -157,60 +144,69 @@ 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::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 << ")"; -} - -void indexed::printtree(std::ostream & os, unsigned indent) const -{ - debugmsg("indexed printtree", LOGLEVEL_PRINT); - GINAC_ASSERT(seq.size() > 0); + if (is_of_type(c, print_tree)) { - os << std::string(indent, ' ') << class_name() << ", " << seq.size()-1 << " indices"; - os << ",hash=" << hashvalue << ",flags=" << flags << std::endl; - printtreeindices(os, indent); -} + 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(c).delta_indent; + seq[0].print(c, level + delta_indent); + printindices(c, level + delta_indent); -void indexed::print(std::ostream & os, unsigned upper_precedence) const -{ - debugmsg("indexed print", LOGLEVEL_PRINT); - GINAC_ASSERT(seq.size() > 0); + } else { - 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); + 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); + } } bool indexed::info(unsigned inf) const @@ -220,6 +216,12 @@ bool indexed::info(unsigned inf) const return inherited::info(inf); } +struct idx_is_not : public std::binary_function { + bool operator() (const ex & e, unsigned inf) const { + return !(ex_to(e).get_value().info(inf)); + } +}; + bool indexed::all_index_values_are(unsigned inf) const { // No indices? Then no property can be fulfilled @@ -227,137 +229,60 @@ bool indexed::all_index_values_are(unsigned inf) const 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(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(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(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(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); + 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 @@ -368,7 +293,7 @@ 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 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_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(*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(); @@ -439,6 +369,20 @@ 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; } ////////// @@ -452,15 +396,7 @@ static bool indices_consistent(const exvector & v1, const exvector & v2) 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 @@ -486,6 +422,17 @@ exvector indexed::get_dummy_indices(const indexed & other) 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; @@ -544,9 +491,146 @@ exvector power::get_free_indices(void) const 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_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: ; + } + + 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, 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) @@ -558,19 +642,19 @@ ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_ 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; ireturn_type() != return_types::commutative); + + // Indexed factor found, get free indices and look for contraction + // candidates + exvector free1, dummy1; + find_free_and_dummy(ex_to(*it1).seq.begin() + 1, ex_to(*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(*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 un(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end()); - un.insert(un.end(), ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end()); 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(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) { - 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) { + // 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)) { - const indexed & o = ex_to_indexed(*it1); - un.insert(un.end(), o.seq.begin() + 1, o.seq.end()); + exvector 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()); + } + 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; } - it1++; } - find_free_and_dummy(un, free_indices, dummy_indices); 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; 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; } /** 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(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; iadd_indexed(sum, term); + sum = ex_to(sum.op(0)).add_indexed(sum, term); else sum += term; } @@ -716,25 +876,55 @@ ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products // 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()); } ////////// @@ -746,6 +936,19 @@ 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