X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=ad17a497a9dc703e52cd435d6901312071beab42;hp=f0726915674bf13ce8df0383013ba0bb4ed7fe24;hb=58f0cc954e01d67cbb42a55e2fc37dcea0757294;hpb=b1da89e057fea6f9c9c6e32bd92ecb5980b6713a diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index f0726915..ad17a497 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) 1999-2004 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 +20,9 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ +#include +#include #include -#include #include "indexed.h" #include "idx.h" @@ -29,196 +30,221 @@ #include "mul.h" #include "ncmul.h" #include "power.h" +#include "relational.h" +#include "symmetry.h" +#include "operators.h" #include "lst.h" -#include "inifcns.h" -#include "print.h" #include "archive.h" #include "utils.h" -#include "debugmsg.h" namespace GiNaC { -GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq) +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(indexed, exprseq, + print_func(&indexed::do_print). + print_func(&indexed::do_print_latex). + print_func(&indexed::do_print_tree)) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// default constructor ////////// -indexed::indexed() : symmetry(unknown) +indexed::indexed() : symtree(not_symmetric()) { - debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_indexed; } -void indexed::copy(const indexed & other) -{ - inherited::copy(other); - symmetry = other.symmetry; -} - -DEFAULT_DESTROY(indexed) - ////////// // other constructors ////////// -indexed::indexed(const ex & b) : inherited(b), symmetry(unknown) +indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric()) { - 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(not_symmetric()) { - 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(not_symmetric()) { - 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(not_symmetric()) { - 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(not_symmetric()) { - 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(not_symmetric()) { - 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, std::auto_ptr vp) : inherited(vp), symtree(symm) { - debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT); tinfo_key = TINFO_indexed; - assert_all_indices_of_type_idx(); } ////////// // archiving ////////// -indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +indexed::indexed(const archive_node &n, 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 = not_symmetric(); + 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 +void indexed::printindices(const print_context & c, unsigned level) const { - debugmsg("indexed print", LOGLEVEL_PRINT); - GINAC_ASSERT(seq.size() > 0); + if (seq.size() > 1) { - if (is_of_type(c, print_tree)) { + exvector::const_iterator it=seq.begin() + 1, itend = seq.end(); - 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; - unsigned delta_indent = static_cast(c).delta_indent; - seq[0].print(c, level + delta_indent); - printindices(c, level + delta_indent); + if (is_a(c)) { - } else { + // TeX output: group by variance + bool first = true; + bool covariant = true; - 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) + while (it != itend) { + bool cur_covariant = (is_a(*it) ? 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 << "}"; - printindices(c, level); + + } else { + + // Ordinary output + while (it != itend) { + it->print(c, level); + it++; + } + } } } +void indexed::print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const +{ + if (precedence() <= level) + c.s << openbrace << '('; + c.s << openbrace; + seq[0].print(c, precedence()); + c.s << closebrace; + printindices(c, level); + if (precedence() <= level) + c.s << ')' << closebrace; +} + +void indexed::do_print(const print_context & c, unsigned level) const +{ + print_indexed(c, "", "", level); +} + +void indexed::do_print_latex(const print_latex & c, unsigned level) const +{ + print_indexed(c, "{", "}", level); +} + +void indexed::do_print_tree(const print_tree & c, unsigned level) const +{ + c.s << std::string(level, ' ') << class_name() << " @" << this + << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec + << ", " << seq.size()-1 << " indices" + << ", symmetry=" << symtree << std::endl; + seq[0].print(c, level + c.delta_indent); + printindices(c, level + c.delta_indent); +} + bool indexed::info(unsigned inf) const { if (inf == info_flags::indexed) return true; @@ -226,9 +252,9 @@ bool indexed::info(unsigned inf) const return inherited::info(inf); } -struct idx_is_not : public binary_function { +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)); } }; @@ -244,138 +270,79 @@ 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)) { + if (is_exactly_a(base) && is_exactly_a(base.op(base.nops() - 1))) { 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); + return f * thiscontainer(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 ex(sig) * thisexprseq(v); + return _ex0; + return ex(sig) * thiscontainer(v); } } // Let the class of the base object perform additional evaluations - return base.bp->eval_indexed(*this); + return ex_to(base).eval_indexed(*this); } -int indexed::degree(const ex & s) const +ex indexed::thiscontainer(const exvector & v) const { - return is_equal(*s.bp) ? 1 : 0; + return indexed(ex_to(symtree), v); } -int indexed::ldegree(const ex & s) const +ex indexed::thiscontainer(std::auto_ptr vp) 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(); -} - -ex indexed::thisexprseq(const exvector & v) const -{ - return indexed(symmetry, v); -} - -ex indexed::thisexprseq(exvector * vp) const -{ - return indexed(symmetry, vp); + return indexed(ex_to(symtree), vp); } ex indexed::expand(unsigned options) const { GINAC_ASSERT(seq.size() > 0); - 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(newbase)) { + ex sum = _ex0; + for (size_t i=0; i(thiscontainer(s)).inherited::expand(options); } - return sum; - - } else - return inherited::expand(options); + } + return inherited::expand(options); } ////////// @@ -388,65 +355,54 @@ ex indexed::expand(unsigned options) const // 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) { - 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() 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)) + if (!is_a(*it)) throw(std::invalid_argument("indices of indexed object must be of type idx")); it++; } + + if (!symtree.is_zero()) { + if (!is_exactly_a(symtree)) + 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; } ////////// // global functions ////////// +struct idx_is_equal_ignore_dim : public std::binary_function { + bool operator() (const ex &lh, const ex &rh) const + { + if (lh.is_equal(rh)) + return true; + else + try { + // Replacing the dimension might cause an error (e.g. with + // index classes that only work in a fixed number of dimensions) + return lh.is_equal(ex_to(rh).replace_dim(ex_to(lh).get_dim())); + } catch (...) { + return false; + } + } +}; + /** Check whether two sorted index vectors are consistent (i.e. equal). */ static bool indices_consistent(const exvector & v1, const exvector & v2) { @@ -454,16 +410,16 @@ static bool indices_consistent(const exvector & v1, const exvector & v2) if (v1.size() != v2.size()) return false; - return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal()); + return equal(v1.begin(), v1.end(), v2.begin(), idx_is_equal_ignore_dim()); } -exvector indexed::get_indices(void) const +exvector indexed::get_indices() const { GINAC_ASSERT(seq.size() >= 1); return exvector(seq.begin() + 1, seq.end()); } -exvector indexed::get_dummy_indices(void) const +exvector indexed::get_dummy_indices() const { exvector free_indices, dummy_indices; find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices); @@ -491,17 +447,17 @@ bool indexed::has_dummy_index_for(const ex & i) const return false; } -exvector indexed::get_free_indices(void) const +exvector indexed::get_free_indices() const { exvector free_indices, dummy_indices; find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices); return free_indices; } -exvector add::get_free_indices(void) const +exvector add::get_free_indices() const { exvector free_indices; - for (unsigned i=0; i { + bool operator()(const ex & e) + { + return is_dummy_pair(e, e); + } +}; + +exvector power::get_free_indices() const { - // Return free indices of basis - return basis.get_free_indices(); + // Get free indices of basis + exvector basis_indices = basis.get_free_indices(); + + if (exponent.info(info_flags::even)) { + // If the exponent is an even number, then any "free" index that + // forms a dummy pair with itself is actually a summation index + exvector really_free; + std::remove_copy_if(basis_indices.begin(), basis_indices.end(), + std::back_inserter(really_free), is_summation_idx()); + return really_free; + } else + return basis_indices; } /** 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 +532,8 @@ 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(); + size_t global_size = global_dummy_indices.size(), + local_size = local_dummy_indices.size(); // Any local dummy indices at all? if (local_size == 0) @@ -570,64 +543,151 @@ 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 + size_t 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()) { + if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(op0_is_equal(), *it)) == global_dummy_indices.end()) { global_dummy_indices.push_back(*it); global_size++; remaining--; } 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.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()), subs_options::no_pattern); + } +} + +/** 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 + ), subs_options::no_pattern); + 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(), subs_options::no_pattern); + 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) { // 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); + bool non_commutative = is_exactly_a(e); // Collect factors in an exvector, store squares twice exvector v; v.reserve(e.nops() * 2); - if (is_ex_exactly_of_type(e, power)) { + if (is_exactly_a(e)) { // 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(f) && 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)) { + } else if (is_exactly_a(f)) { // Noncommutative factor found, split it as well non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later - for (int j=0; j(*it1)) continue; bool first_noncommutative = (it1->return_type() != return_types::commutative); @@ -649,12 +709,12 @@ try_again: // Indexed factor found, get free indices and look for contraction // candidates exvector free1, dummy1; - find_free_and_dummy(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end(), free1, dummy1); + find_free_and_dummy(ex_to(*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)) + if (!is_a(*it2)) continue; bool second_noncommutative = (it2->return_type() != return_types::commutative); @@ -662,54 +722,62 @@ 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) + size_t 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 (sp.is_defined(*it1, *it2)) { - *it1 = sp.evaluate(*it1, *it2); - *it2 = _ex1(); - goto contraction_done; + if (free.empty()) { + + // Find minimal dimension of all indices of both factors + exvector::const_iterator dit = ex_to(*it1).seq.begin() + 1, ditend = ex_to(*it1).seq.end(); + ex dim = ex_to(*dit).get_dim(); + ++dit; + for (; dit != ditend; ++dit) { + dim = minimal_dim(dim, ex_to(*dit).get_dim()); } - } + dit = ex_to(*it2).seq.begin() + 1; + ditend = ex_to(*it2).seq.end(); + for (; dit != ditend; ++dit) { + dim = minimal_dim(dim, ex_to(*dit).get_dim()); + } + + // User-defined scalar product? + if (sp.is_defined(*it1, *it2, dim)) { - // 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(); + // Yes, substitute it + *it1 = sp.evaluate(*it1, *it2, dim); + *it2 = _ex1; + goto contraction_done; + } } // 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: 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)) { + || is_exactly_a(*it1) || is_exactly_a(*it2) + || is_exactly_a(*it1) || is_exactly_a(*it2) + || is_exactly_a(*it1) || is_exactly_a(*it2)) { // 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 + // eval_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); @@ -727,39 +795,132 @@ 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)) { + if (is_a(*it1)) { 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_a(*it1)) + 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) { + exvector dummy_syms; + dummy_syms.reserve(local_dummy_indices.size()); + for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it) + dummy_syms.push_back(it->op(0)); + if (symmetrize(r, dummy_syms).is_zero()) { + free_indices.clear(); + return _ex0; + } + } + // Dummy index renaming r = rename_dummy_indices(r, dummy_indices, local_dummy_indices); // Product of indexed object with a scalar? - if (is_ex_exactly_of_type(r, mul) && r.nops() == 2 - && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed)) - return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1))); + if (is_exactly_a(r) && r.nops() == 2 + && is_exactly_a(r.op(1)) && is_a(r.op(0))) + return ex_to(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to(r.op(1))); else return r; } +/** This structure stores the original and symmetrized versions of terms + * obtained during the simplification of sums. */ +class terminfo { +public: + terminfo(const ex & orig_, const ex & symm_) : orig(orig_), symm(symm_) {} + + ex orig; /**< original term */ + ex symm; /**< symmtrized term */ +}; + +class terminfo_is_less { +public: + bool operator() (const terminfo & ti1, const terminfo & ti2) const + { + return (ti1.symm.compare(ti2.symm) < 0); + } +}; + +/** This structure stores the individual symmetrized terms obtained during + * the simplification of sums. */ +class symminfo { +public: + symminfo() : num(0) {} + + symminfo(const ex & symmterm_, const ex & orig_, size_t num_) : orig(orig_), num(num_) + { + if (is_exactly_a(symmterm_) && is_exactly_a(symmterm_.op(symmterm_.nops()-1))) { + coeff = symmterm_.op(symmterm_.nops()-1); + symmterm = symmterm_ / coeff; + } else { + coeff = 1; + symmterm = symmterm_; + } + } + + ex symmterm; /**< symmetrized term */ + ex coeff; /**< coefficient of symmetrized term */ + ex orig; /**< original term */ + size_t num; /**< how many symmetrized terms resulted from the original term */ +}; + +class symminfo_is_less_by_symmterm { +public: + bool operator() (const symminfo & si1, const symminfo & si2) const + { + return (si1.symmterm.compare(si2.symmterm) < 0); + } +}; + +class symminfo_is_less_by_orig { +public: + bool operator() (const symminfo & si1, const symminfo & si2) const + { + return (si1.orig.compare(si2.orig) < 0); + } +}; + /** Simplify indexed expression, return list of free indices. */ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp) { @@ -767,22 +928,38 @@ 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 - if (is_ex_of_type(e_expanded, indexed)) { - const indexed &i = ex_to_indexed(e_expanded); + // and perform dummy index renaming/repositioning + if (is_a(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)) { + if (is_exactly_a(e_expanded)) { bool first = true; - ex sum = _ex0(); + ex sum; free_indices.clear(); - for (unsigned i=0; iadd_indexed(sum, term); + if (!indices_consistent(free_indices, free_indices_of_term)) { + std::ostringstream s; + s << "simplify_indexed: inconsistent indices in sum: "; + s << exprseq(free_indices) << " vs. " << exprseq(free_indices_of_term); + throw (std::runtime_error(s.str())); + } + if (is_a(sum) && is_a(term)) + sum = ex_to(sum.op(0)).add_indexed(sum, term); else sum += term; } } } - return sum; + // If the sum turns out to be zero, we are finished + if (sum.is_zero()) { + free_indices.clear(); + return sum; + } + + // More than one term and more than one dummy index? + size_t num_terms_orig = (is_exactly_a(sum) ? sum.nops() : 1); + if (num_terms_orig < 2 || dummy_indices.size() < 2) + return sum; + + // Yes, construct vector of all dummy index symbols + exvector dummy_syms; + dummy_syms.reserve(dummy_indices.size()); + for (exvector::const_iterator it = dummy_indices.begin(); it != dummy_indices.end(); ++it) + dummy_syms.push_back(it->op(0)); + + // Chop the sum into terms and symmetrize each one over the dummy + // indices + std::vector terms; + for (size_t i=0; i terms_pass2; + for (std::vector::const_iterator i=terms.begin(); i!=terms.end(); ) { + size_t num = 1; + std::vector::const_iterator j = i + 1; + while (j != terms.end() && j->symm == i->symm) { + num++; + j++; + } + terms_pass2.push_back(terminfo(i->orig * num, i->symm * num)); + i = j; + } + + // If there is only one term left, we are finished + if (terms_pass2.size() == 1) + return terms_pass2[0].orig; + + // Chop the symmetrized terms into subterms + std::vector sy; + for (std::vector::const_iterator i=terms_pass2.begin(); i!=terms_pass2.end(); ++i) { + if (is_exactly_a(i->symm)) { + size_t num = i->symm.nops(); + for (size_t j=0; jsymm.op(j), i->orig, num)); + } else + sy.push_back(symminfo(i->symm, i->orig, 1)); + } + + // Sort by symmetrized subterms + std::sort(sy.begin(), sy.end(), symminfo_is_less_by_symmterm()); + + // Combine equal symmetrized subterms + std::vector sy_pass2; + exvector result; + for (std::vector::const_iterator i=sy.begin(); i!=sy.end(); ) { + + // Combine equal terms + std::vector::const_iterator j = i + 1; + if (j != sy.end() && j->symmterm == i->symmterm) { + + // More than one term, collect the coefficients + ex coeff = i->coeff; + while (j != sy.end() && j->symmterm == i->symmterm) { + coeff += j->coeff; + j++; + } + + // Add combined term to result + if (!coeff.is_zero()) + result.push_back(coeff * i->symmterm); + + } else { + + // Single term, store for second pass + sy_pass2.push_back(*i); + } + + i = j; + } + + // Were there any remaining terms that didn't get combined? + if (sy_pass2.size() > 0) { + + // Yes, sort by their original terms + std::sort(sy_pass2.begin(), sy_pass2.end(), symminfo_is_less_by_orig()); + + for (std::vector::const_iterator i=sy_pass2.begin(); i!=sy_pass2.end(); ) { + + // How many symmetrized terms of this original term are left? + size_t num = 1; + std::vector::const_iterator j = i + 1; + while (j != sy_pass2.end() && j->orig == i->orig) { + num++; + j++; + } + + if (num == i->num) { + + // All terms left, then add the original term to the result + result.push_back(i->orig); + + } else { + + // Some terms were combined with others, add up the remaining symmetrized terms + std::vector::const_iterator k; + for (k=i; k!=j; k++) + result.push_back(k->coeff * k->symmterm); + } + + i = j; + } + } + + // Add all resulting terms + ex sum_symm = (new add(result))->setflag(status_flags::dynallocated); + if (sum_symm.is_zero()) + free_indices.clear(); + return sum_symm; } // 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()))) + if (is_exactly_a(e_expanded) + || is_exactly_a(e_expanded) + || (is_exactly_a(e_expanded) && is_a(e_expanded.op(0)) && e_expanded.op(1).is_equal(_ex2))) return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp); // Cannot do anything @@ -815,90 +1124,148 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi 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(unsigned options) const { exvector free_indices, dummy_indices; scalar_products sp; - return simplify_indexed(e, free_indices, dummy_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, unsigned options) const { exvector free_indices, dummy_indices; - return simplify_indexed(e, free_indices, dummy_indices, sp); + return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp); +} + +/** Symmetrize expression over its free indices. */ +ex ex::symmetrize() const +{ + return GiNaC::symmetrize(*this, get_free_indices()); } -ex symmetrize(const ex & e) +/** Antisymmetrize expression over its free indices. */ +ex ex::antisymmetrize() const { - return symmetrize(e, e.get_free_indices()); + return GiNaC::antisymmetrize(*this, get_free_indices()); } -ex antisymmetrize(const ex & e) +/** Symmetrize expression by cyclic permutation over its free indices. */ +ex ex::symmetrize_cyclic() const { - return antisymmetrize(e, e.get_free_indices()); + return GiNaC::symmetrize_cyclic(*this, get_free_indices()); } ////////// // helper classes ////////// +spmapkey::spmapkey(const ex & v1_, const ex & v2_, const ex & dim_) : dim(dim_) +{ + // If indexed, extract base objects + ex s1 = is_a(v1_) ? v1_.op(0) : v1_; + ex s2 = is_a(v2_) ? v2_.op(0) : v2_; + + // Enforce canonical order in pair + if (s1.compare(s2) > 0) { + v1 = s2; + v2 = s1; + } else { + v1 = s1; + v2 = s2; + } +} + +bool spmapkey::operator==(const spmapkey &other) const +{ + if (!v1.is_equal(other.v1)) + return false; + if (!v2.is_equal(other.v2)) + return false; + if (is_a(dim) || is_a(other.dim)) + return true; + else + return dim.is_equal(other.dim); +} + +bool spmapkey::operator<(const spmapkey &other) const +{ + int cmp = v1.compare(other.v1); + if (cmp) + return cmp < 0; + cmp = v2.compare(other.v2); + if (cmp) + return cmp < 0; + + // Objects are equal, now check dimensions + if (is_a(dim) || is_a(other.dim)) + return false; + else + return dim.compare(other.dim) < 0; +} + +void spmapkey::debugprint() const +{ + std::cerr << "(" << v1 << "," << v2 << "," << dim << ")"; +} + void scalar_products::add(const ex & v1, const ex & v2, const ex & sp) { - spm[make_key(v1, v2)] = sp; + spm[spmapkey(v1, v2)] = sp; } -void scalar_products::add_vectors(const lst & l) +void scalar_products::add(const ex & v1, const ex & v2, const ex & dim, const ex & sp) +{ + spm[spmapkey(v1, v2, dim)] = sp; +} + +void scalar_products::add_vectors(const lst & l, const ex & dim) { // Add all possible pairs of products - unsigned num = l.nops(); - for (unsigned i=0; isecond; + return spm.find(spmapkey(v1, v2, dim))->second; } -void scalar_products::debugprint(void) const +void scalar_products::debugprint() 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; - std::cerr << "item key=(" << k.first << "," << k.second; - std::cerr << "), value=" << cit->second << std::endl; + spmap::const_iterator i = spm.begin(), end = spm.end(); + while (i != end) { + const spmapkey & k = i->first; + std::cerr << "item key="; + k.debugprint(); + 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); -} - } // namespace GiNaC