X-Git-Url: https://ginac.de/ginac.git//ginac.git?a=blobdiff_plain;ds=inline;f=ginac%2Findexed.cpp;h=12561cf1d88f0557ef41c2f3e486a590361e80db;hb=09f37bdbd46f469b3a8a902a43d0f795c41a89bf;hp=acbf7d489967445a4d1e2d52f79cf5d91f06d850;hpb=1c9720626245312534c8311b47a8749dd2e18526;p=ginac.git diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index acbf7d48..12561cf1 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" @@ -29,30 +29,30 @@ #include "mul.h" #include "ncmul.h" #include "power.h" +#include "symmetry.h" +#include "operators.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) @@ -61,97 +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(); } ////////// @@ -160,61 +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 ? ")}" : ")"); } } @@ -225,9 +214,9 @@ 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)); } }; @@ -243,129 +232,66 @@ 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)); + if (is_exactly_a(base) && is_exactly_a(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); -} - -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 { GINAC_ASSERT(seq.size() > 0); - if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) { + if ((options & expand_options::expand_indexed) && is_exactly_a(seq[0])) { // 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_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 << "}"; + c.s << "}{}"; covariant = cur_covariant; if (covariant) c.s << "_{"; @@ -428,18 +355,32 @@ 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(); 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; } ////////// @@ -558,8 +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) @@ -569,6 +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) { @@ -579,25 +521,35 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex } it++; } - } - // Replace index symbols in expression - 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 - return e.subs(local_syms, global_syms); + else { + while (global_uniq.size() > local_uniq.size()) + global_uniq.pop_back(); + return e.subs(lst(local_uniq), lst(global_uniq)); + } } /** Simplify product of indexed expressions (commutative, noncommutative and @@ -606,27 +558,27 @@ ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & du { // 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); @@ -648,12 +600,12 @@ 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); @@ -661,56 +613,47 @@ 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: 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 // the product - ex r = (non_commutative ? ex(ncmul(v)) : ex(mul(v))); + ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v))); return simplify_indexed(r, free_indices, dummy_indices, sp); } @@ -729,9 +672,9 @@ contraction_done: it1 = v.begin(); itend = v.end(); while (it1 != itend) { 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(); @@ -744,17 +687,30 @@ contraction_done: ex r; if (something_changed) - r = non_commutative ? ex(ncmul(v)) : ex(mul(v)); + 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))); + 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; } @@ -767,8 +723,8 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi // 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); + if (is_a(e_expanded)) { + 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); return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices); @@ -776,9 +732,9 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi // 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 = _ex0; free_indices.clear(); for (unsigned i=0; iadd_indexed(sum, term); + if (is_a(sum) && is_a(term)) + sum = ex_to(sum.op(0)).add_indexed(sum, term); else sum += term; } @@ -804,9 +760,9 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi } // 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 @@ -814,17 +770,47 @@ 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(void) 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) 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(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()); } ////////// @@ -869,10 +855,12 @@ 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; } } @@ -880,8 +868,8 @@ void scalar_products::debugprint(void) const 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; + 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)