X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=81230c4d7ff1365822d9831ac6a6c562bc8ecc01;hp=87f53db31ed71c546de02b43a825d02a9cfc39cf;hb=af6809f55c95cf6ea6ef80bd1d19637a06f32e5a;hpb=7bb797bc41e31fe098c94f0b5e57ddbba6cd26b6 diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index 87f53db3..81230c4d 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) 1999-2003 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 @@ -21,6 +21,7 @@ */ #include +#include #include #include "indexed.h" @@ -29,6 +30,7 @@ #include "mul.h" #include "ncmul.h" #include "power.h" +#include "relational.h" #include "symmetry.h" #include "lst.h" #include "print.h" @@ -178,7 +180,7 @@ void indexed::print(const print_context & c, unsigned level) const { 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 @@ -190,21 +192,19 @@ void indexed::print(const print_context & c, unsigned level) const } 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 ? ")}" : ")"); } } @@ -274,24 +274,6 @@ ex indexed::eval(int level) const return ex_to(base).eval_indexed(*this); } -int indexed::degree(const ex & s) const -{ - return is_equal(ex_to(s)) ? 1 : 0; -} - -int indexed::ldegree(const ex & s) const -{ - return is_equal(ex_to(s)) ? 1 : 0; -} - -ex indexed::coeff(const ex & s, int n) const -{ - if (is_equal(ex_to(s))) - return n==1 ? _ex1 : _ex0; - else - return n==0 ? ex(*this) : _ex0; -} - ex indexed::thisexprseq(const exvector & v) const { return indexed(ex_to(symtree), v); @@ -338,7 +320,7 @@ void indexed::printindices(const print_context & c, unsigned level) const exvector::const_iterator it=seq.begin() + 1, itend = seq.end(); - if (is_of_type(c, print_latex)) { + if (is_a(c)) { // TeX output: group by variance bool first = true; @@ -346,9 +328,10 @@ void indexed::printindices(const print_context & c, unsigned level) const while (it != itend) { bool cur_covariant = (is_ex_of_type(*it, varidx) ? ex_to(*it).is_covariant() : true); - if (first || cur_covariant != covariant) { + 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 << "_{"; @@ -405,6 +388,22 @@ ex indexed::derivative(const symbol & s) const // 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) { @@ -412,7 +411,7 @@ 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 @@ -509,7 +508,7 @@ exvector power::get_free_indices(void) const /** Rename dummy indices in an expression. * - * @param e Expression to be worked on + * @param e Expression to work on * @param local_dummy_indices The set of dummy indices that appear in the * expression "e" * @param global_dummy_indices The set of dummy indices that have appeared @@ -532,7 +531,7 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex 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--; @@ -551,7 +550,7 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex for (unsigned i=0; i(*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, exvector & dummy_indices, const scalar_products & sp) @@ -687,8 +760,7 @@ contraction_done: // Find free indices (concatenate them all and call find_free_and_dummy()) // and all dummy indices that appear exvector un, individual_dummy_indices; - it1 = v.begin(); itend = v.end(); - while (it1 != itend) { + for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) { exvector free_indices_of_factor; if (is_ex_of_type(*it1, indexed)) { exvector dummy_indices_of_factor; @@ -697,12 +769,35 @@ contraction_done: } else free_indices_of_factor = it1->get_free_indices(); un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end()); - it1++; } exvector local_dummy_indices; find_free_and_dummy(un, free_indices, local_dummy_indices); local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end()); + // Filter out the dummy indices with variance + exvector variant_dummy_indices; + find_variant_indices(local_dummy_indices, variant_dummy_indices); + + // Any indices with variance present at all? + if (!variant_dummy_indices.empty()) { + + // Yes, bring the product into a canonical order that only depends on + // the base expressions of indexed objects + if (!non_commutative) + std::sort(v.begin(), v.end(), ex_base_is_less()); + + exvector moved_indices; + + // Iterate over all indexed objects in the product + for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) { + if (!is_ex_of_type(*it1, indexed)) + continue; + + if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices)) + something_changed = true; + } + } + ex r; if (something_changed) r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v)); @@ -714,7 +809,7 @@ contraction_done: // zero. This detects things like eps.i.j.k * p.j * p.k = 0. if (local_dummy_indices.size() >= 2) { lst dummy_syms; - for (int i=0; i(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 */ + unsigned 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) { @@ -740,11 +892,27 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi ex e_expanded = e.expand(); // Simplification of single indexed object: just find the free indices - // and perform dummy index renaming + // and perform dummy index renaming/repositioning if (is_ex_of_type(e_expanded, indexed)) { + + // 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); } @@ -752,7 +920,7 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi // free indices in each term if (is_ex_exactly_of_type(e_expanded, add)) { bool first = true; - ex sum = _ex0; + ex sum; free_indices.clear(); for (unsigned i=0; i(sum.op(0)).add_indexed(sum, term); else @@ -774,7 +946,134 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi } } - 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? + int num_terms_orig = (is_exactly_a(sum) ? sum.nops() : 1); + if (num_terms_orig < 2 || dummy_indices.size() < 2) + return sum; + + // Yes, construct list of all dummy index symbols + lst dummy_syms; + for (exvector::size_type i=0; i terms; + for (unsigned i=0; i terms_pass2; + for (std::vector::const_iterator i=terms.begin(); i!=terms.end(); ) { + unsigned 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)) { + unsigned num = i->symm.nops(); + for (unsigned 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? + unsigned 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