From: Christian Bauer Date: Fri, 24 May 2002 19:55:35 +0000 (+0000) Subject: fixed a bug in the raising/lowering of dummy indices and extended it to work X-Git-Tag: release_1-0-9~6 X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=9f015041142625abf6645b3ea39c62b59a5f442c;hp=2e3eaaf5665eba012287220683995817cb371a13 fixed a bug in the raising/lowering of dummy indices and extended it to work on single indexed objects also --- diff --git a/NEWS b/NEWS index 67f36b99..36a5412d 100644 --- a/NEWS +++ b/NEWS @@ -3,7 +3,7 @@ This file records noteworthy changes. 1.0.9 () * simplify_indexed() now raises/lowers dummy indices to canonicalize the index variance. This allows some simplifications that weren't possible before, - like eps~a.b~c~d*X.a*X~b -> 0. + like eps~a.b~c~d*X.a*X~b -> 0 and X.a~a-X~a.a -> 0. 1.0.8 (31 March 2002) * Improvements in memory usage of the expand() methods. diff --git a/check/exam_indexed.cpp b/check/exam_indexed.cpp index 4ba1794b..a8c7cbd6 100644 --- a/check/exam_indexed.cpp +++ b/check/exam_indexed.cpp @@ -337,7 +337,7 @@ static unsigned spinor_check(void) static unsigned dummy_check(void) { - // check dummy index renaming + // check dummy index renaming/repositioning unsigned result = 0; @@ -356,6 +356,15 @@ static unsigned dummy_check(void) e = indexed(p, mu, mu.toggle_variance()) - indexed(p, nu, nu.toggle_variance()); result += check_equal_simplify(e, 0); + e = indexed(p, mu.toggle_variance(), nu, mu) * indexed(q, i) + - indexed(p, mu, nu, mu.toggle_variance()) * indexed(q, i); + result += check_equal_simplify(e, 0); + + e = indexed(p, mu, mu.toggle_variance()) - indexed(p, nu.toggle_variance(), nu); + result += check_equal_simplify(e, 0); + e = indexed(p, mu.toggle_variance(), mu) - indexed(p, nu, nu.toggle_variance()); + result += check_equal_simplify(e, 0); + return result; } diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp index eec7b11f..dcd6d951 100644 --- a/ginac/indexed.cpp +++ b/ginac/indexed.cpp @@ -493,7 +493,7 @@ 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 @@ -554,6 +554,72 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex } } +/** 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 @@ -695,10 +761,7 @@ contraction_done: // Filter out the dummy indices with variance exvector variant_dummy_indices; - for (it1 = local_dummy_indices.begin(), itend = local_dummy_indices.end(); it1 != itend; ++it1) { - if (is_exactly_a(*it1)) - variant_dummy_indices.push_back(*it1); - } + find_variant_indices(local_dummy_indices, variant_dummy_indices); // Any indices with variance present at all? if (!variant_dummy_indices.empty()) { @@ -715,46 +778,8 @@ contraction_done: if (!is_ex_of_type(*it1, indexed)) continue; - ex new_it1; - bool it1_dirty = false; // It this is true, then new_it1 holds a new value for *it1 - - // If a dummy index is encountered for the first time in the - // product, pull it up, otherwise, pull it down - exvector::iterator it2, it2end; - for (it2 = const_cast(ex_to(*it1)).seq.begin(), it2end = const_cast(ex_to(*it1)).seq.end(); 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()) { - new_it1 = (it1_dirty ? new_it1 : *it1).subs(*it2 == ex_to(*it2).toggle_variance()); - it1_dirty = true; - something_changed = true; - } - 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()) { - new_it1 = (it1_dirty ? new_it1 : *it1).subs(*it2 == ex_to(*it2).toggle_variance()); - it1_dirty = true; - something_changed = true; - } - goto next_index; - } - } - -next_index: ; - } - - if (it1_dirty) - *it1 = new_it1; + if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices)) + something_changed = true; } } @@ -795,11 +820,27 @@ 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); } diff --git a/ginac/indexed.h b/ginac/indexed.h index 58c8bbd4..f539444e 100644 --- a/ginac/indexed.h +++ b/ginac/indexed.h @@ -42,6 +42,7 @@ class indexed : public exprseq friend ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp); friend ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp); + friend bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices); // other constructors public: