>From 0a58e91cc7922036f3a121eb2204df54ef726bac Mon Sep 17 00:00:00 2001 From: "Vladimir V. Kisil" Date: Fri, 10 Apr 2020 07:22:57 +0100 Subject: [PATCH] Make a stronger normalisation for expressions with exponents If several exponents have arguments different by a rational number factors they are replaced by monomials of the same variable. Signed-off-by: Vladimir V. Kisil --- ginac/add.h | 2 +- ginac/basic.h | 2 +- ginac/mul.h | 2 +- ginac/normal.cpp | 153 +++++++++++++++++++++++++++++++++++----------- ginac/numeric.h | 2 +- ginac/power.h | 2 +- ginac/pseries.h | 2 +- ginac/structure.h | 2 +- ginac/symbol.h | 2 +- 9 files changed, 127 insertions(+), 42 deletions(-) diff --git a/ginac/add.h b/ginac/add.h index 3e07b2a6..f00facfa 100644 --- a/ginac/add.h +++ b/ginac/add.h @@ -55,7 +55,7 @@ public: ex eval() const override; ex evalm() const override; ex series(const relational & r, int order, unsigned options = 0) const override; - ex normal(exmap & repl, exmap & rev_lookup) const override; + ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const override; numeric integer_content() const override; ex smod(const numeric &xi) const override; numeric max_coefficient() const override; diff --git a/ginac/basic.h b/ginac/basic.h index fd6a7471..8bfdf3a6 100644 --- a/ginac/basic.h +++ b/ginac/basic.h @@ -200,7 +200,7 @@ public: virtual ex series(const relational & r, int order, unsigned options = 0) const; // rational functions - virtual ex normal(exmap & repl, exmap & rev_lookup) const; + virtual ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const; virtual ex to_rational(exmap & repl) const; virtual ex to_polynomial(exmap & repl) const; diff --git a/ginac/mul.h b/ginac/mul.h index 60d56e02..cdaef5fe 100644 --- a/ginac/mul.h +++ b/ginac/mul.h @@ -61,7 +61,7 @@ public: ex imag_part() const override; ex evalm() const override; ex series(const relational & s, int order, unsigned options = 0) const override; - ex normal(exmap & repl, exmap & rev_lookup) const override; + ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const override; numeric integer_content() const override; ex smod(const numeric &xi) const override; numeric max_coefficient() const override; diff --git a/ginac/normal.cpp b/ginac/normal.cpp index a80e1508..ee8f781d 100644 --- a/ginac/normal.cpp +++ b/ginac/normal.cpp @@ -2007,8 +2007,12 @@ ex sqrfree_parfrac(const ex & a, const symbol & x) /** Create a symbol for replacing the expression "e" (or return a previously * assigned symbol). The symbol and expression are appended to repl, for * a later application of subs(). + * An entry in the replacement table repl can be changed in some case. + * If it was altered, we need to provide the modifier for the previously build expression. + * The modifier is a list, because those substitutions need to be done in in the + * incremental order. * @see ex::normal */ -static ex replace_with_symbol(const ex & e, exmap & repl, exmap & rev_lookup) +static ex replace_with_symbol(const ex & e, exmap & repl, exmap & rev_lookup, lst & modifier) { // Since the repl contains replaced expressions we should search for them ex e_replaced = e.subs(repl, subs_options::no_pattern); @@ -2018,6 +2022,38 @@ static ex replace_with_symbol(const ex & e, exmap & repl, exmap & rev_lookup) if (it != rev_lookup.end()) return it->second; + // We treat powers and the exponent functions differently because + // they can be rationalised more efficiently + if (is_a(e_replaced) && ex_to(e_replaced).get_name() == "exp") { + for (auto & it : repl) { + if (is_a(it.second) && ex_to(it.second).get_name() == "exp") { + ex ratio = normal(e_replaced.op(0)/it.second.op(0)) ; + if (is_a(ratio) && ex_to(ratio).is_rational()) { + // Different exponents can be treated as powers of the same basic equation + if (ex_to(ratio).is_integer()) { + // If ratio is an integer then this is simply the power of the existing symbol. + // std::clog << e_replaced << " is a " << ratio << " power of " << it.first << std::endl; + return pow(it.first, ratio); + } else { + // otherwise we need to give the replacement pattern to change + // the previous expression... + ex es = dynallocate(); + modifier.append(it.first == power(es, denom(ratio))); + // ... and modify the replacement tables + rev_lookup.erase(it.second); + rev_lookup.insert(std::make_pair(exp(e_replaced.op(0)/numer(ratio)), es)); + repl.erase(it.first); + repl.insert(std::make_pair(es, exp(e_replaced.op(0)/numer(ratio)))); + // std::clog << e_replaced << " is a " << numer(ratio) << " power and " + // << it.first << " is a " << denom(ratio) << " power of the common base " + // << exp(e_replaced.op(0)/numer(ratio)) << std::endl; + return power(es, numer(ratio)); + } + } + } + } + } + // Otherwise create new symbol and add to list, taking care that the // replacement expression doesn't itself contain symbols from repl, // because subs() is not recursive @@ -2059,19 +2095,27 @@ struct normal_map_function : public map_function { /** Default implementation of ex::normal(). It normalizes the children and * replaces the object with a temporary symbol. * @see ex::normal */ -ex basic::normal(exmap & repl, exmap & rev_lookup) const +ex basic::normal(exmap & repl, exmap & rev_lookup, lst & modifier) const { if (nops() == 0) - return dynallocate({replace_with_symbol(*this, repl, rev_lookup), _ex1}); + return dynallocate({replace_with_symbol(*this, repl, rev_lookup, modifier), _ex1}); normal_map_function map_normal; - return dynallocate({replace_with_symbol(map(map_normal), repl, rev_lookup), _ex1}); + int nmod = modifier.nops(); // To watch new modifiers to the replacement list + lst result = dynallocate({replace_with_symbol(map(map_normal), repl, rev_lookup, modifier), _ex1}); + for (int imod = nmod; imod < modifier.nops(); ++imod) { + exmap this_repl; + this_repl.insert(std::make_pair(modifier.op(imod).op(0), modifier.op(imod).op(1))); + result = ex_to(result.subs(this_repl, subs_options::no_pattern)); + } + + return result; } /** Implementation of ex::normal() for symbols. This returns the unmodified symbol. * @see ex::normal */ -ex symbol::normal(exmap & repl, exmap & rev_lookup) const +ex symbol::normal(exmap & repl, exmap & rev_lookup, lst & modifier) const { return dynallocate({*this, _ex1}); } @@ -2081,19 +2125,19 @@ ex symbol::normal(exmap & repl, exmap & rev_lookup) const * into re+I*im and replaces I and non-rational real numbers with a temporary * symbol. * @see ex::normal */ -ex numeric::normal(exmap & repl, exmap & rev_lookup) const +ex numeric::normal(exmap & repl, exmap & rev_lookup, lst & modifier) const { numeric num = numer(); ex numex = num; if (num.is_real()) { if (!num.is_integer()) - numex = replace_with_symbol(numex, repl, rev_lookup); + numex = replace_with_symbol(numex, repl, rev_lookup, modifier); } else { // complex numeric re = num.real(), im = num.imag(); - ex re_ex = re.is_rational() ? re : replace_with_symbol(re, repl, rev_lookup); - ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl, rev_lookup); - numex = re_ex + im_ex * replace_with_symbol(I, repl, rev_lookup); + ex re_ex = re.is_rational() ? re : replace_with_symbol(re, repl, rev_lookup, modifier); + ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl, rev_lookup, modifier); + numex = re_ex + im_ex * replace_with_symbol(I, repl, rev_lookup, modifier); } // Denominator is always a real integer (see numeric::denom()) @@ -2165,18 +2209,19 @@ static ex frac_cancel(const ex &n, const ex &d) /** Implementation of ex::normal() for a sum. It expands terms and performs * fractional addition. * @see ex::normal */ -ex add::normal(exmap & repl, exmap & rev_lookup) const +ex add::normal(exmap & repl, exmap & rev_lookup, lst & modifier) const { // Normalize children and split each one into numerator and denominator exvector nums, dens; nums.reserve(seq.size()+1); dens.reserve(seq.size()+1); + int nmod = modifier.nops(); // To watch new modifiers to the replacement list for (auto & it : seq) { - ex n = ex_to(recombine_pair_to_ex(it)).normal(repl, rev_lookup); + ex n = ex_to(recombine_pair_to_ex(it)).normal(repl, rev_lookup, modifier); nums.push_back(n.op(0)); dens.push_back(n.op(1)); } - ex n = ex_to(overall_coeff).normal(repl, rev_lookup); + ex n = ex_to(overall_coeff).normal(repl, rev_lookup, modifier); nums.push_back(n.op(0)); dens.push_back(n.op(1)); GINAC_ASSERT(nums.size() == dens.size()); @@ -2189,6 +2234,17 @@ ex add::normal(exmap & repl, exmap & rev_lookup) const auto num_it = nums.begin(), num_itend = nums.end(); auto den_it = dens.begin(), den_itend = dens.end(); //std::clog << " num = " << *num_it << ", den = " << *den_it << std::endl; + for (int imod = nmod; imod < modifier.nops(); ++imod) + while (num_it != num_itend) { + *num_it = num_it->subs(modifier.op(imod), subs_options::no_pattern); + ++num_it; + *den_it = den_it->subs(modifier.op(imod), subs_options::no_pattern); + ++den_it; + } + + num_it = nums.begin(); + den_it = dens.begin(); + ex num = *num_it++, den = *den_it++; while (num_it != num_itend) { //std::clog << " num = " << *num_it << ", den = " << *den_it << std::endl; @@ -2217,35 +2273,45 @@ ex add::normal(exmap & repl, exmap & rev_lookup) const /** Implementation of ex::normal() for a product. It cancels common factors * from fractions. * @see ex::normal() */ -ex mul::normal(exmap & repl, exmap & rev_lookup) const +ex mul::normal(exmap & repl, exmap & rev_lookup, lst & modifier) const { // Normalize children, separate into numerator and denominator exvector num; num.reserve(seq.size()); exvector den; den.reserve(seq.size()); ex n; + int nmod = modifier.nops(); // To watch new modifiers to the replacement list for (auto & it : seq) { - n = ex_to(recombine_pair_to_ex(it)).normal(repl, rev_lookup); + n = ex_to(recombine_pair_to_ex(it)).normal(repl, rev_lookup, modifier); num.push_back(n.op(0)); den.push_back(n.op(1)); } - n = ex_to(overall_coeff).normal(repl, rev_lookup); + n = ex_to(overall_coeff).normal(repl, rev_lookup, modifier); num.push_back(n.op(0)); den.push_back(n.op(1)); + auto num_it = num.begin(), num_itend = num.end(); + auto den_it = den.begin(), den_itend = den.end(); + for (int imod = nmod; imod < modifier.nops(); ++imod) + while (num_it != num_itend) { + *num_it = num_it->subs(modifier.op(imod), subs_options::no_pattern); + ++num_it; + *den_it = den_it->subs(modifier.op(imod), subs_options::no_pattern); + ++den_it; + } // Perform fraction cancellation return frac_cancel(dynallocate(num), dynallocate(den)); } -/** Implementation of ex::normal([B) for powers. It normalizes the basis, +/** Implementation of ex::normal() for powers. It normalizes the basis, * distributes integer exponents to numerator and denominator, and replaces * non-integer powers by temporary symbols. * @see ex::normal */ -ex power::normal(exmap & repl, exmap & rev_lookup) const +ex power::normal(exmap & repl, exmap & rev_lookup, lst & modifier) const { // Normalize basis and exponent (exponent gets reassembled) - ex n_basis = ex_to(basis).normal(repl, rev_lookup); - ex n_exponent = ex_to(exponent).normal(repl, rev_lookup); + ex n_basis = ex_to(basis).normal(repl, rev_lookup, modifier); + ex n_exponent = ex_to(exponent).normal(repl, rev_lookup, modifier); n_exponent = n_exponent.op(0) / n_exponent.op(1); if (n_exponent.info(info_flags::integer)) { @@ -2266,32 +2332,32 @@ ex power::normal(exmap & repl, exmap & rev_lookup) const if (n_exponent.info(info_flags::positive)) { // (a/b)^x -> {sym((a/b)^x), 1} - return dynallocate({replace_with_symbol(pow(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1}); + return dynallocate({replace_with_symbol(pow(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup, modifier), _ex1}); } else if (n_exponent.info(info_flags::negative)) { if (n_basis.op(1).is_equal(_ex1)) { // a^-x -> {1, sym(a^x)} - return dynallocate({_ex1, replace_with_symbol(pow(n_basis.op(0), -n_exponent), repl, rev_lookup)}); + return dynallocate({_ex1, replace_with_symbol(pow(n_basis.op(0), -n_exponent), repl, rev_lookup, modifier)}); } else { // (a/b)^-x -> {sym((b/a)^x), 1} - return dynallocate({replace_with_symbol(pow(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup), _ex1}); + return dynallocate({replace_with_symbol(pow(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup, modifier), _ex1}); } } } // (a/b)^x -> {sym((a/b)^x, 1} - return dynallocate({replace_with_symbol(pow(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1}); + return dynallocate({replace_with_symbol(pow(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup, modifier), _ex1}); } /** Implementation of ex::normal() for pseries. It normalizes each coefficient * and replaces the series by a temporary symbol. * @see ex::normal */ -ex pseries::normal(exmap & repl, exmap & rev_lookup) const +ex pseries::normal(exmap & repl, exmap & rev_lookup, lst & modifier) const { epvector newseq; for (auto & it : seq) { @@ -2300,7 +2366,7 @@ ex pseries::normal(exmap & repl, exmap & rev_lookup) const newseq.push_back(expair(restexp, it.coeff)); } ex n = pseries(relational(var,point), std::move(newseq)); - return dynallocate({replace_with_symbol(n, repl, rev_lookup), _ex1}); + return dynallocate({replace_with_symbol(n, repl, rev_lookup, modifier), _ex1}); } @@ -2318,13 +2384,17 @@ ex pseries::normal(exmap & repl, exmap & rev_lookup) const ex ex::normal() const { exmap repl, rev_lookup; + lst modifier; - ex e = bp->normal(repl, rev_lookup); + ex e = bp->normal(repl, rev_lookup, modifier); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols - if (!repl.empty()) + if (!repl.empty()) { + for(int i=0; i < modifier.nops(); ++i) + e = e.subs(modifier.op(i), subs_options::no_pattern); e = e.subs(repl, subs_options::no_pattern); + } // Convert {numerator, denominator} form back to fraction return e.op(0) / e.op(1); @@ -2339,15 +2409,20 @@ ex ex::normal() const ex ex::numer() const { exmap repl, rev_lookup; + lst modifier; - ex e = bp->normal(repl, rev_lookup); + ex e = bp->normal(repl, rev_lookup, modifier); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols if (repl.empty()) return e.op(0); - else + else { + for(int i=0; i < modifier.nops(); ++i) + e = e.subs(modifier.op(i), subs_options::no_pattern); + return e.op(0).subs(repl, subs_options::no_pattern); + } } /** Get denominator of an expression. If the expression is not of the normal @@ -2359,15 +2434,20 @@ ex ex::numer() const ex ex::denom() const { exmap repl, rev_lookup; + lst modifier; - ex e = bp->normal(repl, rev_lookup); + ex e = bp->normal(repl, rev_lookup, modifier); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols if (repl.empty()) return e.op(1); - else + else { + for(int i=0; i < modifier.nops(); ++i) + e = e.subs(modifier.op(i), subs_options::no_pattern); + return e.op(1).subs(repl, subs_options::no_pattern); + } } /** Get numerator and denominator of an expression. If the expression is not @@ -2379,15 +2459,20 @@ ex ex::denom() const ex ex::numer_denom() const { exmap repl, rev_lookup; + lst modifier; - ex e = bp->normal(repl, rev_lookup); + ex e = bp->normal(repl, rev_lookup, modifier); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols if (repl.empty()) return e; - else + else { + for(int i=0; i < modifier.nops(); ++i) + e = e.subs(modifier.op(i), subs_options::no_pattern); + return e.subs(repl, subs_options::no_pattern); + } } diff --git a/ginac/numeric.h b/ginac/numeric.h index a2933342..975da7a0 100644 --- a/ginac/numeric.h +++ b/ginac/numeric.h @@ -108,7 +108,7 @@ public: ex eval() const override; ex evalf() const override; ex subs(const exmap & m, unsigned options = 0) const override { return subs_one_level(m, options); } // overwrites basic::subs() for performance reasons - ex normal(exmap & repl, exmap & rev_lookup) const override; + ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const override; ex to_rational(exmap & repl) const override; ex to_polynomial(exmap & repl) const override; numeric integer_content() const override; diff --git a/ginac/power.h b/ginac/power.h index 5ca4fbe1..f431b7c2 100644 --- a/ginac/power.h +++ b/ginac/power.h @@ -65,7 +65,7 @@ public: ex series(const relational & s, int order, unsigned options = 0) const override; ex subs(const exmap & m, unsigned options = 0) const override; bool has(const ex & other, unsigned options = 0) const override; - ex normal(exmap & repl, exmap & rev_lookup) const override; + ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const override; ex to_rational(exmap & repl) const override; ex to_polynomial(exmap & repl) const override; ex conjugate() const override; diff --git a/ginac/pseries.h b/ginac/pseries.h index 9300662f..2857bb7e 100644 --- a/ginac/pseries.h +++ b/ginac/pseries.h @@ -54,7 +54,7 @@ public: ex evalf() const override; ex series(const relational & r, int order, unsigned options = 0) const override; ex subs(const exmap & m, unsigned options = 0) const override; - ex normal(exmap & repl, exmap & rev_lookup) const override; + ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const override; ex expand(unsigned options = 0) const override; ex conjugate() const override; ex real_part() const override; diff --git a/ginac/structure.h b/ginac/structure.h index a6b737ea..edd2c048 100644 --- a/ginac/structure.h +++ b/ginac/structure.h @@ -178,7 +178,7 @@ public: ex series(const relational & r, int order, unsigned options = 0) const override { return inherited::series(r, order, options); } // rational functions - ex normal(exmap & repl, exmap & rev_lookup) const override { return inherited::normal(repl, rev_lookup); } + ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const override { return inherited::normal(repl, rev_lookup, modifier); } ex to_rational(exmap & repl) const override { return inherited::to_rational(repl); } ex to_polynomial(exmap & repl) const override { return inherited::to_polynomial(repl); } diff --git a/ginac/symbol.h b/ginac/symbol.h index 5cb84c25..c7535190 100644 --- a/ginac/symbol.h +++ b/ginac/symbol.h @@ -50,7 +50,7 @@ public: ex evalf() const override { return *this; } // overwrites basic::evalf() for performance reasons ex series(const relational & s, int order, unsigned options = 0) const override; ex subs(const exmap & m, unsigned options = 0) const override { return subs_one_level(m, options); } // overwrites basic::subs() for performance reasons - ex normal(exmap & repl, exmap & rev_lookup) const override; + ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const override; ex to_rational(exmap & repl) const override; ex to_polynomial(exmap & repl) const override; ex conjugate() const override; -- 2.25.1