X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=3188dd2297790c801c9e3c1b219300353919e92b;hp=db7cef30d8bfe44234658770726822c578271385;hb=55fcb39a1209898ec43694f7e25ffb4572b0c4d1;hpb=619d77d2676f7f1a562fb9fefc0ba6754fe2d750 diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index db7cef30..3188dd22 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -4,7 +4,7 @@ * methods for series expansion. */ /* - * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2008 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 @@ -23,6 +23,7 @@ #include #include +#include #include "pseries.h" #include "add.h" @@ -292,7 +293,7 @@ int pseries::degree(const ex &s) const epvector::const_iterator it = seq.begin(), itend = seq.end(); if (it == itend) return 0; - int max_pow = INT_MIN; + int max_pow = std::numeric_limits::min(); while (it != itend) { int pow = it->rest.degree(s); if (pow > max_pow) @@ -320,7 +321,7 @@ int pseries::ldegree(const ex &s) const epvector::const_iterator it = seq.begin(), itend = seq.end(); if (it == itend) return 0; - int min_pow = INT_MAX; + int min_pow = std::numeric_limits::max(); while (it != itend) { int pow = it->rest.ldegree(s); if (pow < min_pow) @@ -489,6 +490,34 @@ ex pseries::eval_integ() const return *this; } +ex pseries::evalm() const +{ + // evalm each coefficient + epvector newseq; + bool something_changed = false; + for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + if (something_changed) { + ex newcoeff = i->rest.evalm(); + if (!newcoeff.is_zero()) + newseq.push_back(expair(newcoeff, i->coeff)); + } + else { + ex newcoeff = i->rest.evalm(); + if (!are_ex_trivially_equal(newcoeff, i->rest)) { + something_changed = true; + newseq.reserve(seq.size()); + std::copy(seq.begin(), i, std::back_inserter(newseq)); + if (!newcoeff.is_zero()) + newseq.push_back(expair(newcoeff, i->coeff)); + } + } + } + if (something_changed) + return (new pseries(var==point, newseq))->setflag(status_flags::dynallocated); + else + return *this; +} + ex pseries::subs(const exmap & m, unsigned options) const { // If expansion variable is being substituted, convert the series to a @@ -690,7 +719,7 @@ ex pseries::add_series(const pseries &other) const epvector::const_iterator b = other.seq.begin(); epvector::const_iterator a_end = seq.end(); epvector::const_iterator b_end = other.seq.end(); - int pow_a = INT_MAX, pow_b = INT_MAX; + int pow_a = std::numeric_limits::max(), pow_b = std::numeric_limits::max(); for (;;) { // If a is empty, fill up with elements from b and stop if (a == a_end) { @@ -823,8 +852,8 @@ ex pseries::mul_series(const pseries &other) const int cdeg_min = a_min + b_min; int cdeg_max = a_max + b_max; - int higher_order_a = INT_MAX; - int higher_order_b = INT_MAX; + int higher_order_a = std::numeric_limits::max(); + int higher_order_b = std::numeric_limits::max(); if (is_order_function(coeff(var, a_max))) higher_order_a = a_max + b_min; if (is_order_function(other.coeff(var, b_max))) @@ -845,7 +874,7 @@ ex pseries::mul_series(const pseries &other) const if (!co.is_zero()) new_seq.push_back(expair(co, numeric(cdeg))); } - if (higher_order_c < INT_MAX) + if (higher_order_c < std::numeric_limits::max()) new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c))); return pseries(relational(var, point), new_seq); } @@ -863,10 +892,13 @@ ex mul::series(const relational & r, int order, unsigned options) const // holds ldegrees of the series of individual factors std::vector ldegrees; + std::vector ldegree_redo; // find minimal degrees const epvector::const_iterator itbeg = seq.begin(); const epvector::const_iterator itend = seq.end(); + // first round: obtain a bound up to which minimal degrees have to be + // considered for (epvector::const_iterator it=itbeg; it!=itend; ++it) { ex expon = it->coeff; @@ -880,19 +912,61 @@ ex mul::series(const relational & r, int order, unsigned options) const } int real_ldegree = 0; + bool flag_redo = false; try { real_ldegree = buf.expand().ldegree(sym-r.rhs()); } catch (std::runtime_error) {} if (real_ldegree == 0) { + if ( factor < 0 ) { + // This case must terminate, otherwise we would have division by + // zero. + int orderloop = 0; + do { + orderloop++; + real_ldegree = buf.series(r, orderloop, options).ldegree(sym); + } while (real_ldegree == orderloop); + } else { + // Here it is possible that buf does not have a ldegree, therefore + // check only if ldegree is negative, otherwise reconsider the case + // in the second round. + real_ldegree = buf.series(r, 0, options).ldegree(sym); + if (real_ldegree == 0) + flag_redo = true; + } + } + + ldegrees.push_back(factor * real_ldegree); + ldegree_redo.push_back(flag_redo); + } + + int degbound = order-std::accumulate(ldegrees.begin(), ldegrees.end(), 0); + // Second round: determine the remaining positive ldegrees by the series + // method. + // here we can ignore ldegrees larger than degbound + size_t j = 0; + for (epvector::const_iterator it=itbeg; it!=itend; ++it) { + if ( ldegree_redo[j] ) { + ex expon = it->coeff; + int factor = 1; + ex buf; + if (expon.info(info_flags::integer)) { + buf = it->rest; + factor = ex_to(expon).to_int(); + } else { + buf = recombine_pair_to_ex(*it); + } + int real_ldegree = 0; int orderloop = 0; do { orderloop++; real_ldegree = buf.series(r, orderloop, options).ldegree(sym); - } while (real_ldegree == orderloop); + } while ((real_ldegree == orderloop) + && ( factor*real_ldegree < degbound)); + ldegrees[j] = factor * real_ldegree; + degbound -= factor * real_ldegree; } - - ldegrees.push_back(factor * real_ldegree); + j++; } int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0); @@ -1072,7 +1146,10 @@ ex power::series(const relational & r, int order, unsigned options) const } const ex& sym = r.lhs(); // find existing minimal degree - int real_ldegree = basis.expand().ldegree(sym-r.rhs()); + ex eb = basis.expand(); + int real_ldegree = 0; + if (eb.info(info_flags::rational_function)) + real_ldegree = eb.ldegree(sym-r.rhs()); if (real_ldegree == 0) { int orderloop = 0; do { @@ -1203,11 +1280,7 @@ ex ex::series(const ex & r, int order, unsigned options) const else throw (std::logic_error("ex::series(): expansion point has unknown type")); - try { - e = bp->series(rel_, order, options); - } catch (std::exception &x) { - throw (std::logic_error(std::string("unable to compute series (") + x.what() + ")")); - } + e = bp->series(rel_, order, options); return e; }