X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=0730e3c8bf7fc385c5d4d1c1a97b6c565997cfab;hp=72ec5aa368ae65c3bc8565309e379074e00d134e;hb=dbd9c306a74f1cb258c0d15a346b973b39deaad2;hpb=3a63743e24046766b37c3d1bd38605542ee0a536 diff --git a/ginac/power.cpp b/ginac/power.cpp index 72ec5aa3..0730e3c8 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */ /* - * 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 @@ -33,6 +33,7 @@ #include "constant.h" #include "inifcns.h" // for log() in power::derivative() #include "matrix.h" +#include "indexed.h" #include "symbol.h" #include "print.h" #include "archive.h" @@ -124,7 +125,7 @@ void power::print(const print_context & c, unsigned level) const // Integer powers of symbols are printed in a special, optimized way if (exponent.info(info_flags::integer) - && (is_exactly_a(basis) || is_exactly_a(basis))) { + && (is_a(basis) || is_a(basis))) { int exp = ex_to(exponent).to_int(); if (exp > 0) c.s << '('; @@ -139,7 +140,7 @@ void power::print(const print_context & c, unsigned level) const c.s << ')'; // ^-1 is printed as "1.0/" or with the recip() function of CLN - } else if (exponent.compare(_num_1) == 0) { + } else if (exponent.is_equal(_ex_1)) { if (is_a(c)) c.s << "recip("; else @@ -169,39 +170,39 @@ void power::print(const print_context & c, unsigned level) const } else { - if (exponent.is_equal(_ex1_2)) { - if (is_a(c)) - c.s << "\\sqrt{"; - else - c.s << "sqrt("; + bool is_tex = is_a(c); + + if (is_tex && is_exactly_a(exponent) && ex_to(exponent).is_negative()) { + + // Powers with negative numeric exponents are printed as fractions in TeX + c.s << "\\frac{1}{"; + power(basis, -exponent).eval().print(c); + c.s << "}"; + + } else if (exponent.is_equal(_ex1_2)) { + + // Square roots are printed in a special way + c.s << (is_tex ? "\\sqrt{" : "sqrt("); basis.print(c); - if (is_a(c)) - c.s << '}'; - else - c.s << ')'; + c.s << (is_tex ? '}' : ')'); + } else { - if (precedence() <= level) { - if (is_a(c)) - c.s << "{("; - else - c.s << "("; - } + + // Ordinary output of powers using '^' or '**' + if (precedence() <= level) + c.s << (is_tex ? "{(" : "("); basis.print(c, precedence()); if (is_a(c)) c.s << "**"; else c.s << '^'; - if (is_a(c)) + if (is_tex) c.s << '{'; exponent.print(c, precedence()); - if (is_a(c)) + if (is_tex) c.s << '}'; - if (precedence() <= level) { - if (is_a(c)) - c.s << ")}"; - else - c.s << ')'; - } + if (precedence() <= level) + c.s << (is_tex ? ")}" : ")"); } } } @@ -244,7 +245,9 @@ ex power::map(map_function & f) const int power::degree(const ex & s) const { - if (is_ex_exactly_of_type(exponent, numeric) && ex_to(exponent).is_integer()) { + if (is_equal(ex_to(s))) + return 1; + else if (is_ex_exactly_of_type(exponent, numeric) && ex_to(exponent).is_integer()) { if (basis.is_equal(s)) return ex_to(exponent).to_int(); else @@ -257,7 +260,9 @@ int power::degree(const ex & s) const int power::ldegree(const ex & s) const { - if (is_ex_exactly_of_type(exponent, numeric) && ex_to(exponent).is_integer()) { + if (is_equal(ex_to(s))) + return 1; + else if (is_ex_exactly_of_type(exponent, numeric) && ex_to(exponent).is_integer()) { if (basis.is_equal(s)) return ex_to(exponent).to_int(); else @@ -270,7 +275,9 @@ int power::ldegree(const ex & s) const ex power::coeff(const ex & s, int n) const { - if (!basis.is_equal(s)) { + if (is_equal(ex_to(s))) + return n==1 ? _ex1 : _ex0; + else if (!basis.is_equal(s)) { // basis not equal to s if (n == 0) return *this; @@ -649,31 +656,35 @@ ex power::expand(unsigned options) const // non-virtual functions in this class ////////// -/** expand a^n where a is an add and n is an integer. +/** expand a^n where a is an add and n is a positive integer. * @see power::expand */ ex power::expand_add(const add & a, int n) const { if (n==2) return expand_add_2(a); - - int m = a.nops(); - exvector sum; - sum.reserve((n+1)*(m-1)); + + const int m = a.nops(); + exvector result; + // The number of terms will be the number of combinatorial compositions, + // i.e. the number of unordered arrangement of m nonnegative integers + // which sum up to n. It is frequently written as C_n(m) and directly + // related with binomial coefficients: + result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int()); intvector k(m-1); intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]); intvector upper_limit(m-1); int l; - - for (int l=0; l(b)); GINAC_ASSERT(!is_exactly_a(b) || @@ -687,7 +698,7 @@ ex power::expand_add(const add & a, int n) const else term.push_back(power(b,k[l])); } - + const ex & b = a.op(l); GINAC_ASSERT(!is_exactly_a(b)); GINAC_ASSERT(!is_exactly_a(b) || @@ -700,38 +711,35 @@ ex power::expand_add(const add & a, int n) const term.push_back(expand_mul(ex_to(b),numeric(n-k_cum[m-2]))); else term.push_back(power(b,n-k_cum[m-2])); - + numeric f = binomial(numeric(n),numeric(k[0])); - for (l=1; lsetflag(status_flags::dynallocated)); - + + result.push_back((new mul(term))->setflag(status_flags::dynallocated)); + // increment k[] l = m-2; while ((l>=0) && ((++k[l])>upper_limit[l])) { - k[l] = 0; + k[l] = 0; --l; } if (l<0) break; - + // recalc k_cum[] and upper_limit[] - if (l==0) - k_cum[0] = k[0]; - else - k_cum[l] = k_cum[l-1]+k[l]; - - for (int i=l+1; isetflag(status_flags::dynallocated | - status_flags::expanded ); + + return (new add(result))->setflag(status_flags::dynallocated | + status_flags::expanded); } @@ -743,7 +751,7 @@ ex power::expand_add_2(const add & a) const unsigned a_nops = a.nops(); sum.reserve((a_nops*(a_nops+1))/2); epvector::const_iterator last = a.seq.end(); - + // power(+(x,...,z;c),2)=power(+(x,...,z;0),2)+2*c*+(x,...,z;0)+c*c // first part: ignore overall_coeff and expand other terms for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) { @@ -768,10 +776,10 @@ ex power::expand_add_2(const add & a) const } } else { if (is_ex_exactly_of_type(r,mul)) { - sum.push_back(expair(expand_mul(ex_to(r),_num2), + sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to(r),_num2), ex_to(c).power_dyn(_num2))); } else { - sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated), + sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated), ex_to(c).power_dyn(_num2))); } } @@ -801,28 +809,30 @@ ex power::expand_add_2(const add & a) const return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded); } -/** Expand factors of m in m^n where m is a mul and n is and integer +/** Expand factors of m in m^n where m is a mul and n is and integer. * @see power::expand */ ex power::expand_mul(const mul & m, const numeric & n) const { + GINAC_ASSERT(n.is_integer()); + if (n.is_zero()) return _ex1; - + epvector distrseq; distrseq.reserve(m.seq.size()); epvector::const_iterator last = m.seq.end(); epvector::const_iterator cit = m.seq.begin(); while (cit!=last) { - if (is_ex_exactly_of_type((*cit).rest,numeric)) { - distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit,n)); + if (is_ex_exactly_of_type(cit->rest,numeric)) { + distrseq.push_back(m.combine_pair_with_coeff_to_pair(*cit, n)); } else { // it is safe not to call mul::combine_pair_with_coeff_to_pair() // since n is an integer - distrseq.push_back(expair((*cit).rest, ex_to((*cit).coeff).mul(n))); + distrseq.push_back(expair(cit->rest, ex_to(cit->coeff).mul(n))); } ++cit; } - return (new mul(distrseq,ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated); + return (new mul(distrseq, ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated); } } // namespace GiNaC