X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=a30182ef1b7320d5088d6d3ad542a6336ac33e9c;hp=c1568145d706157e250375ff8189f5caee944872;hb=fd3a53feaa220a02cce19f09b86d96579321fc78;hpb=36c5241d290222f71d501b253e3bbe3097221645 diff --git a/ginac/power.cpp b/ginac/power.cpp index c1568145..a30182ef 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 @@ -23,6 +23,7 @@ #include #include #include +#include #include "power.h" #include "expairseq.h" @@ -31,12 +32,14 @@ #include "ncmul.h" #include "numeric.h" #include "constant.h" +#include "operators.h" #include "inifcns.h" // for log() in power::derivative() #include "matrix.h" +#include "indexed.h" #include "symbol.h" +#include "lst.h" #include "print.h" #include "archive.h" -#include "debugmsg.h" #include "utils.h" namespace GiNaC { @@ -46,25 +49,13 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic) typedef std::vector intvector; ////////// -// default ctor, dtor, copy ctor assignment operator and helpers +// default constructor ////////// -power::power() : inherited(TINFO_power) -{ - debugmsg("power default ctor",LOGLEVEL_CONSTRUCT); -} - -void power::copy(const power & other) -{ - inherited::copy(other); - basis = other.basis; - exponent = other.exponent; -} - -DEFAULT_DESTROY(power) +power::power() : inherited(TINFO_power) { } ////////// -// other ctors +// other constructors ////////// // all inlined @@ -73,9 +64,8 @@ DEFAULT_DESTROY(power) // archiving ////////// -power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +power::power(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) { - debugmsg("power ctor from archive_node", LOGLEVEL_CONSTRUCT); n.find_ex("basis", basis, sym_lst); n.find_ex("exponent", exponent, sym_lst); } @@ -121,8 +111,6 @@ static void print_sym_pow(const print_context & c, const symbol &x, int exp) void power::print(const print_context & c, unsigned level) const { - debugmsg("power print", LOGLEVEL_PRINT); - if (is_a(c)) { inherited::print(c, level); @@ -131,7 +119,7 @@ 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 << '('; @@ -146,7 +134,7 @@ 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 @@ -166,38 +154,49 @@ void power::print(const print_context & c, unsigned level) const c.s << ')'; } + } else if (is_a(c)) { + + c.s << class_name() << '('; + basis.print(c); + c.s << ','; + exponent.print(c); + c.s << ')'; + } 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()); - c.s << '^'; - if (is_a(c)) + if (is_a(c)) + c.s << "**"; + else + c.s << '^'; + 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 ? ")}" : ")"); } } } @@ -220,14 +219,13 @@ bool power::info(unsigned inf) const return inherited::info(inf); } -unsigned power::nops() const +size_t power::nops() const { return 2; } -ex & power::let_op(int i) +ex power::op(size_t i) const { - GINAC_ASSERT(i>=0); GINAC_ASSERT(i<2); return i==0 ? basis : exponent; @@ -240,49 +238,59 @@ ex power::map(map_function & f) const int power::degree(const ex & s) const { - if (is_exactly_of_type(*exponent.bp, numeric) && ex_to(exponent).is_integer()) { + if (is_equal(ex_to(s))) + return 1; + else if (is_exactly_a(exponent) && ex_to(exponent).is_integer()) { if (basis.is_equal(s)) return ex_to(exponent).to_int(); else return basis.degree(s) * ex_to(exponent).to_int(); - } - return 0; + } else if (basis.has(s)) + throw(std::runtime_error("power::degree(): undefined degree because of non-integer exponent")); + else + return 0; } int power::ldegree(const ex & s) const { - if (is_exactly_of_type(*exponent.bp, numeric) && ex_to(exponent).is_integer()) { + if (is_equal(ex_to(s))) + return 1; + else if (is_exactly_a(exponent) && ex_to(exponent).is_integer()) { if (basis.is_equal(s)) return ex_to(exponent).to_int(); else return basis.ldegree(s) * ex_to(exponent).to_int(); - } - return 0; + } else if (basis.has(s)) + throw(std::runtime_error("power::ldegree(): undefined degree because of non-integer exponent")); + else + return 0; } 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; else - return _ex0(); + return _ex0; } else { // basis equal to s - if (is_exactly_of_type(*exponent.bp, numeric) && ex_to(exponent).is_integer()) { + if (is_exactly_a(exponent) && ex_to(exponent).is_integer()) { // integer exponent int int_exp = ex_to(exponent).to_int(); if (n == int_exp) - return _ex1(); + return _ex1; else - return _ex0(); + return _ex0; } else { // non-integer exponents are treated as zero if (n == 0) return *this; else - return _ex0(); + return _ex0; } } } @@ -303,8 +311,6 @@ ex power::coeff(const ex & s, int n) const * @param level cut-off in recursive evaluation */ ex power::eval(int level) const { - debugmsg("power eval",LOGLEVEL_MEMBER_FUNCTION); - if ((level==1) && (flags & status_flags::evaluated)) return *this; else if (level == -max_recursion_level) @@ -318,13 +324,13 @@ ex power::eval(int level) const const numeric *num_basis; const numeric *num_exponent; - if (is_exactly_of_type(*ebasis.bp,numeric)) { + if (is_exactly_a(ebasis)) { basis_is_numerical = true; - num_basis = static_cast(ebasis.bp); + num_basis = &ex_to(ebasis); } - if (is_exactly_of_type(*eexponent.bp,numeric)) { + if (is_exactly_a(eexponent)) { exponent_is_numerical = true; - num_exponent = static_cast(eexponent.bp); + num_exponent = &ex_to(eexponent); } // ^(x,0) -> 1 (0^0 also handled here) @@ -332,11 +338,11 @@ ex power::eval(int level) const if (ebasis.is_zero()) throw (std::domain_error("power::eval(): pow(0,0) is undefined")); else - return _ex1(); + return _ex1; } // ^(x,1) -> x - if (eexponent.is_equal(_ex1())) + if (eexponent.is_equal(_ex1)) return ebasis; // ^(0,c1) -> 0 or exception (depending on real value of c1) @@ -346,12 +352,12 @@ ex power::eval(int level) const else if ((num_exponent->real()).is_negative()) throw (pole_error("power::eval(): division by zero",1)); else - return _ex0(); + return _ex0; } // ^(1,x) -> 1 - if (ebasis.is_equal(_ex1())) - return _ex1(); + if (ebasis.is_equal(_ex1)) + return _ex1; if (exponent_is_numerical) { @@ -413,43 +419,43 @@ ex power::eval(int level) const // ^(^(x,c1),c2) -> ^(x,c1*c2) // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1, // case c1==1 should not happen, see below!) - if (is_ex_exactly_of_type(ebasis,power)) { + if (is_exactly_a(ebasis)) { const power & sub_power = ex_to(ebasis); const ex & sub_basis = sub_power.basis; const ex & sub_exponent = sub_power.exponent; - if (is_ex_exactly_of_type(sub_exponent,numeric)) { + if (is_exactly_a(sub_exponent)) { const numeric & num_sub_exponent = ex_to(sub_exponent); GINAC_ASSERT(num_sub_exponent!=numeric(1)); - if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1()).is_negative()) + if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative()) return power(sub_basis,num_sub_exponent.mul(*num_exponent)); } } // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer) - if (num_exponent->is_integer() && is_ex_exactly_of_type(ebasis,mul)) { + if (num_exponent->is_integer() && is_exactly_a(ebasis)) { return expand_mul(ex_to(ebasis), *num_exponent); } // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0) // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0) - if (is_ex_exactly_of_type(ebasis,mul)) { + if (is_exactly_a(ebasis)) { GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above const mul & mulref = ex_to(ebasis); - if (!mulref.overall_coeff.is_equal(_ex1())) { + if (!mulref.overall_coeff.is_equal(_ex1)) { const numeric & num_coeff = ex_to(mulref.overall_coeff); if (num_coeff.is_real()) { if (num_coeff.is_positive()) { mul *mulp = new mul(mulref); - mulp->overall_coeff = _ex1(); + mulp->overall_coeff = _ex1; mulp->clearflag(status_flags::evaluated); mulp->clearflag(status_flags::hash_calculated); return (new mul(power(*mulp,exponent), power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated); } else { - GINAC_ASSERT(num_coeff.compare(_num0())<0); - if (num_coeff.compare(_num_1())!=0) { + GINAC_ASSERT(num_coeff.compare(_num0)<0); + if (!num_coeff.is_equal(_num_1)) { mul *mulp = new mul(mulref); - mulp->overall_coeff = _ex_1(); + mulp->overall_coeff = _ex_1; mulp->clearflag(status_flags::evaluated); mulp->clearflag(status_flags::hash_calculated); return (new mul(power(*mulp,exponent), @@ -463,7 +469,7 @@ ex power::eval(int level) const // ^(nc,c1) -> ncmul(nc,nc,...) (c1 positive integer, unless nc is a matrix) if (num_exponent->is_pos_integer() && ebasis.return_type() != return_types::commutative && - !is_ex_of_type(ebasis,matrix)) { + !is_a(ebasis)) { return ncmul(exvector(num_exponent->to_int(), ebasis), true); } } @@ -478,8 +484,6 @@ ex power::eval(int level) const ex power::evalf(int level) const { - debugmsg("power evalf",LOGLEVEL_MEMBER_FUNCTION); - ex ebasis; ex eexponent; @@ -490,7 +494,7 @@ ex power::evalf(int level) const throw(std::runtime_error("max recursion level reached")); } else { ebasis = basis.evalf(level-1); - if (!is_ex_exactly_of_type(eexponent,numeric)) + if (!is_exactly_a(exponent)) eexponent = exponent.evalf(level-1); else eexponent = exponent; @@ -499,33 +503,46 @@ ex power::evalf(int level) const return power(ebasis,eexponent); } -ex power::evalm(void) const +ex power::evalm() const { const ex ebasis = basis.evalm(); const ex eexponent = exponent.evalm(); - if (is_ex_of_type(ebasis,matrix)) { - if (is_ex_of_type(eexponent,numeric)) { + if (is_a(ebasis)) { + if (is_exactly_a(eexponent)) { return (new matrix(ex_to(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated); } } return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated); } -ex power::subs(const lst & ls, const lst & lr, bool no_pattern) const -{ - const ex &subsed_basis = basis.subs(ls, lr, no_pattern); - const ex &subsed_exponent = exponent.subs(ls, lr, no_pattern); +// from mul.cpp +extern bool tryfactsubs(const ex &, const ex &, int &, lst &); - if (are_ex_trivially_equal(basis, subsed_basis) - && are_ex_trivially_equal(exponent, subsed_exponent)) - return basic::subs(ls, lr, no_pattern); - else - return ex(power(subsed_basis, subsed_exponent)).bp->basic::subs(ls, lr, no_pattern); +ex power::subs(const exmap & m, unsigned options) const +{ + const ex &subsed_basis = basis.subs(m, options); + const ex &subsed_exponent = exponent.subs(m, options); + + if (!are_ex_trivially_equal(basis, subsed_basis) + || !are_ex_trivially_equal(exponent, subsed_exponent)) + return power(subsed_basis, subsed_exponent).subs_one_level(m, options); + + if (!(options & subs_options::subs_algebraic)) + return subs_one_level(m, options); + + for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) { + int nummatches = std::numeric_limits::max(); + lst repls; + if (tryfactsubs(*this, it->first, nummatches, repls)) + return (ex_to((*this) * power(it->second.subs(ex(repls), subs_options::subs_no_pattern) / it->first.subs(ex(repls), subs_options::subs_no_pattern), nummatches))).subs_one_level(m, options); + } + + return subs_one_level(m, options); } -ex power::simplify_ncmul(const exvector & v) const +ex power::eval_ncmul(const exvector & v) const { - return inherited::simplify_ncmul(v); + return inherited::eval_ncmul(v); } // protected @@ -538,20 +555,20 @@ ex power::derivative(const symbol & s) const // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below) epvector newseq; newseq.reserve(2); - newseq.push_back(expair(basis, exponent - _ex1())); - newseq.push_back(expair(basis.diff(s), _ex1())); + newseq.push_back(expair(basis, exponent - _ex1)); + newseq.push_back(expair(basis.diff(s), _ex1)); return mul(newseq, exponent); } else { // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b) return mul(*this, add(mul(exponent.diff(s), log(basis)), - mul(mul(exponent, basis.diff(s)), power(basis, _ex_1())))); + mul(mul(exponent, basis.diff(s)), power(basis, _ex_1)))); } } int power::compare_same_type(const basic & other) const { - GINAC_ASSERT(is_exactly_of_type(other, power)); + GINAC_ASSERT(is_exactly_a(other)); const power &o = static_cast(other); int cmpval = basis.compare(o.basis); @@ -561,12 +578,12 @@ int power::compare_same_type(const basic & other) const return exponent.compare(o.exponent); } -unsigned power::return_type(void) const +unsigned power::return_type() const { return basis.return_type(); } -unsigned power::return_type_tinfo(void) const +unsigned power::return_type_tinfo() const { return basis.return_type_tinfo(); } @@ -580,7 +597,7 @@ ex power::expand(unsigned options) const const ex expanded_exponent = exponent.expand(options); // x^(a+b) -> x^a * x^b - if (is_ex_exactly_of_type(expanded_exponent, add)) { + if (is_exactly_a(expanded_exponent)) { const add &a = ex_to(expanded_exponent); exvector distrseq; distrseq.reserve(a.seq.size() + 1); @@ -595,7 +612,7 @@ ex power::expand(unsigned options) const if (ex_to(a.overall_coeff).is_integer()) { const numeric &num_exponent = ex_to(a.overall_coeff); int int_exponent = num_exponent.to_int(); - if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add)) + if (int_exponent > 0 && is_exactly_a(expanded_basis)) distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent)); else distrseq.push_back(power(expanded_basis, a.overall_coeff)); @@ -607,7 +624,7 @@ ex power::expand(unsigned options) const return r.expand(); } - if (!is_ex_exactly_of_type(expanded_exponent, numeric) || + if (!is_exactly_a(expanded_exponent) || !ex_to(expanded_exponent).is_integer()) { if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) { return this->hold(); @@ -621,11 +638,11 @@ ex power::expand(unsigned options) const int int_exponent = num_exponent.to_int(); // (x+y)^n, n>0 - if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add)) + if (int_exponent > 0 && is_exactly_a(expanded_basis)) return expand_add(ex_to(expanded_basis), int_exponent); // (x*y)^n -> x^n * y^n - if (is_ex_exactly_of_type(expanded_basis,mul)) + if (is_exactly_a(expanded_basis)) return expand_mul(ex_to(expanded_basis), num_exponent); // cannot expand further @@ -645,89 +662,90 @@ 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 size_t 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).exponent,numeric) || + GINAC_ASSERT(!is_exactly_a(b)); + GINAC_ASSERT(!is_exactly_a(b) || + !is_exactly_a(ex_to(b).exponent) || !ex_to(ex_to(b).exponent).is_pos_integer() || - !is_ex_exactly_of_type(ex_to(b).basis,add) || - !is_ex_exactly_of_type(ex_to(b).basis,mul) || - !is_ex_exactly_of_type(ex_to(b).basis,power)); - if (is_ex_exactly_of_type(b,mul)) + !is_exactly_a(ex_to(b).basis) || + !is_exactly_a(ex_to(b).basis) || + !is_exactly_a(ex_to(b).basis)); + if (is_exactly_a(b)) term.push_back(expand_mul(ex_to(b),numeric(k[l]))); else term.push_back(power(b,k[l])); } - + const ex & b = a.op(l); - GINAC_ASSERT(!is_ex_exactly_of_type(b,add)); - GINAC_ASSERT(!is_ex_exactly_of_type(b,power) || - !is_ex_exactly_of_type(ex_to(b).exponent,numeric) || + GINAC_ASSERT(!is_exactly_a(b)); + GINAC_ASSERT(!is_exactly_a(b) || + !is_exactly_a(ex_to(b).exponent) || !ex_to(ex_to(b).exponent).is_pos_integer() || - !is_ex_exactly_of_type(ex_to(b).basis,add) || - !is_ex_exactly_of_type(ex_to(b).basis,mul) || - !is_ex_exactly_of_type(ex_to(b).basis,power)); - if (is_ex_exactly_of_type(b,mul)) + !is_exactly_a(ex_to(b).basis) || + !is_exactly_a(ex_to(b).basis) || + !is_exactly_a(ex_to(b).basis)); + if (is_exactly_a(b)) 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); } @@ -736,47 +754,47 @@ ex power::expand_add(const add & a, int n) const ex power::expand_add_2(const add & a) const { epvector sum; - unsigned a_nops = a.nops(); + size_t 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) { const ex & r = cit0->rest; const ex & c = cit0->coeff; - GINAC_ASSERT(!is_ex_exactly_of_type(r,add)); - GINAC_ASSERT(!is_ex_exactly_of_type(r,power) || - !is_ex_exactly_of_type(ex_to(r).exponent,numeric) || + GINAC_ASSERT(!is_exactly_a(r)); + GINAC_ASSERT(!is_exactly_a(r) || + !is_exactly_a(ex_to(r).exponent) || !ex_to(ex_to(r).exponent).is_pos_integer() || - !is_ex_exactly_of_type(ex_to(r).basis,add) || - !is_ex_exactly_of_type(ex_to(r).basis,mul) || - !is_ex_exactly_of_type(ex_to(r).basis,power)); + !is_exactly_a(ex_to(r).basis) || + !is_exactly_a(ex_to(r).basis) || + !is_exactly_a(ex_to(r).basis)); - if (are_ex_trivially_equal(c,_ex1())) { - if (is_ex_exactly_of_type(r,mul)) { - sum.push_back(expair(expand_mul(ex_to(r),_num2()), - _ex1())); + if (c.is_equal(_ex1)) { + if (is_exactly_a(r)) { + sum.push_back(expair(expand_mul(ex_to(r),_num2), + _ex1)); } else { - sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated), - _ex1())); + sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated), + _ex1)); } } else { - if (is_ex_exactly_of_type(r,mul)) { - sum.push_back(expair(expand_mul(ex_to(r),_num2()), - ex_to(c).power_dyn(_num2()))); + if (is_exactly_a(r)) { + 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), - ex_to(c).power_dyn(_num2()))); + sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated), + ex_to(c).power_dyn(_num2))); } } - + for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) { const ex & r1 = cit1->rest; const ex & c1 = cit1->coeff; sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated), - _num2().mul(ex_to(c)).mul_dyn(ex_to(c1)))); + _num2.mul(ex_to(c)).mul_dyn(ex_to(c1)))); } } @@ -786,10 +804,10 @@ ex power::expand_add_2(const add & a) const if (!a.overall_coeff.is_zero()) { epvector::const_iterator i = a.seq.begin(), end = a.seq.end(); while (i != end) { - sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to(a.overall_coeff).mul_dyn(_num2()))); + sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to(a.overall_coeff).mul_dyn(_num2))); ++i; } - sum.push_back(expair(ex_to(a.overall_coeff).power_dyn(_num2()),_ex1())); + sum.push_back(expair(ex_to(a.overall_coeff).power_dyn(_num2),_ex1)); } GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2); @@ -797,35 +815,30 @@ 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(); - + 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_exactly_a(cit->rest)) { + 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); -} - -// helper function - -ex sqrt(const ex & a) -{ - return power(a,_ex1_2()); + return (new mul(distrseq, ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated); } } // namespace GiNaC