X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=faa0d05cc61eb156e0554a9b787b6db4ff8a7e19;hp=a30182ef1b7320d5088d6d3ad542a6336ac33e9c;hb=9e1051ad0a532338a6f995b9f41f17ac5cdc47a6;hpb=5ef801553eb39aed7bd2df9dd1aff9d752c3ea9d diff --git a/ginac/power.cpp b/ginac/power.cpp index a30182ef..faa0d05c 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2007 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 @@ -17,7 +17,7 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ #include @@ -38,13 +38,19 @@ #include "indexed.h" #include "symbol.h" #include "lst.h" -#include "print.h" #include "archive.h" #include "utils.h" +#include "relational.h" +#include "compiler.h" namespace GiNaC { -GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic) +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(power, basic, + print_func(&power::do_print_dflt). + print_func(&power::do_print_latex). + print_func(&power::do_print_csrc). + print_func(&power::do_print_python). + print_func(&power::do_print_python_repr)) typedef std::vector intvector; @@ -52,7 +58,7 @@ typedef std::vector intvector; // default constructor ////////// -power::power() : inherited(TINFO_power) { } +power::power() : inherited(&power::tinfo_static) { } ////////// // other constructors @@ -85,11 +91,58 @@ DEFAULT_UNARCHIVE(power) // public +void power::print_power(const print_context & c, const char *powersymbol, const char *openbrace, const char *closebrace, unsigned level) const +{ + // Ordinary output of powers using '^' or '**' + if (precedence() <= level) + c.s << openbrace << '('; + basis.print(c, precedence()); + c.s << powersymbol; + c.s << openbrace; + exponent.print(c, precedence()); + c.s << closebrace; + if (precedence() <= level) + c.s << ')' << closebrace; +} + +void power::do_print_dflt(const print_dflt & c, unsigned level) const +{ + if (exponent.is_equal(_ex1_2)) { + + // Square roots are printed in a special way + c.s << "sqrt("; + basis.print(c); + c.s << ')'; + + } else + print_power(c, "^", "", "", level); +} + +void power::do_print_latex(const print_latex & c, unsigned level) const +{ + if (is_exactly_a(exponent) && ex_to(exponent).is_negative()) { + + // Powers with negative numeric exponents are printed as fractions + 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 << "\\sqrt{"; + basis.print(c); + c.s << '}'; + + } else + print_power(c, "^", "{", "}", level); +} + static void print_sym_pow(const print_context & c, const symbol &x, int exp) { // Optimal output of integer powers of symbols to aid compiler CSE. // C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15 - // to learn why such a parenthisation is really necessary. + // to learn why such a parenthesation is really necessary. if (exp == 1) { x.print(c); } else if (exp == 2) { @@ -109,96 +162,58 @@ static void print_sym_pow(const print_context & c, const symbol &x, int exp) } } -void power::print(const print_context & c, unsigned level) const +void power::do_print_csrc(const print_csrc & c, unsigned level) const { - if (is_a(c)) { - - inherited::print(c, level); - - } else if (is_a(c)) { - - // Integer powers of symbols are printed in a special, optimized way - if (exponent.info(info_flags::integer) - && (is_a(basis) || is_a(basis))) { - int exp = ex_to(exponent).to_int(); - if (exp > 0) - c.s << '('; - else { - exp = -exp; - if (is_a(c)) - c.s << "recip("; - else - c.s << "1.0/("; - } - print_sym_pow(c, ex_to(basis), exp); - c.s << ')'; - - // ^-1 is printed as "1.0/" or with the recip() function of CLN - } else if (exponent.is_equal(_ex_1)) { + // Integer powers of symbols are printed in a special, optimized way + if (exponent.info(info_flags::integer) + && (is_a(basis) || is_a(basis))) { + int exp = ex_to(exponent).to_int(); + if (exp > 0) + c.s << '('; + else { + exp = -exp; if (is_a(c)) c.s << "recip("; else c.s << "1.0/("; - basis.print(c); - c.s << ')'; - - // Otherwise, use the pow() or expt() (CLN) functions - } else { - if (is_a(c)) - c.s << "expt("; - else - c.s << "pow("; - basis.print(c); - c.s << ','; - exponent.print(c); - c.s << ')'; } + print_sym_pow(c, ex_to(basis), exp); + c.s << ')'; - } else if (is_a(c)) { + // ^-1 is printed as "1.0/" or with the recip() function of CLN + } else if (exponent.is_equal(_ex_1)) { + if (is_a(c)) + c.s << "recip("; + else + c.s << "1.0/("; + basis.print(c); + c.s << ')'; - c.s << class_name() << '('; + // Otherwise, use the pow() or expt() (CLN) functions + } else { + if (is_a(c)) + c.s << "expt("; + else + c.s << "pow("; basis.print(c); c.s << ','; exponent.print(c); c.s << ')'; + } +} - } else { - - 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); - c.s << (is_tex ? '}' : ')'); - - } else { +void power::do_print_python(const print_python & c, unsigned level) const +{ + print_power(c, "**", "", "", level); +} - // 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_tex) - c.s << '{'; - exponent.print(c, precedence()); - if (is_tex) - c.s << '}'; - if (precedence() <= level) - c.s << (is_tex ? ")}" : ")"); - } - } +void power::do_print_python_repr(const print_python_repr & c, unsigned level) const +{ + c.s << class_name() << '('; + basis.print(c); + c.s << ','; + exponent.print(c); + c.s << ')'; } bool power::info(unsigned inf) const @@ -209,12 +224,16 @@ bool power::info(unsigned inf) const case info_flags::cinteger_polynomial: case info_flags::rational_polynomial: case info_flags::crational_polynomial: - return exponent.info(info_flags::nonnegint); + return exponent.info(info_flags::nonnegint) && + basis.info(inf); case info_flags::rational_function: - return exponent.info(info_flags::integer); + return exponent.info(info_flags::integer) && + basis.info(inf); case info_flags::algebraic: - return (!exponent.info(info_flags::integer) || - basis.info(inf)); + return !exponent.info(info_flags::integer) || + basis.info(inf); + case info_flags::expanded: + return (flags & status_flags::expanded); } return inherited::info(inf); } @@ -233,7 +252,23 @@ ex power::op(size_t i) const ex power::map(map_function & f) const { - return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated); + const ex &mapped_basis = f(basis); + const ex &mapped_exponent = f(exponent); + + if (!are_ex_trivially_equal(basis, mapped_basis) + || !are_ex_trivially_equal(exponent, mapped_exponent)) + return (new power(mapped_basis, mapped_exponent))->setflag(status_flags::dynallocated); + else + return *this; +} + +bool power::is_polynomial(const ex & var) const +{ + if (exponent.has(var)) + return false; + if (!exponent.info(info_flags::nonnegint)) + return false; + return basis.is_polynomial(var); } int power::degree(const ex & s) const @@ -303,6 +338,7 @@ ex power::coeff(const ex & s, int n) const * - ^(0,c) -> 0 or exception (depending on the real part of c) * - ^(1,x) -> 1 * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1) + * - ^(^(x,c1),c2) -> ^(x,c1*c2) if x is positive and c1 is real. * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!) * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer) * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0) @@ -359,6 +395,14 @@ ex power::eval(int level) const if (ebasis.is_equal(_ex1)) return _ex1; + // power of a function calculated by separate rules defined for this function + if (is_exactly_a(ebasis)) + return ex_to(ebasis).power(eexponent); + + // Turn (x^c)^d into x^(c*d) in the case that x is positive and c is real. + if (is_exactly_a(ebasis) && ebasis.op(0).info(info_flags::positive) && ebasis.op(1).info(info_flags::real)) + return power(ebasis.op(0), ebasis.op(1) * eexponent); + if (exponent_is_numerical) { // ^(c1,c2) -> c1^c2 (c1, c2 numeric(), @@ -426,16 +470,45 @@ ex power::eval(int level) const 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_p)).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_exactly_a(ebasis)) { - return expand_mul(ex_to(ebasis), *num_exponent); + return expand_mul(ex_to(ebasis), *num_exponent, 0); } - + + // (2*x + 6*y)^(-4) -> 1/16*(x + 3*y)^(-4) + if (num_exponent->is_integer() && is_exactly_a(ebasis)) { + numeric icont = ebasis.integer_content(); + const numeric& lead_coeff = + ex_to(ex_to(ebasis).seq.begin()->coeff).div_dyn(icont); + + const bool canonicalizable = lead_coeff.is_integer(); + const bool unit_normal = lead_coeff.is_pos_integer(); + if (canonicalizable && (! unit_normal)) + icont = icont.mul(*_num_1_p); + + if (canonicalizable && (icont != *_num1_p)) { + const add& addref = ex_to(ebasis); + add* addp = new add(addref); + addp->setflag(status_flags::dynallocated); + addp->clearflag(status_flags::hash_calculated); + addp->overall_coeff = ex_to(addp->overall_coeff).div_dyn(icont); + for (epvector::iterator i = addp->seq.begin(); i != addp->seq.end(); ++i) + i->coeff = ex_to(i->coeff).div_dyn(icont); + + const numeric c = icont.power(*num_exponent); + if (likely(c != *_num1_p)) + return (new mul(power(*addp, *num_exponent), c))->setflag(status_flags::dynallocated); + else + return power(*addp, *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_exactly_a(ebasis)) { @@ -452,8 +525,8 @@ ex power::eval(int level) const 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.is_equal(_num_1)) { + GINAC_ASSERT(num_coeff.compare(*_num0_p)<0); + if (!num_coeff.is_equal(*_num_1_p)) { mul *mulp = new mul(mulref); mulp->overall_coeff = _ex_1; mulp->clearflag(status_flags::evaluated); @@ -515,6 +588,30 @@ ex power::evalm() const return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated); } +bool power::has(const ex & other, unsigned options) const +{ + if (!(options & has_options::algebraic)) + return basic::has(other, options); + if (!is_a(other)) + return basic::has(other, options); + if (!exponent.info(info_flags::integer) + || !other.op(1).info(info_flags::integer)) + return basic::has(other, options); + if (exponent.info(info_flags::posint) + && other.op(1).info(info_flags::posint) + && ex_to(exponent).to_int() + > ex_to(other.op(1)).to_int() + && basis.match(other.op(0))) + return true; + if (exponent.info(info_flags::negint) + && other.op(1).info(info_flags::negint) + && ex_to(exponent).to_int() + < ex_to(other.op(1)).to_int() + && basis.match(other.op(0))) + return true; + return basic::has(other, options); +} + // from mul.cpp extern bool tryfactsubs(const ex &, const ex &, int &, lst &); @@ -527,14 +624,14 @@ ex power::subs(const exmap & m, unsigned options) const || !are_ex_trivially_equal(exponent, subsed_exponent)) return power(subsed_basis, subsed_exponent).subs_one_level(m, options); - if (!(options & subs_options::subs_algebraic)) + if (!(options & subs_options::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 (ex_to((*this) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches))).subs_one_level(m, options); } return subs_one_level(m, options); @@ -545,13 +642,76 @@ ex power::eval_ncmul(const exvector & v) const return inherited::eval_ncmul(v); } +ex power::conjugate() const +{ + ex newbasis = basis.conjugate(); + ex newexponent = exponent.conjugate(); + if (are_ex_trivially_equal(basis, newbasis) && are_ex_trivially_equal(exponent, newexponent)) { + return *this; + } + return (new power(newbasis, newexponent))->setflag(status_flags::dynallocated); +} + +ex power::real_part() const +{ + if (exponent.info(info_flags::integer)) { + ex basis_real = basis.real_part(); + if (basis_real == basis) + return *this; + realsymbol a("a"),b("b"); + ex result; + if (exponent.info(info_flags::posint)) + result = power(a+I*b,exponent); + else + result = power(a/(a*a+b*b)-I*b/(a*a+b*b),-exponent); + result = result.expand(); + result = result.real_part(); + result = result.subs(lst( a==basis_real, b==basis.imag_part() )); + return result; + } + + ex a = basis.real_part(); + ex b = basis.imag_part(); + ex c = exponent.real_part(); + ex d = exponent.imag_part(); + return power(abs(basis),c)*exp(-d*atan2(b,a))*cos(c*atan2(b,a)+d*log(abs(basis))); +} + +ex power::imag_part() const +{ + if (exponent.info(info_flags::integer)) { + ex basis_real = basis.real_part(); + if (basis_real == basis) + return 0; + realsymbol a("a"),b("b"); + ex result; + if (exponent.info(info_flags::posint)) + result = power(a+I*b,exponent); + else + result = power(a/(a*a+b*b)-I*b/(a*a+b*b),-exponent); + result = result.expand(); + result = result.imag_part(); + result = result.subs(lst( a==basis_real, b==basis.imag_part() )); + return result; + } + + ex a=basis.real_part(); + ex b=basis.imag_part(); + ex c=exponent.real_part(); + ex d=exponent.imag_part(); + return + power(abs(basis),c)*exp(-d*atan2(b,a))*sin(c*atan2(b,a)+d*log(abs(basis))); +} + +// protected + // protected /** Implementation of ex::diff() for a power. * @see ex::diff */ ex power::derivative(const symbol & s) const { - if (exponent.info(info_flags::real)) { + if (is_a(exponent)) { // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below) epvector newseq; newseq.reserve(2); @@ -582,8 +742,8 @@ unsigned power::return_type() const { return basis.return_type(); } - -unsigned power::return_type_tinfo() const + +tinfo_t power::return_type_tinfo() const { return basis.return_type_tinfo(); } @@ -613,7 +773,7 @@ ex power::expand(unsigned options) const const numeric &num_exponent = ex_to(a.overall_coeff); int int_exponent = num_exponent.to_int(); if (int_exponent > 0 && is_exactly_a(expanded_basis)) - distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent)); + distrseq.push_back(expand_add(ex_to(expanded_basis), int_exponent, options)); else distrseq.push_back(power(expanded_basis, a.overall_coeff)); } else @@ -621,7 +781,7 @@ ex power::expand(unsigned options) const // Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a ex r = (new mul(distrseq))->setflag(status_flags::dynallocated); - return r.expand(); + return r.expand(options); } if (!is_exactly_a(expanded_exponent) || @@ -639,11 +799,11 @@ ex power::expand(unsigned options) const // (x+y)^n, n>0 if (int_exponent > 0 && is_exactly_a(expanded_basis)) - return expand_add(ex_to(expanded_basis), int_exponent); + return expand_add(ex_to(expanded_basis), int_exponent, options); // (x*y)^n -> x^n * y^n if (is_exactly_a(expanded_basis)) - return expand_mul(ex_to(expanded_basis), num_exponent); + return expand_mul(ex_to(expanded_basis), num_exponent, options, true); // cannot expand further if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) @@ -664,15 +824,15 @@ ex power::expand(unsigned options) const /** 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 +ex power::expand_add(const add & a, int n, unsigned options) const { if (n==2) - return expand_add_2(a); + return expand_add_2(a, options); 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 + // i.e. the number of unordered arrangements 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()); @@ -700,7 +860,7 @@ ex power::expand_add(const add & a, int n) const !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]))); + term.push_back(expand_mul(ex_to(b), numeric(k[l]), options, true)); else term.push_back(power(b,k[l])); } @@ -714,7 +874,7 @@ ex power::expand_add(const add & a, int n) const !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]))); + term.push_back(expand_mul(ex_to(b), numeric(n-k_cum[m-2]), options, true)); else term.push_back(power(b,n-k_cum[m-2])); @@ -724,7 +884,7 @@ ex power::expand_add(const add & a, int n) const term.push_back(f); - result.push_back((new mul(term))->setflag(status_flags::dynallocated)); + result.push_back(ex((new mul(term))->setflag(status_flags::dynallocated)).expand(options)); // increment k[] l = m-2; @@ -751,7 +911,7 @@ ex power::expand_add(const add & a, int n) const /** Special case of power::expand_add. Expands a^2 where a is an add. * @see power::expand_add */ -ex power::expand_add_2(const add & a) const +ex power::expand_add_2(const add & a, unsigned options) const { epvector sum; size_t a_nops = a.nops(); @@ -774,7 +934,7 @@ ex power::expand_add_2(const add & a) const if (c.is_equal(_ex1)) { if (is_exactly_a(r)) { - sum.push_back(expair(expand_mul(ex_to(r),_num2), + sum.push_back(expair(expand_mul(ex_to(r), *_num2_p, options, true), _ex1)); } else { sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated), @@ -782,11 +942,11 @@ ex power::expand_add_2(const add & a) const } } else { 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))); + sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to(r), *_num2_p, options, true), + ex_to(c).power_dyn(*_num2_p))); } else { sum.push_back(a.combine_ex_with_coeff_to_pair((new power(r,_ex2))->setflag(status_flags::dynallocated), - ex_to(c).power_dyn(_num2))); + ex_to(c).power_dyn(*_num2_p))); } } @@ -794,7 +954,7 @@ ex power::expand_add_2(const add & a) const 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_p->mul(ex_to(c)).mul_dyn(ex_to(c1)))); } } @@ -804,10 +964,10 @@ 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_p))); ++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_p),_ex1)); } GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2); @@ -815,30 +975,50 @@ 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 an integer. * @see power::expand */ -ex power::expand_mul(const mul & m, const numeric & n) const +ex power::expand_mul(const mul & m, const numeric & n, unsigned options, bool from_expand) const { GINAC_ASSERT(n.is_integer()); - if (n.is_zero()) + if (n.is_zero()) { return _ex1; + } + + // Leave it to multiplication since dummy indices have to be renamed + if (get_all_dummy_indices(m).size() > 0 && n.is_positive()) { + ex result = m; + exvector va = get_all_dummy_indices(m); + sort(va.begin(), va.end(), ex_is_less()); + + for (int i=1; i < n.to_int(); i++) + result *= rename_dummy_indices_uniquely(va, m); + return result; + } epvector distrseq; distrseq.reserve(m.seq.size()); + bool need_reexpand = false; + epvector::const_iterator last = m.seq.end(); epvector::const_iterator cit = m.seq.begin(); while (cit!=last) { - 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))); + expair p = m.combine_pair_with_coeff_to_pair(*cit, n); + if (from_expand && is_exactly_a(cit->rest) && ex_to(p.coeff).is_pos_integer()) { + // this happens when e.g. (a+b)^(1/2) gets squared and + // the resulting product needs to be reexpanded + need_reexpand = true; } + distrseq.push_back(p); ++cit; } - return (new mul(distrseq, ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated); + + const mul & result = static_cast((new mul(distrseq, ex_to(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated)); + if (need_reexpand) + return ex(result).expand(options); + if (from_expand) + return result.setflag(status_flags::expanded); + return result; } } // namespace GiNaC