X-Git-Url: https://ginac.de/ginac.git//ginac.git?a=blobdiff_plain;ds=inline;f=ginac%2Fpower.cpp;h=3dd0f48f487cc6c397ae13e70019f41e9fe2f7e9;hb=ea5d361d94e49ca3f3b73db8c9812ee519f0633f;hp=2cff577eabdc80e55972a2c18dd68776e08b306e;hpb=be376425f421903c387720307036bbd1ab07afb5;p=ginac.git diff --git a/ginac/power.cpp b/ginac/power.cpp index 2cff577e..3dd0f48f 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) 1999-2005 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 @@ -222,12 +222,14 @@ 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); } return inherited::info(inf); } @@ -246,7 +248,14 @@ 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; } int power::degree(const ex & s) const @@ -372,6 +381,10 @@ 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); + if (exponent_is_numerical) { // ^(c1,c2) -> c1^c2 (c1, c2 numeric(), @@ -439,7 +452,7 @@ 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)); } } @@ -465,8 +478,8 @@ 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); @@ -558,6 +571,16 @@ 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); +} + // protected /** Implementation of ex::diff() for a power. @@ -595,7 +618,7 @@ unsigned power::return_type() const { return basis.return_type(); } - + unsigned power::return_type_tinfo() const { return basis.return_type_tinfo(); @@ -656,7 +679,7 @@ ex power::expand(unsigned options) const // (x*y)^n -> x^n * y^n if (is_exactly_a(expanded_basis)) - return expand_mul(ex_to(expanded_basis), num_exponent, options); + 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)) @@ -685,7 +708,7 @@ ex power::expand_add(const add & a, int n, unsigned options) const 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()); @@ -713,7 +736,7 @@ ex power::expand_add(const add & a, int n, unsigned options) 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]), options)); + term.push_back(expand_mul(ex_to(b), numeric(k[l]), options, true)); else term.push_back(power(b,k[l])); } @@ -727,7 +750,7 @@ ex power::expand_add(const add & a, int n, unsigned options) 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]), options)); + 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])); @@ -787,7 +810,7 @@ ex power::expand_add_2(const add & a, unsigned options) const if (c.is_equal(_ex1)) { if (is_exactly_a(r)) { - sum.push_back(expair(expand_mul(ex_to(r), _num2, options), + 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), @@ -795,11 +818,11 @@ ex power::expand_add_2(const add & a, unsigned options) const } } else { if (is_exactly_a(r)) { - sum.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to(r), _num2, options), - 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))); } } @@ -807,7 +830,7 @@ ex power::expand_add_2(const add & a, unsigned options) 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)))); } } @@ -817,10 +840,10 @@ ex power::expand_add_2(const add & a, unsigned options) 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); @@ -830,12 +853,21 @@ ex power::expand_add_2(const add & a, unsigned options) const /** 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, unsigned options) 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; + for (int i=1; i < n.to_int(); i++) + result *= rename_dummy_indices_uniquely(m,m); + return result; + } epvector distrseq; distrseq.reserve(m.seq.size()); @@ -850,7 +882,7 @@ ex power::expand_mul(const mul & m, const numeric & n, unsigned options) const // it is safe not to call mul::combine_pair_with_coeff_to_pair() // since n is an integer numeric new_coeff = ex_to(cit->coeff).mul(n); - if (is_exactly_a(cit->rest) && new_coeff.is_pos_integer()) { + if (from_expand && is_exactly_a(cit->rest) && new_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; @@ -863,8 +895,9 @@ ex power::expand_mul(const mul & m, const numeric & n, unsigned options) const 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); - else + if (from_expand) return result.setflag(status_flags::expanded); + return result; } } // namespace GiNaC