X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=ec339b9a660afc6aac21fa9307b6bec5e26144ce;hp=309d529a69cffebb3825f96e2d1bcd13e6ff0916;hb=1d09676118944532e6100c93383d1659b1253a60;hpb=23acc666fcef311fd97092aee7f8c55e80395351 diff --git a/ginac/power.cpp b/ginac/power.cpp index 309d529a..ec339b9a 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */ /* - * GiNaC Copyright (C) 1999-2004 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 @@ -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 @@ -40,6 +40,8 @@ #include "lst.h" #include "archive.h" #include "utils.h" +#include "relational.h" +#include "compiler.h" namespace GiNaC { @@ -48,7 +50,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(power, basic, 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)) + print_func(&power::do_print_python_repr). + print_func(&power::do_print_csrc_cl_N)) typedef std::vector intvector; @@ -56,7 +59,7 @@ typedef std::vector intvector; // default constructor ////////// -power::power() : inherited(TINFO_power) { } +power::power() : inherited(&power::tinfo_static) { } ////////// // other constructors @@ -160,6 +163,21 @@ static void print_sym_pow(const print_context & c, const symbol &x, int exp) } } +void power::do_print_csrc_cl_N(const print_csrc_cl_N& c, unsigned level) const +{ + if (exponent.is_equal(_ex_1)) { + c.s << "recip("; + basis.print(c); + c.s << ')'; + return; + } + c.s << "expt("; + basis.print(c); + c.s << ", "; + exponent.print(c); + c.s << ')'; +} + void power::do_print_csrc(const print_csrc & c, unsigned level) const { // Integer powers of symbols are printed in a special, optimized way @@ -170,29 +188,20 @@ void power::do_print_csrc(const print_csrc & c, unsigned level) const c.s << '('; else { exp = -exp; - if (is_a(c)) - c.s << "recip("; - else - c.s << "1.0/("; + 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)) { - if (is_a(c)) - c.s << "recip("; - else - c.s << "1.0/("; + c.s << "1.0/("; basis.print(c); c.s << ')'; - // Otherwise, use the pow() or expt() (CLN) functions + // Otherwise, use the pow() function } else { - if (is_a(c)) - c.s << "expt("; - else - c.s << "pow("; + c.s << "pow("; basis.print(c); c.s << ','; exponent.print(c); @@ -222,12 +231,31 @@ 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); + case info_flags::has_indices: { + if (flags & status_flags::has_indices) + return true; + else if (flags & status_flags::has_no_indices) + return false; + else if (basis.info(info_flags::has_indices)) { + setflag(status_flags::has_indices); + clearflag(status_flags::has_no_indices); + return true; + } else { + clearflag(status_flags::has_indices); + setflag(status_flags::has_no_indices); + return false; + } + } } return inherited::info(inf); } @@ -256,6 +284,15 @@ ex power::map(map_function & f) const 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 { if (is_equal(ex_to(s))) @@ -323,6 +360,7 @@ 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) @@ -379,6 +417,14 @@ 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(), @@ -446,8 +492,9 @@ 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)); + } } } @@ -455,7 +502,35 @@ ex power::eval(int level) const if (num_exponent->is_integer() && is_exactly_a(ebasis)) { 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(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)) { @@ -472,8 +547,8 @@ 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); @@ -535,6 +610,30 @@ 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 &); @@ -575,13 +674,66 @@ ex power::conjugate() const 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); @@ -612,17 +764,20 @@ 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(); } ex power::expand(unsigned options) const { - if (options == 0 && (flags & status_flags::expanded)) + if (is_a(basis) && exponent.info(info_flags::integer)) { + // A special case worth optimizing. + setflag(status_flags::expanded); return *this; - + } + const ex expanded_basis = basis.expand(options); const ex expanded_exponent = exponent.expand(options); @@ -702,7 +857,7 @@ 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()); @@ -804,7 +959,7 @@ 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, true), + 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), @@ -812,11 +967,11 @@ 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, true), - 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))); } } @@ -824,7 +979,7 @@ 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)))); } } @@ -834,10 +989,10 @@ 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); @@ -845,14 +1000,31 @@ ex power::expand_add_2(const add & a, unsigned options) 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, unsigned options, bool from_expand) const { GINAC_ASSERT(n.is_integer()); - if (n.is_zero()) + if (n.is_zero()) { return _ex1; + } + + // do not bother to rename indices if there are no any. + if ((!(options & expand_options::expand_rename_idx)) + && m.info(info_flags::has_indices)) + options |= expand_options::expand_rename_idx; + // Leave it to multiplication since dummy indices have to be renamed + if ((options & expand_options::expand_rename_idx) && + (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()); @@ -861,19 +1033,13 @@ ex power::expand_mul(const mul & m, const numeric & n, unsigned options, bool fr 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 - numeric new_coeff = ex_to(cit->coeff).mul(n); - 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; - } - distrseq.push_back(expair(cit->rest, new_coeff)); + 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; }