X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpower.cpp;h=eefd438f9bb334415694e313bf0018e0bae48df7;hp=53342a9e57eef4bd751a614bda3f3d61b543524a;hb=0917777d60656298ba44e092712c2b403bfaf559;hpb=9e2d60e206395fc9908e1f9025e50c76b3d7c182 diff --git a/ginac/power.cpp b/ginac/power.cpp index 53342a9e..eefd438f 100644 --- a/ginac/power.cpp +++ b/ginac/power.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's symbolic exponentiation (basis^exponent). */ /* - * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2001 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 @@ -28,106 +28,67 @@ #include "expairseq.h" #include "add.h" #include "mul.h" +#include "ncmul.h" #include "numeric.h" #include "inifcns.h" -#include "relational.h" +#include "matrix.h" #include "symbol.h" +#include "print.h" #include "archive.h" #include "debugmsg.h" #include "utils.h" -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_NAMESPACE_GINAC GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic) typedef std::vector intvector; ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// default ctor, dtor, copy ctor assignment operator and helpers ////////// -// public - power::power() : basic(TINFO_power) { - debugmsg("power default constructor",LOGLEVEL_CONSTRUCT); -} - -power::~power() -{ - debugmsg("power destructor",LOGLEVEL_DESTRUCT); - destroy(false); -} - -power::power(const power & other) -{ - debugmsg("power copy constructor",LOGLEVEL_CONSTRUCT); - copy(other); -} - -const power & power::operator=(const power & other) -{ - debugmsg("power operator=",LOGLEVEL_ASSIGNMENT); - if (this != &other) { - destroy(true); - copy(other); - } - return *this; + debugmsg("power default ctor",LOGLEVEL_CONSTRUCT); } -// protected - void power::copy(const power & other) { inherited::copy(other); - basis=other.basis; - exponent=other.exponent; + basis = other.basis; + exponent = other.exponent; } -void power::destroy(bool call_parent) -{ - if (call_parent) inherited::destroy(call_parent); -} +DEFAULT_DESTROY(power) ////////// -// other constructors +// other ctors ////////// -// public - power::power(const ex & lh, const ex & rh) : basic(TINFO_power), basis(lh), exponent(rh) { - debugmsg("power constructor from ex,ex",LOGLEVEL_CONSTRUCT); - GINAC_ASSERT(basis.return_type()==return_types::commutative); + debugmsg("power ctor from ex,ex",LOGLEVEL_CONSTRUCT); } +/** Ctor from an ex and a bare numeric. This is somewhat more efficient than + * the normal ctor from two ex whenever it can be used. */ power::power(const ex & lh, const numeric & rh) : basic(TINFO_power), basis(lh), exponent(rh) { - debugmsg("power constructor from ex,numeric",LOGLEVEL_CONSTRUCT); - GINAC_ASSERT(basis.return_type()==return_types::commutative); + debugmsg("power ctor from ex,numeric",LOGLEVEL_CONSTRUCT); } ////////// // archiving ////////// -/** Construct object from archive_node. */ power::power(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) { - debugmsg("power constructor from archive_node", LOGLEVEL_CONSTRUCT); + debugmsg("power ctor from archive_node", LOGLEVEL_CONSTRUCT); n.find_ex("basis", basis, sym_lst); n.find_ex("exponent", exponent, sym_lst); } -/** Unarchive the object. */ -ex power::unarchive(const archive_node &n, const lst &sym_lst) -{ - return (new power(n, sym_lst))->setflag(status_flags::dynallocated); -} - -/** Archive the object. */ void power::archive(archive_node &n) const { inherited::archive(n); @@ -135,116 +96,118 @@ void power::archive(archive_node &n) const n.add_ex("exponent", exponent); } +DEFAULT_UNARCHIVE(power) + ////////// // functions overriding virtual functions from bases classes ////////// // public -basic * power::duplicate() const -{ - debugmsg("power duplicate",LOGLEVEL_DUPLICATE); - return new power(*this); -} - -void power::print(std::ostream & os, unsigned upper_precedence) const +static void print_sym_pow(const print_context & c, const symbol &x, int exp) { - debugmsg("power print",LOGLEVEL_PRINT); - if (exponent.is_equal(_ex1_2())) { - os << "sqrt(" << basis << ")"; + // 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 hack is really necessary. + if (exp == 1) { + x.print(c); + } else if (exp == 2) { + x.print(c); + c.s << "*"; + x.print(c); + } else if (exp & 1) { + x.print(c); + c.s << "*"; + print_sym_pow(c, x, exp-1); } else { - if (precedence<=upper_precedence) os << "("; - basis.print(os,precedence); - os << "^"; - exponent.print(os,precedence); - if (precedence<=upper_precedence) os << ")"; + c.s << "("; + print_sym_pow(c, x, exp >> 1); + c.s << ")*("; + print_sym_pow(c, x, exp >> 1); + c.s << ")"; } } -void power::printraw(std::ostream & os) const +void power::print(const print_context & c, unsigned level) const { - debugmsg("power printraw",LOGLEVEL_PRINT); + debugmsg("power print", LOGLEVEL_PRINT); - os << "power("; - basis.printraw(os); - os << ","; - exponent.printraw(os); - os << ",hash=" << hashvalue << ",flags=" << flags << ")"; -} + if (is_of_type(c, print_tree)) { -void power::printtree(std::ostream & os, unsigned indent) const -{ - debugmsg("power printtree",LOGLEVEL_PRINT); - - os << std::string(indent,' ') << "power: " - << "hash=" << hashvalue - << " (0x" << std::hex << hashvalue << std::dec << ")" - << ", flags=" << flags << std::endl; - basis.printtree(os, indent+delta_indent); - exponent.printtree(os, indent+delta_indent); -} + inherited::print(c, level); -static void print_sym_pow(std::ostream & os, unsigned type, const symbol &x, int exp) -{ - // Optimal output of integer powers of symbols to aid compiler CSE - if (exp == 1) { - x.printcsrc(os, type, 0); - } else if (exp == 2) { - x.printcsrc(os, type, 0); - os << "*"; - x.printcsrc(os, type, 0); - } else if (exp & 1) { - x.printcsrc(os, 0); - os << "*"; - print_sym_pow(os, type, x, exp-1); - } else { - os << "("; - print_sym_pow(os, type, x, exp >> 1); - os << ")*("; - print_sym_pow(os, type, x, exp >> 1); - os << ")"; - } -} + } else if (is_of_type(c, print_csrc)) { -void power::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const -{ - debugmsg("power print csrc", LOGLEVEL_PRINT); - - // Integer powers of symbols are printed in a special, optimized way - if (exponent.info(info_flags::integer) - && (is_ex_exactly_of_type(basis, symbol) || is_ex_exactly_of_type(basis, constant))) { - int exp = ex_to_numeric(exponent).to_int(); - if (exp > 0) - os << "("; - else { - exp = -exp; - if (type == csrc_types::ctype_cl_N) - os << "recip("; + // Integer powers of symbols are printed in a special, optimized way + if (exponent.info(info_flags::integer) + && (is_ex_exactly_of_type(basis, symbol) || is_ex_exactly_of_type(basis, constant))) { + int exp = ex_to_numeric(exponent).to_int(); + if (exp > 0) + c.s << '('; + else { + exp = -exp; + if (is_of_type(c, print_csrc_cl_N)) + c.s << "recip("; + else + c.s << "1.0/("; + } + print_sym_pow(c, ex_to_symbol(basis), exp); + c.s << ')'; + + // ^-1 is printed as "1.0/" or with the recip() function of CLN + } else if (exponent.compare(_num_1()) == 0) { + if (is_of_type(c, print_csrc_cl_N)) + c.s << "recip("; else - os << "1.0/("; - } - print_sym_pow(os, type, static_cast(*basis.bp), exp); - os << ")"; + c.s << "1.0/("; + basis.print(c); + c.s << ')'; - // ^-1 is printed as "1.0/" or with the recip() function of CLN - } else if (exponent.compare(_num_1()) == 0) { - if (type == csrc_types::ctype_cl_N) - os << "recip("; - else - os << "1.0/("; - basis.bp->printcsrc(os, type, 0); - os << ")"; + // Otherwise, use the pow() or expt() (CLN) functions + } else { + if (is_of_type(c, print_csrc_cl_N)) + c.s << "expt("; + else + c.s << "pow("; + basis.print(c); + c.s << ','; + exponent.print(c); + c.s << ')'; + } - // Otherwise, use the pow() or expt() (CLN) functions } else { - if (type == csrc_types::ctype_cl_N) - os << "expt("; - else - os << "pow("; - basis.bp->printcsrc(os, type, 0); - os << ","; - exponent.bp->printcsrc(os, type, 0); - os << ")"; + + if (exponent.is_equal(_ex1_2())) { + if (is_of_type(c, print_latex)) + c.s << "\\sqrt{"; + else + c.s << "sqrt("; + basis.print(c); + if (is_of_type(c, print_latex)) + c.s << '}'; + else + c.s << ')'; + } else { + if (precedence() <= level) { + if (is_of_type(c, print_latex)) + c.s << "{("; + else + c.s << "("; + } + basis.print(c, precedence()); + c.s << '^'; + if (is_of_type(c, print_latex)) + c.s << '{'; + exponent.print(c, precedence()); + if (is_of_type(c, print_latex)) + c.s << '}'; + if (precedence() <= level) { + if (is_of_type(c, print_latex)) + c.s << ")}"; + else + c.s << ')'; + } + } } } @@ -279,43 +242,64 @@ ex & power::let_op(int i) return i==0 ? basis : exponent; } -int power::degree(const symbol & s) const +ex power::map(map_func f) const +{ + return (new power(f(basis), f(exponent)))->setflag(status_flags::dynallocated); +} + +int power::degree(const ex & s) const { if (is_exactly_of_type(*exponent.bp,numeric)) { - if ((*basis.bp).compare(s)==0) - return ex_to_numeric(exponent).to_int(); - else + if (basis.is_equal(s)) { + if (ex_to_numeric(exponent).is_integer()) + return ex_to_numeric(exponent).to_int(); + else + return 0; + } else return basis.degree(s) * ex_to_numeric(exponent).to_int(); } return 0; } -int power::ldegree(const symbol & s) const +int power::ldegree(const ex & s) const { if (is_exactly_of_type(*exponent.bp,numeric)) { - if ((*basis.bp).compare(s)==0) - return ex_to_numeric(exponent).to_int(); - else + if (basis.is_equal(s)) { + if (ex_to_numeric(exponent).is_integer()) + return ex_to_numeric(exponent).to_int(); + else + return 0; + } else return basis.ldegree(s) * ex_to_numeric(exponent).to_int(); } return 0; } -ex power::coeff(const symbol & s, int n) const +ex power::coeff(const ex & s, int n) const { - if ((*basis.bp).compare(s)!=0) { + if (!basis.is_equal(s)) { // basis not equal to s - if (n==0) { + if (n == 0) return *this; - } else { + else return _ex0(); + } else { + // basis equal to s + if (is_exactly_of_type(*exponent.bp, numeric) && ex_to_numeric(exponent).is_integer()) { + // integer exponent + int int_exp = ex_to_numeric(exponent).to_int(); + if (n == int_exp) + return _ex1(); + else + return _ex0(); + } else { + // non-integer exponents are treated as zero + if (n == 0) + return *this; + else + return _ex0(); } - } else if (is_exactly_of_type(*exponent.bp,numeric)&& - (static_cast(*exponent.bp).compare(numeric(n))==0)) { - return _ex1(); } - - return _ex0(); } ex power::eval(int level) const @@ -340,26 +324,27 @@ ex power::eval(int level) const const ex & ebasis = level==1 ? basis : basis.eval(level-1); const ex & eexponent = level==1 ? exponent : exponent.eval(level-1); - bool basis_is_numerical = 0; - bool exponent_is_numerical = 0; + bool basis_is_numerical = false; + bool exponent_is_numerical = false; numeric * num_basis; numeric * num_exponent; if (is_exactly_of_type(*ebasis.bp,numeric)) { - basis_is_numerical = 1; + basis_is_numerical = true; num_basis = static_cast(ebasis.bp); } if (is_exactly_of_type(*eexponent.bp,numeric)) { - exponent_is_numerical = 1; + exponent_is_numerical = true; num_exponent = static_cast(eexponent.bp); } // ^(x,0) -> 1 (0^0 also handled here) - if (eexponent.is_zero()) + if (eexponent.is_zero()) { if (ebasis.is_zero()) throw (std::domain_error("power::eval(): pow(0,0) is undefined")); else return _ex1(); + } // ^(x,1) -> x if (eexponent.is_equal(_ex1())) @@ -379,92 +364,101 @@ ex power::eval(int level) const if (ebasis.is_equal(_ex1())) return _ex1(); - if (basis_is_numerical && exponent_is_numerical) { + if (exponent_is_numerical) { + // ^(c1,c2) -> c1^c2 (c1, c2 numeric(), // except if c1,c2 are rational, but c1^c2 is not) - bool basis_is_crational = num_basis->is_crational(); - bool exponent_is_crational = num_exponent->is_crational(); - numeric res = (*num_basis).power(*num_exponent); + if (basis_is_numerical) { + bool basis_is_crational = num_basis->is_crational(); + bool exponent_is_crational = num_exponent->is_crational(); + numeric res = num_basis->power(*num_exponent); - if ((!basis_is_crational || !exponent_is_crational) - || res.is_crational()) { - return res; - } - GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now - // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer - if (basis_is_crational && exponent_is_crational - && num_exponent->is_real() - && !num_exponent->is_integer()) { - numeric n = num_exponent->numer(); - numeric m = num_exponent->denom(); - numeric r; - numeric q = iquo(n, m, r); - if (r.is_negative()) { - r = r.add(m); - q = q.sub(_num1()); + if ((!basis_is_crational || !exponent_is_crational) + || res.is_crational()) { + return res; } - if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1 - return this->hold(); - else { - epvector res; - res.push_back(expair(ebasis,r.div(m))); - return (new mul(res,ex(num_basis->power(q))))->setflag(status_flags::dynallocated | status_flags::evaluated); + GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now + + // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer + if (basis_is_crational && exponent_is_crational + && num_exponent->is_real() + && !num_exponent->is_integer()) { + numeric n = num_exponent->numer(); + numeric m = num_exponent->denom(); + numeric r; + numeric q = iquo(n, m, r); + if (r.is_negative()) { + r = r.add(m); + q = q.sub(_num1()); + } + if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1 + return this->hold(); + else { + epvector res; + res.push_back(expair(ebasis,r.div(m))); + return (new mul(res,ex(num_basis->power_dyn(q))))->setflag(status_flags::dynallocated | status_flags::evaluated); + } } } - } - // ^(^(x,c1),c2) -> ^(x,c1*c2) - // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1, - // case c1==1 should not happen, see below!) - if (exponent_is_numerical && is_ex_exactly_of_type(ebasis,power)) { - const power & sub_power = ex_to_power(ebasis); - const ex & sub_basis = sub_power.basis; - const ex & sub_exponent = sub_power.exponent; - if (is_ex_exactly_of_type(sub_exponent,numeric)) { - const numeric & num_sub_exponent = ex_to_numeric(sub_exponent); - GINAC_ASSERT(num_sub_exponent!=numeric(1)); - if (num_exponent->is_integer() || abs(num_sub_exponent)<1) { - return power(sub_basis,num_sub_exponent.mul(*num_exponent)); + // ^(^(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)) { + const power & sub_power = ex_to_power(ebasis); + const ex & sub_basis = sub_power.basis; + const ex & sub_exponent = sub_power.exponent; + if (is_ex_exactly_of_type(sub_exponent,numeric)) { + const numeric & num_sub_exponent = ex_to_numeric(sub_exponent); + GINAC_ASSERT(num_sub_exponent!=numeric(1)); + 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 (exponent_is_numerical && num_exponent->is_integer() && - is_ex_exactly_of_type(ebasis,mul)) { - return expand_mul(ex_to_mul(ebasis), *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)) { + return expand_mul(ex_to_mul(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 (exponent_is_numerical && is_ex_exactly_of_type(ebasis,mul)) { - GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above - const mul & mulref=ex_to_mul(ebasis); - if (!mulref.overall_coeff.is_equal(_ex1())) { - const numeric & num_coeff=ex_to_numeric(mulref.overall_coeff); - if (num_coeff.is_real()) { - if (num_coeff.is_positive()>0) { - mul * mulp=new mul(mulref); - 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) { - mul * mulp=new mul(mulref); - mulp->overall_coeff=_ex_1(); + // ^(*(...,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)) { + GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above + const mul & mulref = ex_to_mul(ebasis); + if (!mulref.overall_coeff.is_equal(_ex1())) { + const numeric & num_coeff = ex_to_numeric(mulref.overall_coeff); + if (num_coeff.is_real()) { + if (num_coeff.is_positive()) { + mul * mulp = new mul(mulref); + mulp->overall_coeff = _ex1(); mulp->clearflag(status_flags::evaluated); mulp->clearflag(status_flags::hash_calculated); return (new mul(power(*mulp,exponent), - power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated); + power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated); + } else { + GINAC_ASSERT(num_coeff.compare(_num0())<0); + if (num_coeff.compare(_num_1())!=0) { + mul * mulp = new mul(mulref); + mulp->overall_coeff = _ex_1(); + mulp->clearflag(status_flags::evaluated); + mulp->clearflag(status_flags::hash_calculated); + return (new mul(power(*mulp,exponent), + power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated); + } } } } } + + // ^(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)) { + return ncmul(exvector(num_exponent->to_int(), ebasis), true); + } } - + if (are_ex_trivially_equal(ebasis,basis) && are_ex_trivially_equal(eexponent,exponent)) { return this->hold(); @@ -496,17 +490,28 @@ ex power::evalf(int level) const return power(ebasis,eexponent); } -ex power::subs(const lst & ls, const lst & lr) const +ex power::evalm(void) const { - const ex & subsed_basis=basis.subs(ls,lr); - const ex & subsed_exponent=exponent.subs(ls,lr); - - if (are_ex_trivially_equal(basis,subsed_basis)&& - are_ex_trivially_equal(exponent,subsed_exponent)) { - return *this; + ex ebasis = basis.evalm(); + ex eexponent = exponent.evalm(); + if (is_ex_of_type(ebasis,matrix)) { + if (is_ex_of_type(eexponent,numeric)) { + return (new matrix(ex_to_matrix(ebasis).pow(eexponent)))->setflag(status_flags::dynallocated); + } } - - return power(subsed_basis, subsed_exponent); + 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); + + 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::simplify_ncmul(const exvector & v) const @@ -529,9 +534,9 @@ ex power::derivative(const symbol & s) const return mul(newseq, exponent); } else { // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b) - return mul(power(basis, exponent), + return mul(*this, add(mul(exponent.diff(s), log(basis)), - mul(mul(exponent, basis.diff(s)), power(basis, -1)))); + mul(mul(exponent, basis.diff(s)), power(basis, _ex_1())))); } } @@ -564,34 +569,62 @@ ex power::expand(unsigned options) const return *this; ex expanded_basis = basis.expand(options); + ex expanded_exponent = exponent.expand(options); - if (!is_ex_exactly_of_type(exponent,numeric) || - !ex_to_numeric(exponent).is_integer()) { - if (are_ex_trivially_equal(basis,expanded_basis)) { + // x^(a+b) -> x^a * x^b + if (is_ex_exactly_of_type(expanded_exponent, add)) { + const add &a = ex_to_add(expanded_exponent); + exvector distrseq; + distrseq.reserve(a.seq.size() + 1); + epvector::const_iterator last = a.seq.end(); + epvector::const_iterator cit = a.seq.begin(); + while (cit!=last) { + distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(*cit))); + cit++; + } + + // Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor + if (ex_to_numeric(a.overall_coeff).is_integer()) { + const numeric &num_exponent = ex_to_numeric(a.overall_coeff); + int int_exponent = num_exponent.to_int(); + if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis, add)) + distrseq.push_back(expand_add(ex_to_add(expanded_basis), int_exponent)); + else + distrseq.push_back(power(expanded_basis, a.overall_coeff)); + } else + distrseq.push_back(power(expanded_basis, a.overall_coeff)); + + // 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(); + } + + if (!is_ex_exactly_of_type(expanded_exponent, numeric) || + !ex_to_numeric(expanded_exponent).is_integer()) { + if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) { return this->hold(); } else { - return (new power(expanded_basis,exponent))->setflag(status_flags::dynallocated | status_flags::expanded); + return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | status_flags::expanded); } } // integer numeric exponent - const numeric & num_exponent = ex_to_numeric(exponent); + const numeric & num_exponent = ex_to_numeric(expanded_exponent); int int_exponent = num_exponent.to_int(); - if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add)) { + // (x+y)^n, n>0 + if (int_exponent > 0 && is_ex_exactly_of_type(expanded_basis,add)) return expand_add(ex_to_add(expanded_basis), int_exponent); - } - if (is_ex_exactly_of_type(expanded_basis,mul)) { + // (x*y)^n -> x^n * y^n + if (is_ex_exactly_of_type(expanded_basis,mul)) return expand_mul(ex_to_mul(expanded_basis), num_exponent); - } // cannot expand further - if (are_ex_trivially_equal(basis,expanded_basis)) { + if (are_ex_trivially_equal(basis,expanded_basis) && are_ex_trivially_equal(exponent,expanded_exponent)) return this->hold(); - } else { - return (new power(expanded_basis,exponent))->setflag(status_flags::dynallocated | status_flags::expanded); - } + else + return (new power(expanded_basis,expanded_exponent))->setflag(status_flags::dynallocated | status_flags::expanded); } ////////// @@ -637,11 +670,10 @@ ex power::expand_add(const add & a, int n) const !is_ex_exactly_of_type(ex_to_power(b).basis,add) || !is_ex_exactly_of_type(ex_to_power(b).basis,mul) || !is_ex_exactly_of_type(ex_to_power(b).basis,power)); - if (is_ex_exactly_of_type(b,mul)) { + if (is_ex_exactly_of_type(b,mul)) term.push_back(expand_mul(ex_to_mul(b),numeric(k[l]))); - } else { + else term.push_back(power(b,k[l])); - } } const ex & b = a.op(l); @@ -652,18 +684,17 @@ ex power::expand_add(const add & a, int n) const !is_ex_exactly_of_type(ex_to_power(b).basis,add) || !is_ex_exactly_of_type(ex_to_power(b).basis,mul) || !is_ex_exactly_of_type(ex_to_power(b).basis,power)); - if (is_ex_exactly_of_type(b,mul)) { + if (is_ex_exactly_of_type(b,mul)) term.push_back(expand_mul(ex_to_mul(b),numeric(n-k_cum[m-2]))); - } else { + 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)); // increment k[] - l=m-2; + 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 ); @@ -712,15 +739,15 @@ 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(); + unsigned a_nops = a.nops(); sum.reserve((a_nops*(a_nops+1))/2); - epvector::const_iterator last=a.seq.end(); - + 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; + 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) || @@ -729,7 +756,7 @@ ex power::expand_add_2(const add & a) const !is_ex_exactly_of_type(ex_to_power(r).basis,add) || !is_ex_exactly_of_type(ex_to_power(r).basis,mul) || !is_ex_exactly_of_type(ex_to_power(r).basis,power)); - + if (are_ex_trivially_equal(c,_ex1())) { if (is_ex_exactly_of_type(r,mul)) { sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()), @@ -749,23 +776,23 @@ ex power::expand_add_2(const add & a) const } for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) { - const ex & r1=(*cit1).rest; - const ex & c1=(*cit1).coeff; + 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_numeric(c)).mul_dyn(ex_to_numeric(c1)))); } } - + GINAC_ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2); - + // second part: add terms coming from overall_factor (if != 0) - if (!a.overall_coeff.is_equal(_ex0())) { + if (!a.overall_coeff.is_zero()) { for (epvector::const_iterator cit=a.seq.begin(); cit!=a.seq.end(); ++cit) { sum.push_back(a.combine_pair_with_coeff_to_pair(*cit,ex_to_numeric(a.overall_coeff).mul_dyn(_num2()))); } sum.push_back(expair(ex_to_numeric(a.overall_coeff).power_dyn(_num2()),_ex1())); } - + GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2); return (new add(sum))->setflag(status_flags::dynallocated | status_flags::expanded); @@ -775,7 +802,7 @@ ex power::expand_add_2(const add & a) const * @see power::expand */ ex power::expand_mul(const mul & m, const numeric & n) const { - if (n.is_equal(_num0())) + if (n.is_zero()) return _ex1(); epvector distrseq; @@ -795,31 +822,6 @@ ex power::expand_mul(const mul & m, const numeric & n) const return (new mul(distrseq,ex_to_numeric(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated); } -/* -ex power::expand_commutative_3(const ex & basis, const numeric & exponent, - unsigned options) const -{ - // obsolete - - exvector distrseq; - epvector splitseq; - - const add & addref=static_cast(*basis.bp); - - splitseq=addref.seq; - splitseq.pop_back(); - ex first_operands=add(splitseq); - ex last_operand=addref.recombine_pair_to_ex(*(addref.seq.end()-1)); - - int n=exponent.to_int(); - for (int k=0; k<=n; k++) { - distrseq.push_back(binomial(n,k) * power(first_operands,numeric(k)) - * power(last_operand,numeric(n-k))); - } - return ex((new add(distrseq))->setflag(status_flags::expanded | status_flags::dynallocated)).expand(options); -} -*/ - /* ex power::expand_noncommutative(const ex & basis, const numeric & exponent, unsigned options) const @@ -832,21 +834,6 @@ ex power::expand_noncommutative(const ex & basis, const numeric & exponent, } */ -////////// -// static member variables -////////// - -// protected - -unsigned power::precedence = 60; - -////////// -// global constants -////////// - -const power some_power; -const std::type_info & typeid_power=typeid(some_power); - // helper function ex sqrt(const ex & a) @@ -854,6 +841,4 @@ ex sqrt(const ex & a) return power(a,_ex1_2()); } -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC