X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Fpower.cpp;h=8ec1945f718ea833571b978448ceee7d68469f3f;hb=e009cb7984c4971df3b9e036eaead640095f46d5;hp=a459150dbe4d5a692bf0a47e05ee13e8285f97a8;hpb=487e5659efe401683eee0381b0d23f967ffffc3c;p=ginac.git diff --git a/ginac/power.cpp b/ginac/power.cpp index a459150d..8ec1945f 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 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2000 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 @@ -29,8 +29,18 @@ #include "add.h" #include "mul.h" #include "numeric.h" +#include "inifcns.h" #include "relational.h" #include "symbol.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 vector intvector; @@ -51,13 +61,13 @@ power::~power() destroy(0); } -power::power(power const & other) +power::power(const power & other) { debugmsg("power copy constructor",LOGLEVEL_CONSTRUCT); copy(other); } -power const & power::operator=(power const & other) +const power & power::operator=(const power & other) { debugmsg("power operator=",LOGLEVEL_ASSIGNMENT); if (this != &other) { @@ -69,16 +79,16 @@ power const & power::operator=(power const & other) // protected -void power::copy(power const & other) +void power::copy(const power & other) { - basic::copy(other); + inherited::copy(other); basis=other.basis; exponent=other.exponent; } void power::destroy(bool call_parent) { - if (call_parent) basic::destroy(call_parent); + if (call_parent) inherited::destroy(call_parent); } ////////// @@ -87,16 +97,42 @@ void power::destroy(bool call_parent) // public -power::power(ex const & lh, ex const & rh) : basic(TINFO_power), basis(lh), exponent(rh) +power::power(const ex & lh, const ex & rh) : basic(TINFO_power), basis(lh), exponent(rh) { debugmsg("power constructor from ex,ex",LOGLEVEL_CONSTRUCT); - ASSERT(basis.return_type()==return_types::commutative); + GINAC_ASSERT(basis.return_type()==return_types::commutative); } -power::power(ex const & lh, numeric const & rh) : basic(TINFO_power), basis(lh), exponent(rh) +power::power(const ex & lh, const numeric & rh) : basic(TINFO_power), basis(lh), exponent(rh) { debugmsg("power constructor from ex,numeric",LOGLEVEL_CONSTRUCT); - ASSERT(basis.return_type()==return_types::commutative); + GINAC_ASSERT(basis.return_type()==return_types::commutative); +} + +////////// +// 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); + 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); + n.add_ex("basis", basis); + n.add_ex("exponent", exponent); } ////////// @@ -111,34 +147,142 @@ basic * power::duplicate() const return new power(*this); } -bool power::info(unsigned inf) const +void power::print(ostream & os, unsigned upper_precedence) const +{ + debugmsg("power print",LOGLEVEL_PRINT); + if (exponent.is_equal(_ex1_2())) { + os << "sqrt(" << basis << ")"; + } else { + if (precedence<=upper_precedence) os << "("; + basis.print(os,precedence); + os << "^"; + exponent.print(os,precedence); + if (precedence<=upper_precedence) os << ")"; + } +} + +void power::printraw(ostream & os) const +{ + debugmsg("power printraw",LOGLEVEL_PRINT); + + os << "power("; + basis.printraw(os); + os << ","; + exponent.printraw(os); + os << ",hash=" << hashvalue << ",flags=" << flags << ")"; +} + +void power::printtree(ostream & os, unsigned indent) const +{ + debugmsg("power printtree",LOGLEVEL_PRINT); + + os << string(indent,' ') << "power: " + << "hash=" << hashvalue << " (0x" << hex << hashvalue << dec << ")" + << ", flags=" << flags << endl; + basis.printtree(os,indent+delta_indent); + exponent.printtree(os,indent+delta_indent); +} + +static void print_sym_pow(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 << ")"; + } +} + +void power::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const { - if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial) { - return exponent.info(info_flags::nonnegint); - } else if (inf==info_flags::rational_function) { - return exponent.info(info_flags::integer); + 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("; + else + os << "1.0/("; + } + print_sym_pow(os, type, static_cast(*basis.bp), exp); + os << ")"; + + // ^-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 { - return basic::info(inf); + 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 << ")"; } } -int power::nops() const +bool power::info(unsigned inf) const +{ + switch (inf) { + case info_flags::polynomial: + case info_flags::integer_polynomial: + case info_flags::cinteger_polynomial: + case info_flags::rational_polynomial: + case info_flags::crational_polynomial: + return exponent.info(info_flags::nonnegint); + case info_flags::rational_function: + return exponent.info(info_flags::integer); + case info_flags::algebraic: + return (!exponent.info(info_flags::integer) || + basis.info(inf)); + } + return inherited::info(inf); +} + +unsigned power::nops() const { return 2; } -ex & power::let_op(int const i) +ex & power::let_op(int i) { - ASSERT(i>=0); - ASSERT(i<2); + GINAC_ASSERT(i>=0); + GINAC_ASSERT(i<2); return i==0 ? basis : exponent; } -int power::degree(symbol const & s) const +int power::degree(const symbol & s) const { if (is_exactly_of_type(*exponent.bp,numeric)) { - if ((*basis.bp).compare(s)==0) + if ((*basis.bp).compare(s)==0) return ex_to_numeric(exponent).to_int(); else return basis.degree(s) * ex_to_numeric(exponent).to_int(); @@ -146,10 +290,10 @@ int power::degree(symbol const & s) const return 0; } -int power::ldegree(symbol const & s) const +int power::ldegree(const symbol & s) const { if (is_exactly_of_type(*exponent.bp,numeric)) { - if ((*basis.bp).compare(s)==0) + if ((*basis.bp).compare(s)==0) return ex_to_numeric(exponent).to_int(); else return basis.ldegree(s) * ex_to_numeric(exponent).to_int(); @@ -157,28 +301,28 @@ int power::ldegree(symbol const & s) const return 0; } -ex power::coeff(symbol const & s, int const n) const +ex power::coeff(const symbol & s, int n) const { if ((*basis.bp).compare(s)!=0) { // basis not equal to s if (n==0) { return *this; } else { - return exZERO(); + return _ex0(); } } else if (is_exactly_of_type(*exponent.bp,numeric)&& - (static_cast(*exponent.bp).compare(numeric(n))==0)) { - return exONE(); + (static_cast(*exponent.bp).compare(numeric(n))==0)) { + return _ex1(); } - return exZERO(); + return _ex0(); } ex power::eval(int level) const { // simplifications: ^(x,0) -> 1 (0^0 handled here) // ^(x,1) -> x - // ^(0,x) -> 0 (except if x is real and negative, in which case an exception is thrown) + // ^(0,c1) -> 0 or exception (depending on real value of c1) // ^(1,x) -> 1 // ^(c1,c2) -> *(c1^n,c1^(c2-n)) (c1, c2 numeric(), 0<(c2-n)<1 except if c1,c2 are rational, but c1^c2 is not) // ^(^(x,c1),c2) -> ^(x,c1*c2) (c1, c2 numeric(), c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!) @@ -187,101 +331,98 @@ ex power::eval(int level) const // ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1, c2 numeric(), c1<0) debugmsg("power eval",LOGLEVEL_MEMBER_FUNCTION); - - if ((level==1)&&(flags & status_flags::evaluated)) { + + if ((level==1) && (flags & status_flags::evaluated)) return *this; - } else if (level == -max_recursion_level) { + else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); - } - ex const & ebasis = level==1 ? basis : basis.eval(level-1); - ex const & eexponent = level==1 ? exponent : exponent.eval(level-1); - - bool basis_is_numerical=0; - bool exponent_is_numerical=0; + 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; numeric * num_basis; numeric * num_exponent; - + if (is_exactly_of_type(*ebasis.bp,numeric)) { - basis_is_numerical=1; - num_basis=static_cast(ebasis.bp); + basis_is_numerical = 1; + num_basis = static_cast(ebasis.bp); } if (is_exactly_of_type(*eexponent.bp,numeric)) { - exponent_is_numerical=1; - num_exponent=static_cast(eexponent.bp); + exponent_is_numerical = 1; + num_exponent = static_cast(eexponent.bp); } - + // ^(x,0) -> 1 (0^0 also handled here) if (eexponent.is_zero()) - return exONE(); - + 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(exONE())) + if (eexponent.is_equal(_ex1())) return ebasis; - - // ^(0,x) -> 0 (except if x is real and negative) - if (ebasis.is_zero()) { - if (exponent_is_numerical && num_exponent->is_negative()) { - throw(std::overflow_error("power::eval(): division by zero")); - } else - return exZERO(); + + // ^(0,c1) -> 0 or exception (depending on real value of c1) + if (ebasis.is_zero() && exponent_is_numerical) { + if ((num_exponent->real()).is_zero()) + throw (std::domain_error("power::eval(): pow(0,I) is undefined")); + else if ((num_exponent->real()).is_negative()) + throw (std::overflow_error("power::eval(): division by zero")); + else + return _ex0(); } - + // ^(1,x) -> 1 - if (ebasis.is_equal(exONE())) - return exONE(); - + if (ebasis.is_equal(_ex1())) + return _ex1(); + if (basis_is_numerical && exponent_is_numerical) { // ^(c1,c2) -> c1^c2 (c1, c2 numeric(), // except if c1,c2 are rational, but c1^c2 is not) - bool basis_is_rational = num_basis->is_rational(); - bool exponent_is_rational = num_exponent->is_rational(); + 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_rational || !exponent_is_rational) - || res.is_rational()) { + if ((!basis_is_crational || !exponent_is_crational) + || res.is_crational()) { return res; } - ASSERT(!num_exponent->is_integer()); // has been handled by now + 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_rational && exponent_is_rational + if (basis_is_crational && exponent_is_crational && num_exponent->is_real() && !num_exponent->is_integer()) { - numeric r, q, n, m; - n = num_exponent->numer(); - m = num_exponent->denom(); - q = iquo(n, m, r); + 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(numONE()); + 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(2); + epvector res; res.push_back(expair(ebasis,r.div(m))); - res.push_back(expair(ex(num_basis->power(q)),exONE())); - return (new mul(res))->setflag(status_flags::dynallocated | status_flags::evaluated); - /*return mul(num_basis->power(q), - power(ex(*num_basis),ex(r.div(m)))).hold(); - */ - /* return (new mul(num_basis->power(q), - power(*num_basis,r.div(m)).hold()))->setflag(status_flags::dynallocated | status_flags::evaluated); - */ + return (new mul(res,ex(num_basis->power(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!) + // case c1==1 should not happen, see below!) if (exponent_is_numerical && is_ex_exactly_of_type(ebasis,power)) { - power const & sub_power=ex_to_power(ebasis); - ex const & sub_basis=sub_power.basis; - ex const & sub_exponent=sub_power.exponent; + 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)) { - numeric const & num_sub_exponent=ex_to_numeric(sub_exponent); - ASSERT(num_sub_exponent!=numeric(1)); + 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)); } @@ -293,28 +434,28 @@ ex power::eval(int level) const 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)) { - ASSERT(!num_exponent->is_integer()); // should have been handled above - mul const & mulref=ex_to_mul(ebasis); - if (!mulref.overall_coeff.is_equal(exONE())) { - numeric const & num_coeff=ex_to_numeric(mulref.overall_coeff); + 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=exONE(); + 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 { - ASSERT(num_coeff.compare(numZERO())<0); - if (num_coeff.compare(numMINUSONE())!=0) { + GINAC_ASSERT(num_coeff.compare(_num0())<0); + if (num_coeff.compare(_num_1())!=0) { mul * mulp=new mul(mulref); - mulp->overall_coeff=exMINUSONE(); + mulp->overall_coeff=_ex_1(); mulp->clearflag(status_flags::evaluated); mulp->clearflag(status_flags::hash_calculated); return (new mul(power(*mulp,exponent), @@ -342,22 +483,25 @@ ex power::evalf(int level) const ex eexponent; if (level==1) { - ebasis=basis; - eexponent=exponent; + ebasis = basis; + eexponent = exponent; } else if (level == -max_recursion_level) { throw(std::runtime_error("max recursion level reached")); } else { - ebasis=basis.evalf(level-1); - eexponent=exponent.evalf(level-1); + ebasis = basis.evalf(level-1); + if (!is_ex_exactly_of_type(eexponent,numeric)) + eexponent = exponent.evalf(level-1); + else + eexponent = exponent; } return power(ebasis,eexponent); } -ex power::subs(lst const & ls, lst const & lr) const +ex power::subs(const lst & ls, const lst & lr) const { - ex const & subsed_basis=basis.subs(ls,lr); - ex const & subsed_exponent=exponent.subs(ls,lr); + 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)) { @@ -367,17 +511,32 @@ ex power::subs(lst const & ls, lst const & lr) const return power(subsed_basis, subsed_exponent); } -ex power::simplify_ncmul(exvector const & v) const +ex power::simplify_ncmul(const exvector & v) const { - return basic::simplify_ncmul(v); + return inherited::simplify_ncmul(v); } // protected -int power::compare_same_type(basic const & other) const +/** Implementation of ex::diff() for a power. + * @see ex::diff */ +ex power::derivative(const symbol & s) const { - ASSERT(is_exactly_of_type(other, power)); - power const & o=static_cast(const_cast(other)); + if (exponent.info(info_flags::real)) { + // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below) + return mul(mul(exponent, power(basis, exponent - _ex1())), basis.diff(s)); + } else { + // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b) + return mul(power(basis, exponent), + add(mul(exponent.diff(s), log(basis)), + mul(mul(exponent, basis.diff(s)), power(basis, -1)))); + } +} + +int power::compare_same_type(const basic & other) const +{ + GINAC_ASSERT(is_exactly_of_type(other, power)); + const power & o=static_cast(const_cast(other)); int cmpval; cmpval=basis.compare(o.basis); @@ -399,36 +558,41 @@ unsigned power::return_type_tinfo(void) const ex power::expand(unsigned options) const { - ex expanded_basis=basis.expand(options); - - if (!is_ex_exactly_of_type(exponent,numeric)|| + if (flags & status_flags::expanded) + return *this; + + ex expanded_basis = basis.expand(options); + + if (!is_ex_exactly_of_type(exponent,numeric) || !ex_to_numeric(exponent).is_integer()) { if (are_ex_trivially_equal(basis,expanded_basis)) { return this->hold(); } else { return (new power(expanded_basis,exponent))-> - setflag(status_flags::dynallocated); + setflag(status_flags::dynallocated | + status_flags::expanded); } } - + // integer numeric exponent - numeric const & num_exponent=ex_to_numeric(exponent); + const numeric & num_exponent = ex_to_numeric(exponent); int int_exponent = num_exponent.to_int(); - + 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)) { return expand_mul(ex_to_mul(expanded_basis), num_exponent); } - + // cannot expand further if (are_ex_trivially_equal(basis,expanded_basis)) { return this->hold(); } else { return (new power(expanded_basis,exponent))-> - setflag(status_flags::dynallocated); + setflag(status_flags::dynallocated | + status_flags::expanded); } } @@ -442,15 +606,14 @@ ex power::expand(unsigned options) const // non-virtual functions in this class ////////// -ex power::expand_add(add const & a, int const n) const +/** expand a^n where a is an add and n is an integer. + * @see power::expand */ +ex power::expand_add(const add & a, int n) const { - // expand a^n where a is an add and n is an integer - - if (n==2) { + if (n==2) return expand_add_2(a); - } - int m=a.nops(); + int m = a.nops(); exvector sum; sum.reserve((n+1)*(m-1)); intvector k(m-1); @@ -459,39 +622,45 @@ ex power::expand_add(add const & a, int const n) const int l; for (int l=0; lsetflag(status_flags::dynallocated)); // increment k[] @@ -535,48 +704,15 @@ ex power::expand_add(add const & a, int const n) const upper_limit[i]=n-k_cum[i-1]; } } - return (new add(sum))->setflag(status_flags::dynallocated); + return (new add(sum))->setflag(status_flags::dynallocated | + status_flags::expanded ); } -/* -ex power::expand_add_2(add const & a) const -{ - // special case: expand a^2 where a is an add - epvector sum; - sum.reserve((a.seq.size()*(a.seq.size()+1))/2); - epvector::const_iterator last=a.seq.end(); - - for (epvector::const_iterator cit0=a.seq.begin(); cit0!=last; ++cit0) { - ex const & b=a.recombine_pair_to_ex(*cit0); - ASSERT(!is_ex_exactly_of_type(b,add)); - ASSERT(!is_ex_exactly_of_type(b,power)|| - !is_ex_exactly_of_type(ex_to_power(b).exponent,numeric)|| - !ex_to_numeric(ex_to_power(b).exponent).is_pos_integer()); - if (is_ex_exactly_of_type(b,mul)) { - sum.push_back(a.split_ex_to_pair(expand_mul(ex_to_mul(b),numTWO()))); - } else { - sum.push_back(a.split_ex_to_pair((new power(b,exTWO()))-> - setflag(status_flags::dynallocated))); - } - for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) { - sum.push_back(a.split_ex_to_pair((new mul(a.recombine_pair_to_ex(*cit0), - a.recombine_pair_to_ex(*cit1)))-> - setflag(status_flags::dynallocated), - exTWO())); - } - } - - ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2); - - return (new add(sum))->setflag(status_flags::dynallocated); -} -*/ - -ex power::expand_add_2(add const & a) 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 { - // special case: expand a^2 where a is an add - epvector sum; unsigned a_nops=a.nops(); sum.reserve((a_nops*(a_nops+1))/2); @@ -585,69 +721,69 @@ ex power::expand_add_2(add const & a) const // 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) { - ex const & r=(*cit0).rest; - ex const & c=(*cit0).coeff; + const ex & r=(*cit0).rest; + const ex & c=(*cit0).coeff; - ASSERT(!is_ex_exactly_of_type(r,add)); - ASSERT(!is_ex_exactly_of_type(r,power)|| + 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_power(r).exponent,numeric)|| !ex_to_numeric(ex_to_power(r).exponent).is_pos_integer()|| !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,exONE())) { + 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),numTWO()),exONE())); + sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()),_ex1())); } else { - sum.push_back(expair((new power(r,exTWO()))->setflag(status_flags::dynallocated), - exONE())); + 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_mul(r),numTWO()), - ex_to_numeric(c).power_dyn(numTWO()))); + sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()), + ex_to_numeric(c).power_dyn(_num2()))); } else { - sum.push_back(expair((new power(r,exTWO()))->setflag(status_flags::dynallocated), - ex_to_numeric(c).power_dyn(numTWO()))); + sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated), + ex_to_numeric(c).power_dyn(_num2()))); } } for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) { - ex const & r1=(*cit1).rest; - ex const & 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), - numTWO().mul(ex_to_numeric(c)).mul_dyn(ex_to_numeric(c1)))); + _num2().mul(ex_to_numeric(c)).mul_dyn(ex_to_numeric(c1)))); } } - ASSERT(sum.size()==(a.seq.size()*(a.seq.size()+1))/2); + 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(exZERO())) { + if (!a.overall_coeff.is_equal(_ex0())) { 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(numTWO()))); + 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(numTWO()),exONE())); + sum.push_back(expair(ex_to_numeric(a.overall_coeff).power_dyn(_num2()),_ex1())); } - ASSERT(sum.size()==(a_nops*(a_nops+1))/2); + GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2); - return (new add(sum))->setflag(status_flags::dynallocated); + return (new add(sum))->setflag(status_flags::dynallocated | + status_flags::expanded ); } -ex power::expand_mul(mul const & m, numeric const & n) 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) const { - // expand m^n where m is a mul and n is and integer - - if (n.is_equal(numZERO())) { - return exONE(); - } + if (n.is_equal(_num0())) + return _ex1(); epvector distrseq; distrseq.reserve(m.seq.size()); - epvector::const_iterator last=m.seq.end(); - epvector::const_iterator cit=m.seq.begin(); + 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)); @@ -660,11 +796,11 @@ ex power::expand_mul(mul const & m, numeric const & n) const ++cit; } return (new mul(distrseq,ex_to_numeric(m.overall_coeff).power_dyn(n))) - ->setflag(status_flags::dynallocated); + ->setflag(status_flags::dynallocated); } /* -ex power::expand_commutative_3(ex const & basis, numeric const & exponent, +ex power::expand_commutative_3(const ex & basis, const numeric & exponent, unsigned options) const { // obsolete @@ -672,7 +808,7 @@ ex power::expand_commutative_3(ex const & basis, numeric const & exponent, exvector distrseq; epvector splitseq; - add const & addref=static_cast(*basis.bp); + const add & addref=static_cast(*basis.bp); splitseq=addref.seq; splitseq.pop_back(); @@ -684,18 +820,17 @@ ex power::expand_commutative_3(ex const & basis, numeric const & exponent, 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::sub_expanded | - status_flags::expanded | - status_flags::dynallocated )). + return ex((new add(distrseq))->setflag(status_flags::expanded | + status_flags::dynallocated )). expand(options); } */ /* -ex power::expand_noncommutative(ex const & basis, numeric const & exponent, +ex power::expand_noncommutative(const ex & basis, const numeric & exponent, unsigned options) const { - ex rest_power=ex(power(basis,exponent.add(numMINUSONE()))). + ex rest_power=ex(power(basis,exponent.add(_num_1()))). expand(options | expand_options::internal_do_not_expand_power_operands); return ex(mul(rest_power,basis),0). @@ -709,11 +844,22 @@ ex power::expand_noncommutative(ex const & basis, numeric const & exponent, // protected -unsigned power::precedence=60; +unsigned power::precedence = 60; ////////// // global constants ////////// const power some_power; -type_info const & typeid_power=typeid(some_power); +const type_info & typeid_power=typeid(some_power); + +// helper function + +ex sqrt(const ex & a) +{ + return power(a,_ex1_2()); +} + +#ifndef NO_NAMESPACE_GINAC +} // namespace GiNaC +#endif // ndef NO_NAMESPACE_GINAC