* 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
#include "expairseq.h"
#include "add.h"
#include "mul.h"
+#include "ncmul.h"
#include "numeric.h"
-#include "inifcns.h"
-#include "relational.h"
+#include "constant.h"
+#include "inifcns.h" // for log() in power::derivative()
+#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<int> 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)
+power::power() : inherited(TINFO_power)
{
- 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)
+power::power(const ex & lh, const ex & rh) : inherited(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);
}
-power::power(const ex & lh, const numeric & rh) : basic(TINFO_power), basis(lh), exponent(rh)
+/** 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) : inherited(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);
n.add_ex("exponent", exponent);
}
+DEFAULT_UNARCHIVE(power)
+
//////////
// functions overriding virtual functions from bases classes
//////////
// public
-basic * power::duplicate() const
+static void print_sym_pow(const print_context & c, const symbol &x, int exp)
{
- debugmsg("power duplicate",LOGLEVEL_DUPLICATE);
- return new power(*this);
-}
-
-void power::print(std::ostream & os, unsigned upper_precedence) const
-{
- 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_a<print_tree>(c)) {
-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_a<print_csrc>(c)) {
-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_exactly_a<symbol>(basis) || is_exactly_a<constant>(basis))) {
+ int exp = ex_to<numeric>(exponent).to_int();
+ if (exp > 0)
+ c.s << '(';
+ else {
+ exp = -exp;
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "recip(";
+ else
+ c.s << "1.0/(";
+ }
+ print_sym_pow(c, ex_to<symbol>(basis), exp);
+ c.s << ')';
+
+ // <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
+ } else if (exponent.compare(_num_1()) == 0) {
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "recip(";
else
- os << "1.0/(";
- }
- print_sym_pow(os, type, static_cast<const symbol &>(*basis.bp), exp);
- os << ")";
+ c.s << "1.0/(";
+ basis.print(c);
+ c.s << ')';
- // <expr>^-1 is printed as "1.0/<expr>" 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_a<print_csrc_cl_N>(c))
+ 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_a<print_latex>(c))
+ c.s << "\\sqrt{";
+ else
+ c.s << "sqrt(";
+ basis.print(c);
+ if (is_a<print_latex>(c))
+ c.s << '}';
+ else
+ c.s << ')';
+ } else {
+ if (precedence() <= level) {
+ if (is_a<print_latex>(c))
+ c.s << "{(";
+ else
+ c.s << "(";
+ }
+ basis.print(c, precedence());
+ c.s << '^';
+ if (is_a<print_latex>(c))
+ c.s << '{';
+ exponent.print(c, precedence());
+ if (is_a<print_latex>(c))
+ c.s << '}';
+ if (precedence() <= level) {
+ if (is_a<print_latex>(c))
+ c.s << ")}";
+ else
+ c.s << ')';
+ }
+ }
}
}
return i==0 ? basis : exponent;
}
-int power::degree(const symbol & s) const
+ex power::map(map_function & 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) {
- if (ex_to_numeric(exponent).is_integer())
- return ex_to_numeric(exponent).to_int();
+ 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 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) {
- if (ex_to_numeric(exponent).is_integer())
- return ex_to_numeric(exponent).to_int();
+ 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 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)
return *this;
return _ex0();
} else {
// basis equal to s
- if (is_exactly_of_type(*exponent.bp, numeric) && ex_to_numeric(exponent).is_integer()) {
+ 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();
+ int int_exp = ex_to<numeric>(exponent).to_int();
if (n == int_exp)
return _ex1();
else
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<numeric *>(ebasis.bp);
}
if (is_exactly_of_type(*eexponent.bp,numeric)) {
- exponent_is_numerical = 1;
+ exponent_is_numerical = true;
num_exponent = static_cast<numeric *>(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()))
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();
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
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()))));
}
}
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)) {
- return expand_add(ex_to_add(expanded_basis), int_exponent);
- }
+ // (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)) {
- return expand_mul(ex_to_mul(expanded_basis), num_exponent);
- }
+ // (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);
}
//////////
const ex & b = a.op(l);
GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
GINAC_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() ||
- !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)) {
- term.push_back(expand_mul(ex_to_mul(b),numeric(k[l])));
- } else {
+ !is_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+ !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
+ !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))
+ term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
+ else
term.push_back(power(b,k[l]));
- }
}
const ex & b = a.op(l);
GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
GINAC_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() ||
- !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)) {
- term.push_back(expand_mul(ex_to_mul(b),numeric(n-k_cum[m-2])));
- } else {
+ !is_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+ !ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
+ !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))
+ term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
+ else
term.push_back(power(b,n-k_cum[m-2]));
- }
numeric f = binomial(numeric(n),numeric(k[0]));
- for (l=1; l<m-1; l++) {
- f=f*binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
- }
+ for (l=1; l<m-1; l++)
+ f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
+
term.push_back(f);
-
+
/*
cout << "begin term" << endl;
for (int i=0; i<m-1; i++) {
cout << "k_cum[" << i << "]=" << k_cum[i] << endl;
cout << "upper_limit[" << i << "]=" << upper_limit[i] << endl;
}
- for (exvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
- cout << *cit << endl;
- }
+ for_each(term.begin(), term.end(), ostream_iterator<ex>(cout, "\n"));
cout << "end term" << endl;
*/
-
+
// TODO: optimize this
sum.push_back((new mul(term))->setflag(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; i<m-1; i++) {
- k_cum[i]=k_cum[i-1]+k[i];
- }
-
- for (int i=l+1; i<m-1; i++) {
- upper_limit[i]=n-k_cum[i-1];
- }
+ if (l==0)
+ k_cum[0] = k[0];
+ else
+ k_cum[l] = k_cum[l-1]+k[l];
+
+ for (int i=l+1; i<m-1; i++)
+ k_cum[i] = k_cum[i-1]+k[i];
+
+ for (int i=l+1; i<m-1; i++)
+ upper_limit[i] = n-k_cum[i-1];
}
return (new add(sum))->setflag(status_flags::dynallocated |
status_flags::expanded );
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) ||
- !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));
-
+ !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,_ex1())) {
if (is_ex_exactly_of_type(r,mul)) {
- sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()),
+ sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2()),
_ex1()));
} else {
sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated),
}
} else {
if (is_ex_exactly_of_type(r,mul)) {
- sum.push_back(expair(expand_mul(ex_to_mul(r),_num2()),
- ex_to_numeric(c).power_dyn(_num2())));
+ 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,_ex2()))->setflag(status_flags::dynallocated),
- ex_to_numeric(c).power_dyn(_num2())));
+ ex_to<numeric>(c).power_dyn(_num2())));
}
}
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))));
+ _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(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()));
+ 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);
* @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;
} 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_numeric((*cit).coeff).mul(n)));
+ distrseq.push_back(expair((*cit).rest, ex_to<numeric>((*cit).coeff).mul(n)));
}
++cit;
}
- 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<const add &>(*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);
+ return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
}
-*/
/*
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)
return power(a,_ex1_2());
}
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff