* 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
#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<int> intvector;
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) {
// 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);
}
//////////
// 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);
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);
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);
+}
+
//////////
// functions overriding virtual functions from bases classes
//////////
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<const symbol &>(*basis.bp), exp);
+ os << ")";
+
+ // <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 {
- 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)
{
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();
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();
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<numeric const &>(*exponent.bp).compare(numeric(n))==0)) {
- return exONE();
+ (static_cast<const numeric &>(*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!)
// ^(*(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<numeric *>(ebasis.bp);
+ basis_is_numerical = 1;
+ num_basis = static_cast<numeric *>(ebasis.bp);
}
if (is_exactly_of_type(*eexponent.bp,numeric)) {
- exponent_is_numerical=1;
- num_exponent=static_cast<numeric *>(eexponent.bp);
+ exponent_is_numerical = 1;
+ num_exponent = static_cast<numeric *>(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;
}
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);
+ 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));
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
- mul const & mulref=ex_to_mul(ebasis);
- if (!mulref.overall_coeff.is_equal(exONE())) {
- numeric const & num_coeff=ex_to_numeric(mulref.overall_coeff);
+ 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 {
- GINAC_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),
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)) {
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
+{
+ 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));
- power const & o=static_cast<power const &>(const_cast<basic &>(other));
+ const power & o=static_cast<const power &>(const_cast<basic &>(other));
int cmpval;
cmpval=basis.compare(o.basis);
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);
}
}
// 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);
int l;
for (int l=0; l<m-1; l++) {
- k[l]=0;
- k_cum[l]=0;
- upper_limit[l]=n;
+ k[l] = 0;
+ k_cum[l] = 0;
+ upper_limit[l] = n;
}
-
+
while (1) {
exvector term;
term.reserve(m+1);
for (l=0; l<m-1; l++) {
- ex const & b=a.op(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).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]));
}
}
-
- ex const & b=a.op(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).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]));
+
+ 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]));
}
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);
- 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());
- 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()));
- }
- }
-
- GINAC_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);
// 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;
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).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))));
}
}
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()));
}
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));
++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
exvector distrseq;
epvector splitseq;
- add const & addref=static_cast<add const &>(*basis.bp);
+ const add & addref=static_cast<const add &>(*basis.bp);
splitseq=addref.seq;
splitseq.pop_back();
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).
// 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
git://www.ginac.de / ginac.git / blobdiff