#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_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
GINAC_IMPLEMENT_REGISTERED_CLASS(power, basic)
bool power::info(unsigned inf) const
{
- if (inf==info_flags::polynomial ||
- inf==info_flags::integer_polynomial ||
- inf==info_flags::cinteger_polynomial ||
- inf==info_flags::rational_polynomial ||
- inf==info_flags::crational_polynomial) {
- return exponent.info(info_flags::nonnegint);
- } else if (inf==info_flags::rational_function) {
- return exponent.info(info_flags::integer);
- } else {
- return inherited::info(inf);
+ 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
{
// 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"));
- }
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 = 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 _ex1();
-
+ 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()))
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
+
+ // ^(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(_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)
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(_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)),_ex1()));
- 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)) {
- const power & sub_power=ex_to_power(ebasis);
- const ex & sub_basis=sub_power.basis;
- const ex & 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)) {
- const numeric & 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)) {
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);
// protected
+/** 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));
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
- const numeric & 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
//////////
+/** 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++) {
- const ex & 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]));
}
}
-
- const ex & 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 );
}
+
+/** 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);
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 );
}
+/** 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(_num0())) {
+ 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);
}
/*
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);
}
*/
// protected
-unsigned power::precedence=60;
+unsigned power::precedence = 60;
//////////
// global constants
return power(a,_ex1_2());
}
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff