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 (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));
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::expand(unsigned options) const
{
- ex expanded_basis=basis.expand(options);
-
+ 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)) {
setflag(status_flags::dynallocated);
}
}
-
+
// integer 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();
// 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);
k_cum[l]=0;
upper_limit[l]=n;
}
-
+
while (1) {
exvector term;
term.reserve(m+1);
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)||
} 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]));
return (new add(sum))->setflag(status_flags::dynallocated);
}
+
+/** Special case of power::expand. 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);
return (new add(sum))->setflag(status_flags::dynallocated);
}
+/** Expand 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());
// protected
-unsigned power::precedence=60;
+unsigned power::precedence = 60;
//////////
// global constants
git://www.ginac.de / ginac.git / blobdiff