// Turn (x^c)^d into x^(c*d) in the case that x is positive and c is real.
if (is_exactly_a<power>(basis) && basis.op(0).info(info_flags::positive) && basis.op(1).info(info_flags::real))
- return power(basis.op(0), basis.op(1) * exponent);
+ return dynallocate<power>(basis.op(0), basis.op(1) * exponent);
if ( num_exponent ) {
// because otherwise we'll end up with something like
// (7/8)^(4/3) -> 7/8*(1/2*7^(1/3))
// instead of 7/16*7^(1/3).
- ex prod = power(*num_basis,r.div(m));
- return prod*power(*num_basis,q);
+ return pow(basis, r.div(m)) * pow(basis, q);
}
}
}
GINAC_ASSERT(num_sub_exponent!=numeric(1));
if (num_exponent->is_integer() || (abs(num_sub_exponent) - (*_num1_p)).is_negative() ||
(num_sub_exponent == *_num_1_p && num_exponent->is_positive())) {
- return power(sub_basis,num_sub_exponent.mul(*num_exponent));
+ return dynallocate<power>(sub_basis, num_sub_exponent.mul(*num_exponent));
}
}
}
// ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
if (num_exponent->is_integer() && is_exactly_a<mul>(basis)) {
- return expand_mul(ex_to<mul>(basis), *num_exponent, 0);
+ return expand_mul(ex_to<mul>(basis), *num_exponent, false);
}
// (2*x + 6*y)^(-4) -> 1/16*(x + 3*y)^(-4)
eexponent = exponent;
}
- return power(ebasis,eexponent);
+ return dynallocate<power>(ebasis, eexponent);
}
ex power::evalm() const
if (tryfactsubs(*this, it.first, nummatches, repls)) {
ex anum = it.second.subs(repls, subs_options::no_pattern);
ex aden = it.first.subs(repls, subs_options::no_pattern);
- ex result = (*this)*power(anum/aden, nummatches);
+ ex result = (*this) * pow(anum/aden, nummatches);
return (ex_to<basic>(result)).subs_one_level(m, options);
}
}
// Re((a+I*b)^c) w/ c ∈ ℤ
long N = ex_to<numeric>(c).to_long();
// Use real terms in Binomial expansion to construct
- // Re(expand(power(a+I*b, N))).
+ // Re(expand(pow(a+I*b, N))).
long NN = N > 0 ? N : -N;
- ex numer = N > 0 ? _ex1 : power(power(a,2) + power(b,2), NN);
+ ex numer = N > 0 ? _ex1 : pow(pow(a,2) + pow(b,2), NN);
ex result = 0;
for (long n = 0; n <= NN; n += 2) {
- ex term = binomial(NN, n) * power(a, NN-n) * power(b, n) / numer;
+ ex term = binomial(NN, n) * pow(a, NN-n) * pow(b, n) / numer;
if (n % 4 == 0) {
result += term; // sign: I^n w/ n == 4*m
} else {
// Re((a+I*b)^(c+I*d))
const ex d = exponent.imag_part();
- return power(abs(basis),c)*exp(-d*atan2(b,a))*cos(c*atan2(b,a)+d*log(abs(basis)));
+ return pow(abs(basis),c) * exp(-d*atan2(b,a)) * cos(c*atan2(b,a)+d*log(abs(basis)));
}
ex power::imag_part() const
{
+ // basis == a+I*b, exponent == c+I*d
const ex a = basis.real_part();
const ex c = exponent.real_part();
if (basis.is_equal(a) && exponent.is_equal(c)) {
// Im((a+I*b)^c) w/ c ∈ ℤ
long N = ex_to<numeric>(c).to_long();
// Use imaginary terms in Binomial expansion to construct
- // Im(expand(power(a+I*b, N))).
+ // Im(expand(pow(a+I*b, N))).
long p = N > 0 ? 1 : 3; // modulus for positive sign
long NN = N > 0 ? N : -N;
- ex numer = N > 0 ? _ex1 : power(power(a,2) + power(b,2), NN);
+ ex numer = N > 0 ? _ex1 : pow(pow(a,2) + pow(b,2), NN);
ex result = 0;
for (long n = 1; n <= NN; n += 2) {
- ex term = binomial(NN, n) * power(a, NN-n) * power(b, n) / numer;
+ ex term = binomial(NN, n) * pow(a, NN-n) * pow(b, n) / numer;
if (n % 4 == p) {
result += term; // sign: I^n w/ n == 4*m+p
} else {
// Im((a+I*b)^(c+I*d))
const ex d = exponent.imag_part();
- return power(abs(basis),c)*exp(-d*atan2(b,a))*sin(c*atan2(b,a)+d*log(abs(basis)));
+ return pow(abs(basis),c) * exp(-d*atan2(b,a)) * sin(c*atan2(b,a)+d*log(abs(basis)));
}
// protected
{
if (is_a<numeric>(exponent)) {
// D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
- epvector newseq;
- newseq.reserve(2);
- newseq.push_back(expair(basis, exponent - _ex1));
- newseq.push_back(expair(basis.diff(s), _ex1));
- return mul(std::move(newseq), exponent);
+ const epvector newseq = {expair(basis, exponent - _ex1), expair(basis.diff(s), _ex1)};
+ return dynallocate<mul>(std::move(newseq), exponent);
} else {
// D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
- return mul(*this,
- add(mul(exponent.diff(s), log(basis)),
- mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
+ return *this * (exponent.diff(s)*log(basis) + exponent*basis.diff(s)*pow(basis, _ex_1));
}
}
// take care on the numeric coefficient
ex coeff=(possign? _ex1 : _ex_1);
if (m.overall_coeff.info(info_flags::positive) && m.overall_coeff != _ex1)
- prodseq.push_back(power(m.overall_coeff, exponent));
+ prodseq.push_back(pow(m.overall_coeff, exponent));
else if (m.overall_coeff.info(info_flags::negative) && m.overall_coeff != _ex_1)
- prodseq.push_back(power(-m.overall_coeff, exponent));
+ prodseq.push_back(pow(-m.overall_coeff, exponent));
else
coeff *= m.overall_coeff;
// In either case we set a flag to avoid the second run on a part
// which does not have positive/negative terms.
if (prodseq.size() > 0) {
- ex newbasis = coeff*mul(std::move(powseq));
+ ex newbasis = dynallocate<mul>(std::move(powseq), coeff);
ex_to<basic>(newbasis).setflag(status_flags::purely_indefinite);
return dynallocate<mul>(std::move(prodseq)) * pow(newbasis, exponent);
} else
exvector distrseq;
distrseq.reserve(a.seq.size() + 1);
for (auto & cit : a.seq) {
- distrseq.push_back(power(expanded_basis, a.recombine_pair_to_ex(cit)));
+ distrseq.push_back(pow(expanded_basis, a.recombine_pair_to_ex(cit)));
}
// Make sure that e.g. (x+y)^(2+a) expands the (x+y)^2 factor
if (int_exponent > 0 && is_exactly_a<add>(expanded_basis))
distrseq.push_back(expand_add(ex_to<add>(expanded_basis), int_exponent, options));
else
- distrseq.push_back(power(expanded_basis, a.overall_coeff));
+ distrseq.push_back(pow(expanded_basis, a.overall_coeff));
} else
- distrseq.push_back(power(expanded_basis, a.overall_coeff));
+ distrseq.push_back(pow(expanded_basis, a.overall_coeff));
// Make sure that e.g. (x+y)^(1+a) -> x*(x+y)^a + y*(x+y)^a
ex r = dynallocate<mul>(distrseq);
git://www.ginac.de / ginac.git / blobdiff