case info_flags::rational_function:
return exponent.info(info_flags::integer) &&
basis.info(inf);
- case info_flags::algebraic:
- return !exponent.info(info_flags::integer) ||
- basis.info(inf);
case info_flags::expanded:
return (flags & status_flags::expanded);
case info_flags::positive:
* - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
* - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
* - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
- *
- * @param level cut-off in recursive evaluation */
-ex power::eval(int level) const
+ */
+ex power::eval() const
{
- if ((level==1) && (flags & status_flags::evaluated))
+ if (flags & status_flags::evaluated)
return *this;
- 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);
-
+
const numeric *num_basis = nullptr;
const numeric *num_exponent = nullptr;
-
- if (is_exactly_a<numeric>(ebasis)) {
- num_basis = &ex_to<numeric>(ebasis);
+
+ if (is_exactly_a<numeric>(basis)) {
+ num_basis = &ex_to<numeric>(basis);
}
- if (is_exactly_a<numeric>(eexponent)) {
- num_exponent = &ex_to<numeric>(eexponent);
+ if (is_exactly_a<numeric>(exponent)) {
+ num_exponent = &ex_to<numeric>(exponent);
}
// ^(x,0) -> 1 (0^0 also handled here)
- if (eexponent.is_zero()) {
- if (ebasis.is_zero())
+ if (exponent.is_zero()) {
+ if (basis.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;
+ if (exponent.is_equal(_ex1))
+ return basis;
// ^(0,c1) -> 0 or exception (depending on real value of c1)
- if ( ebasis.is_zero() && num_exponent ) {
+ if (basis.is_zero() && num_exponent) {
if ((num_exponent->real()).is_zero())
throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
else if ((num_exponent->real()).is_negative())
}
// ^(1,x) -> 1
- if (ebasis.is_equal(_ex1))
+ if (basis.is_equal(_ex1))
return _ex1;
// power of a function calculated by separate rules defined for this function
- if (is_exactly_a<function>(ebasis))
- return ex_to<function>(ebasis).power(eexponent);
+ if (is_exactly_a<function>(basis))
+ return ex_to<function>(basis).power(exponent);
// Turn (x^c)^d into x^(c*d) in the case that x is positive and c is real.
- if (is_exactly_a<power>(ebasis) && ebasis.op(0).info(info_flags::positive) && ebasis.op(1).info(info_flags::real))
- return power(ebasis.op(0), ebasis.op(1) * eexponent);
+ if (is_exactly_a<power>(basis) && basis.op(0).info(info_flags::positive) && basis.op(1).info(info_flags::real))
+ 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);
}
}
}
// ^(^(x,c1),c2) -> ^(x,c1*c2)
// (c1, c2 numeric(), c2 integer or -1 < c1 <= 1 or (c1=-1 and c2>0),
// case c1==1 should not happen, see below!)
- if (is_exactly_a<power>(ebasis)) {
- const power & sub_power = ex_to<power>(ebasis);
+ if (is_exactly_a<power>(basis)) {
+ const power & sub_power = ex_to<power>(basis);
const ex & sub_basis = sub_power.basis;
const ex & sub_exponent = sub_power.exponent;
if (is_exactly_a<numeric>(sub_exponent)) {
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>(ebasis)) {
- return expand_mul(ex_to<mul>(ebasis), *num_exponent, 0);
+ if (num_exponent->is_integer() && is_exactly_a<mul>(basis)) {
+ return expand_mul(ex_to<mul>(basis), *num_exponent, false);
}
// (2*x + 6*y)^(-4) -> 1/16*(x + 3*y)^(-4)
- if (num_exponent->is_integer() && is_exactly_a<add>(ebasis)) {
- numeric icont = ebasis.integer_content();
+ if (num_exponent->is_integer() && is_exactly_a<add>(basis)) {
+ numeric icont = basis.integer_content();
const numeric lead_coeff =
- ex_to<numeric>(ex_to<add>(ebasis).seq.begin()->coeff).div(icont);
+ ex_to<numeric>(ex_to<add>(basis).seq.begin()->coeff).div(icont);
const bool canonicalizable = lead_coeff.is_integer();
const bool unit_normal = lead_coeff.is_pos_integer();
icont = icont.mul(*_num_1_p);
if (canonicalizable && (icont != *_num1_p)) {
- const add& addref = ex_to<add>(ebasis);
+ const add& addref = ex_to<add>(basis);
add & addp = dynallocate<add>(addref);
addp.clearflag(status_flags::hash_calculated);
addp.overall_coeff = ex_to<numeric>(addp.overall_coeff).div_dyn(icont);
// ^(*(...,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_exactly_a<mul>(ebasis)) {
+ if (is_exactly_a<mul>(basis)) {
GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
- const mul & mulref = ex_to<mul>(ebasis);
+ const mul & mulref = ex_to<mul>(basis);
if (!mulref.overall_coeff.is_equal(_ex1)) {
const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
if (num_coeff.is_real()) {
// ^(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_a<matrix>(ebasis)) {
- return ncmul(exvector(num_exponent->to_int(), ebasis));
+ basis.return_type() != return_types::commutative &&
+ !is_a<matrix>(basis)) {
+ return ncmul(exvector(num_exponent->to_int(), basis));
}
}
-
- if (are_ex_trivially_equal(ebasis,basis) &&
- are_ex_trivially_equal(eexponent,exponent)) {
- return this->hold();
- }
- return dynallocate<power>(ebasis, eexponent).setflag(status_flags::evaluated);
+
+ return this->hold();
}
ex power::evalf(int level) const
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);
composition_generator compositions(partition);
do {
const std::vector<int>& exponent = compositions.current();
- exvector monomial;
+ epvector monomial;
monomial.reserve(msize);
numeric factor = coeff;
for (unsigned i = 0; i < exponent.size(); ++i) {
// optimize away
} else if (exponent[i] == 1) {
// optimized
- monomial.push_back(r);
+ monomial.push_back(expair(r, _ex1));
if (c != *_num1_p)
factor = factor.mul(c);
} else { // general case exponent[i] > 1
- monomial.push_back(dynallocate<power>(r, exponent[i]));
+ monomial.push_back(expair(r, exponent[i]));
if (c != *_num1_p)
factor = factor.mul(c.power(exponent[i]));
}
}
- result.push_back(a.combine_ex_with_coeff_to_pair(mul(monomial).expand(options), factor));
+ result.push_back(expair(mul(monomial).expand(options), factor));
} while (compositions.next());
} while (partitions.next());
}
GINAC_ASSERT(result.size() == result_size);
-
if (a.overall_coeff.is_zero()) {
return dynallocate<add>(std::move(result)).setflag(status_flags::expanded);
} else {
if (c.is_equal(_ex1)) {
if (is_exactly_a<mul>(r)) {
- result.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r), *_num2_p, options, true),
- _ex1));
+ result.push_back(expair(expand_mul(ex_to<mul>(r), *_num2_p, options, true),
+ _ex1));
} else {
- result.push_back(
a.combine_ex_with_coeff_to_pair(dynallocate<power>(r, _ex2),
- _ex1));
+ result.push_back(
expair(dynallocate<power>(r, _ex2),
+ _ex1));
}
} else {
if (is_exactly_a<mul>(r)) {
- result.push_back(a.combine_ex_with_coeff_to_pair(expand_mul(ex_to<mul>(r), *_num2_p, options, true),
- ex_to<numeric>(c).power_dyn(*_num2_p)));
+ result.push_back(expair(expand_mul(ex_to<mul>(r), *_num2_p, options, true),
+ ex_to<numeric>(c).power_dyn(*_num2_p)));
} else {
- result.push_back(
a.combine_ex_with_coeff_to_pair(dynallocate<power>(r, _ex2),
- ex_to<numeric>(c).power_dyn(*_num2_p)));
+ result.push_back(
expair(dynallocate<power>(r, _ex2),
+ ex_to<numeric>(c).power_dyn(*_num2_p)));
}
}
for (epvector::const_iterator cit1=cit0+1; cit1!=last; ++cit1) {
const ex & r1 = cit1->rest;
const ex & c1 = cit1->coeff;
- result.push_back(a.combine_ex_with_coeff_to_pair(mul(r,r1).expand(options),
- _num2_p->mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
+ result.push_back(expair(mul(r,r1).expand(options),
+ _num2_p->mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
}
}
git://www.ginac.de / ginac.git / blobdiff