ex basic::series(const relational & r, int order, unsigned options) const
{
epvector seq;
+ const symbol &s = ex_to<symbol>(r.lhs());
// default for order-values that make no sense for Taylor expansion
- if (order <= 0) {
+ if ((order <= 0) && this->has(s)) {
seq.push_back(expair(Order(_ex1), order));
return pseries(r, seq);
}
numeric fac = 1;
ex deriv = *this;
ex coeff = deriv.subs(r, subs_options::no_pattern);
- const symbol &s = ex_to<symbol>(r.lhs());
-
+
if (!coeff.is_zero()) {
seq.push_back(expair(coeff, _ex0));
}
const epvector::const_iterator itbeg = seq.begin();
const epvector::const_iterator itend = seq.end();
for (epvector::const_iterator it=itbeg; it!=itend; ++it) {
-
- ex buf = recombine_pair_to_ex(*it);
-
- int real_ldegree = buf.expand().ldegree(sym-r.rhs());
+
+ ex expon = it->coeff;
+ int factor = 1;
+ ex buf;
+ if (expon.info(info_flags::integer)) {
+ buf = it->rest;
+ factor = ex_to<numeric>(expon).to_int();
+ } else {
+ buf = recombine_pair_to_ex(*it);
+ }
+
+ int real_ldegree = 0;
+ try {
+ real_ldegree = buf.expand().ldegree(sym-r.rhs());
+ } catch (std::runtime_error) {}
+
if (real_ldegree == 0) {
int orderloop = 0;
do {
} while (real_ldegree == orderloop);
}
- ldegrees.push_back(real_ldegree);
+ ldegrees.push_back(factor * real_ldegree);
}
int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0);
-
+
+ if (degsum >= order) {
+ epvector epv;
+ epv.push_back(expair(Order(_ex1), order));
+ return (new pseries(r, epv))->setflag(status_flags::dynallocated);
+ }
+
// Multiply with remaining terms
std::vector<int>::const_iterator itd = ldegrees.begin();
for (epvector::const_iterator it=itbeg; it!=itend; ++it, ++itd) {
ex op = recombine_pair_to_ex(*it).series(r, order-degsum+(*itd), options);
// Series multiplication
- if (it==itbeg)
+ if (it == itbeg)
acc = ex_to<pseries>(op);
else
acc = ex_to<pseries>(acc.mul_series(ex_to<pseries>(op)));
throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series");
// adjust number of coefficients
- deg = deg - p.to_int()*ldeg;
+ deg = deg - (p*ldeg).to_int();
// O(x^n)^(-m) is undefined
if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative())
}
// Is the expression of type something^(-int)?
- if (!must_expand_basis && !exponent.info(info_flags::negint))
+ if (!must_expand_basis && !exponent.info(info_flags::negint) && !is_a<add>(basis))
return basic::series(r, order, options);
// Is the expression of type 0^something?
- if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero())
+ if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero() && !is_a<add>(basis))
return basic::series(r, order, options);
// Singularity encountered, is the basis equal to (var - point)?
// No, expand basis into series
- int intexp = ex_to<numeric>(exponent).to_int();
+ numeric numexp;
+ if (is_a<numeric>(exponent)) {
+ numexp = ex_to<numeric>(exponent);
+ } else {
+ numexp = 0;
+ }
const ex& sym = r.lhs();
// find existing minimal degree
int real_ldegree = basis.expand().ldegree(sym-r.rhs());
} while (real_ldegree == orderloop);
}
- ex e = basis.series(r, order + real_ldegree*(1-intexp), options);
+ if (!(real_ldegree*numexp).is_integer())
+ throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series");
+ ex e = basis.series(r, (order + real_ldegree*(1-numexp)).to_int(), options);
ex result;
try {
- result = ex_to<pseries>(e).power_const(intexp, order);
- }
- catch (pole_error) {
+ result = ex_to<pseries>(e).power_const(numexp, order);
+ } catch (pole_error) {
epvector ser;
ser.push_back(expair(Order(_ex1), order));
result = pseries(r, ser);