pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_)
{
debugmsg("pseries ctor from ex,epvector", LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(is_ex_exactly_of_type(rel_, relational));
- GINAC_ASSERT(is_ex_exactly_of_type(rel_.lhs(),symbol));
+ GINAC_ASSERT(is_exactly_a<relational>(rel_));
+ GINAC_ASSERT(is_exactly_a<symbol>(rel_.lhs()));
point = rel_.rhs();
- var = *static_cast<symbol *>(rel_.lhs().bp);
+ var = rel_.lhs();
}
int lo = 0, hi = seq.size() - 1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
- GINAC_ASSERT(is_ex_exactly_of_type(seq[mid].coeff, numeric));
+ GINAC_ASSERT(is_exactly_a<numeric>(seq[mid].coeff));
int cmp = ex_to<numeric>(seq[mid].coeff).compare(looking_for);
switch (cmp) {
case -1:
numeric fac(1);
ex deriv = *this;
ex coeff = deriv.subs(r);
- const symbol &s = static_cast<symbol &>(*r.lhs().bp);
+ const symbol &s = ex_to<symbol>(r.lhs());
if (!coeff.is_zero())
seq.push_back(expair(coeff, _ex0()));
int n;
for (n=1; n<order; ++n) {
- fac = fac.mul(numeric(n));
+ fac = fac.mul(n);
+ // We need to test for zero in order to see if the series terminates.
+ // The problem is that there is no such thing as a perfect test for
+ // zero. Expanding the term occasionally helps a little...
deriv = deriv.diff(s).expand();
- if (deriv.is_zero()) {
- // Series terminates
+ if (deriv.is_zero()) // Series terminates
return pseries(r, seq);
- }
+
coeff = deriv.subs(r);
if (!coeff.is_zero())
- seq.push_back(expair(fac.inverse() * coeff, numeric(n)));
+ seq.push_back(expair(fac.inverse() * coeff, n));
}
// Higher-order terms, if present
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
- seq.push_back(expair(Order(_ex1()), numeric(n)));
+ seq.push_back(expair(Order(_ex1()), n));
return pseries(r, seq);
}
{
epvector seq;
const ex point = r.rhs();
- GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- ex s = r.lhs();
-
- if (this->is_equal(*s.bp)) {
+ GINAC_ASSERT(is_exactly_a<symbol>(r.lhs()));
+
+ if (this->is_equal_same_type(ex_to<symbol>(r.lhs()))) {
if (order > 0 && !point.is_zero())
seq.push_back(expair(point, _ex0()));
if (order > 1)
const epvector::const_iterator itbeg = seq.begin();
const epvector::const_iterator itend = seq.end();
for (epvector::const_iterator it=itbeg; it!=itend; ++it) {
- ex op = it->rest;
- if (!is_ex_exactly_of_type(op, pseries))
- op = op.series(r, order, options);
- if (!it->coeff.is_equal(_ex1()))
- op = ex_to<pseries>(op).power_const(ex_to<numeric>(it->coeff), order);
+ ex op = recombine_pair_to_ex(*it).series(r, order, options);
// Series multiplication
if (it==itbeg)
const int ldeg = ldegree(var);
if (!(p*ldeg).is_integer())
throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series");
+
+ // O(x^n)^(-m) is undefined
+ if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative())
+ throw pole_error("pseries::power_const(): division by zero",1);
// Compute coefficients of the powered series
exvector co;
* @see ex::series */
ex power::series(const relational & r, int order, unsigned options) const
{
- ex e;
- if (!is_ex_exactly_of_type(basis, pseries)) {
- // Basis is not a series, may there be a singularity?
- bool must_expand_basis = false;
- try {
- basis.subs(r);
- } catch (pole_error) {
- must_expand_basis = true;
- }
-
- // Is the expression of type something^(-int)?
- if (!must_expand_basis && !exponent.info(info_flags::negint))
- return basic::series(r, order, options);
+ // If basis is already a series, just power it
+ if (is_ex_exactly_of_type(basis, pseries))
+ return ex_to<pseries>(basis).power_const(ex_to<numeric>(exponent), order);
+
+ // Basis is not a series, may there be a singularity?
+ bool must_expand_basis = false;
+ try {
+ basis.subs(r);
+ } catch (pole_error) {
+ must_expand_basis = true;
+ }
- // Is the expression of type 0^something?
- if (!must_expand_basis && !basis.subs(r).is_zero())
- return basic::series(r, order, options);
+ // Is the expression of type something^(-int)?
+ if (!must_expand_basis && !exponent.info(info_flags::negint))
+ return basic::series(r, order, options);
- // Singularity encountered, expand basis into series
- e = basis.series(r, order, options);
- } else {
- // Basis is a series
- e = basis;
+ // Is the expression of type 0^something?
+ if (!must_expand_basis && !basis.subs(r).is_zero())
+ return basic::series(r, order, options);
+
+ // Singularity encountered, is the basis equal to (var - point)?
+ if (basis.is_equal(r.lhs() - r.rhs())) {
+ epvector new_seq;
+ if (ex_to<numeric>(exponent).to_int() < order)
+ new_seq.push_back(expair(_ex1(), exponent));
+ else
+ new_seq.push_back(expair(Order(_ex1()), exponent));
+ return pseries(r, new_seq);
}
-
- // Power e
+
+ // No, expand basis into series
+ ex e = basis.series(r, order, options);
return ex_to<pseries>(e).power_const(ex_to<numeric>(exponent), order);
}
ex pseries::series(const relational & r, int order, unsigned options) const
{
const ex p = r.rhs();
- GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol &s = static_cast<symbol &>(*r.lhs().bp);
+ GINAC_ASSERT(is_exactly_a<symbol>(r.lhs()));
+ const symbol &s = ex_to<symbol>(r.lhs());
if (var.is_equal(s) && point.is_equal(p)) {
if (order > degree(s))
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