* @param rel_ expansion variable and point (must hold a relational)
* @param ops_ vector of {coefficient, power} pairs (coefficient must not be zero)
* @return newly constructed pseries */
-pseries::pseries(const ex &rel_, const epvector &ops_) : seq(ops_)
+pseries::pseries(const ex &rel_, const epvector &ops_)
+ : seq(ops_)
+{
+ GINAC_ASSERT(is_a<relational>(rel_));
+ GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
+ point = rel_.rhs();
+ var = rel_.lhs();
+}
+pseries::pseries(const ex &rel_, epvector &&ops_)
+ : seq(std::move(ops_))
{
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
}
}
} else
- Order(power(var-point,i->coeff)).print(c);
+ Order(pow(var - point, i->coeff)).print(c);
++i;
}
throw (std::out_of_range("op() out of range"));
if (is_order_function(seq[i].rest))
- return Order(power(var-point, seq[i].coeff));
- return seq[i].rest * power(var - point, seq[i].coeff);
+ return Order(pow(var-point, seq[i].coeff));
+ return seq[i].rest * pow(var - point, seq[i].coeff);
}
/** Return degree of highest power of the series. This is usually the exponent
}
/** Perform coefficient-wise automatic term rewriting rules in this class. */
-ex pseries::eval(int level) const
+ex pseries::eval() const
{
- if (level == 1)
- return this->hold();
-
- if (level == -max_recursion_level)
- throw (std::runtime_error("pseries::eval(): recursion limit exceeded"));
+ if (flags & status_flags::evaluated) {
+ return *this;
+ }
// Construct a new series with evaluated coefficients
epvector new_seq;
new_seq.reserve(seq.size());
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- new_seq.push_back(expair(it->rest.eval(level-1), it->coeff));
+ new_seq.push_back(expair(it->rest, it->coeff));
++it;
}
- return (new pseries(relational(var,point), std::move(new_seq)))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
}
/** Evaluate coefficients numerically. */
new_seq.push_back(expair(it->rest.evalf(level-1), it->coeff));
++it;
}
- return (new pseries(relational(var,point), std::move(new_seq)))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
}
ex pseries::conjugate() const
return *this;
}
- return (new pseries(var==newpoint, newseq ? std::move(*newseq) : seq))->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==newpoint, newseq ? std::move(*newseq) : seq);
}
ex pseries::real_part() const
v.reserve(seq.size());
for (auto & it : seq)
v.push_back(expair((it.rest).real_part(), it.coeff));
- return (new pseries(var==point, std::move(v)))->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==point, std::move(v));
}
ex pseries::imag_part() const
v.reserve(seq.size());
for (auto & it : seq)
v.push_back(expair((it.rest).imag_part(), it.coeff));
- return (new pseries(var==point, std::move(v)))->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==point, std::move(v));
}
ex pseries::eval_integ() const
{
- epvector *newseq = nullptr;
+ std::unique_ptr<epvector> newseq(nullptr);
for (auto i=seq.begin(); i!=seq.end(); ++i) {
if (newseq) {
newseq->push_back(expair(i->rest.eval_integ(), i->coeff));
}
ex newterm = i->rest.eval_integ();
if (!are_ex_trivially_equal(newterm, i->rest)) {
- newseq = new epvector;
+ newseq.reset(new epvector);
newseq->reserve(seq.size());
for (auto j=seq.begin(); j!=i; ++j)
newseq->push_back(*j);
ex newpoint = point.eval_integ();
if (newseq || !are_ex_trivially_equal(newpoint, point))
- return (new pseries(var==newpoint, *newseq))
- ->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==newpoint, std::move(*newseq));
return *this;
}
ex newcoeff = i->rest.evalm();
if (!newcoeff.is_zero())
newseq.push_back(expair(newcoeff, i->coeff));
- }
- else {
+ } else {
ex newcoeff = i->rest.evalm();
if (!are_ex_trivially_equal(newcoeff, i->rest)) {
something_changed = true;
}
}
if (something_changed)
- return (new pseries(var==point, std::move(newseq)))->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==point, std::move(newseq));
else
return *this;
}
newseq.reserve(seq.size());
for (auto & it : seq)
newseq.push_back(expair(it.rest.subs(m, options), it.coeff));
- return (new pseries(relational(var,point.subs(m, options)), newseq))->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(relational(var,point.subs(m, options)), std::move(newseq));
}
/** Implementation of ex::expand() for a power series. It expands all the
if (!restexp.is_zero())
newseq.push_back(expair(restexp, it.coeff));
}
- return (new pseries(relational(var,point), std::move(newseq)))
- ->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+ return dynallocate<pseries>(relational(var,point), std::move(newseq)).setflag(options == 0 ? status_flags::expanded : 0);
}
/** Implementation of ex::diff() for a power series.
for (auto & it : seq) {
if (is_order_function(it.rest)) {
if (!no_order)
- e += Order(power(var - point, it.coeff));
+ e += Order(pow(var - point, it.coeff));
} else
- e += it.rest * power(var - point, it.coeff);
+ e += it.rest * pow(var - point, it.coeff);
}
return e;
}
// default for order-values that make no sense for Taylor expansion
if ((order <= 0) && this->has(s)) {
seq.push_back(expair(Order(_ex1), order));
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
}
// do Taylor expansion
int n;
for (n=1; n<order; ++n) {
- fac = fac.mul(n);
+ fac = fac.div(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
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
coeff = deriv.subs(r, subs_options::no_pattern);
if (!coeff.is_zero())
- seq.push_back(expair(fac.inverse() * coeff, n));
+ seq.push_back(expair(fac * coeff, n));
}
// Higher-order terms, if present
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
seq.push_back(expair(Order(_ex1), n));
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
}
seq.push_back(expair(Order(_ex1), numeric(order)));
} else
seq.push_back(expair(*this, _ex0));
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
}
// Adding two series with different variables or expansion points
// results in an empty (constant) series
if (!is_compatible_to(other)) {
- epvector nul;
- nul.push_back(expair(Order(_ex1), _ex0));
- return pseries(relational(var,point), nul);
+ epvector nul { expair(Order(_ex1), _ex0) };
+ return pseries(relational(var,point), std::move(nul));
}
// Series addition
else
new_seq.push_back(it);
}
- return pseries(relational(var,point), new_seq);
+ return pseries(relational(var,point), std::move(new_seq));
}
// Multiplying two series with different variables or expansion points
// results in an empty (constant) series
if (!is_compatible_to(other)) {
- epvector nul;
- nul.push_back(expair(Order(_ex1), _ex0));
- return pseries(relational(var,point), nul);
+ epvector nul { expair(Order(_ex1), _ex0) };
+ return pseries(relational(var,point), std::move(nul));
}
if (seq.empty() || other.seq.empty()) {
- return (new pseries(var==point, epvector()))
- ->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==point, epvector());
}
// Series multiplication
epvector new_seq;
- int a_max = degree(var);
- int b_max = other.degree(var);
- int a_min = ldegree(var);
- int b_min = other.ldegree(var);
- int cdeg_min = a_min + b_min;
+ const int a_max = degree(var);
+ const int b_max = other.degree(var);
+ const int a_min = ldegree(var);
+ const int b_min = other.ldegree(var);
+ const int cdeg_min = a_min + b_min;
int cdeg_max = a_max + b_max;
int higher_order_a = std::numeric_limits<int>::max();
higher_order_a = a_max + b_min;
if (is_order_function(other.coeff(var, b_max)))
higher_order_b = b_max + a_min;
- int higher_order_c = std::min(higher_order_a, higher_order_b);
+ const int higher_order_c = std::min(higher_order_a, higher_order_b);
if (cdeg_max >= higher_order_c)
cdeg_max = higher_order_c - 1;
-
+
+ std::map<int, ex> rest_map_a, rest_map_b;
+ for (const auto& it : seq)
+ rest_map_a[ex_to<numeric>(it.coeff).to_int()] = it.rest;
+
+ if (other.var.is_equal(var))
+ for (const auto& it : other.seq)
+ rest_map_b[ex_to<numeric>(it.coeff).to_int()] = it.rest;
+
for (int cdeg=cdeg_min; cdeg<=cdeg_max; ++cdeg) {
ex co = _ex0;
// c(i)=a(0)b(i)+...+a(i)b(0)
for (int i=a_min; cdeg-i>=b_min; ++i) {
- ex a_coeff = coeff(var, i);
- ex b_coeff = other.coeff(var, cdeg-i);
- if (!is_order_function(a_coeff) && !is_order_function(b_coeff))
- co += a_coeff * b_coeff;
+ const auto& ita = rest_map_a.find(i);
+ if (ita == rest_map_a.end())
+ continue;
+ const auto& itb = rest_map_b.find(cdeg-i);
+ if (itb == rest_map_b.end())
+ continue;
+ if (!is_order_function(ita->second) && !is_order_function(itb->second))
+ co += ita->second * itb->second;
}
if (!co.is_zero())
new_seq.push_back(expair(co, numeric(cdeg)));
}
if (higher_order_c < std::numeric_limits<int>::max())
new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c)));
- return pseries(relational(var, point), new_seq);
+ return pseries(relational(var, point), std::move(new_seq));
}
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);
+ epvector epv { expair(Order(_ex1), order) };
+ return dynallocate<pseries>(r, std::move(epv));
}
// Multiply with remaining terms
// adjust number of coefficients
int numcoeff = deg - (p*ldeg).to_int();
if (numcoeff <= 0) {
- epvector epv;
- epv.reserve(1);
- epv.push_back(expair(Order(_ex1), deg));
- return (new pseries(relational(var,point), epv))
- ->setflag(status_flags::dynallocated);
+ epvector epv { expair(Order(_ex1), deg) };
+ return dynallocate<pseries>(relational(var,point), std::move(epv));
}
// O(x^n)^(-m) is undefined
// Compute coefficients of the powered series
exvector co;
co.reserve(numcoeff);
- co.push_back(power(coeff(var, ldeg), p));
+ co.push_back(pow(coeff(var, ldeg), p));
for (int i=1; i<numcoeff; ++i) {
ex sum = _ex0;
for (int j=1; j<=i; ++j) {
if (!higher_order)
new_seq.push_back(expair(Order(_ex1), p * ldeg + numcoeff));
- return pseries(relational(var,point), new_seq);
+ return pseries(relational(var,point), std::move(new_seq));
}
new_seq.push_back(expair(_ex1, exponent));
else
new_seq.push_back(expair(Order(_ex1), exponent));
- return pseries(r, new_seq);
+ return pseries(r, std::move(new_seq));
}
// No, expand basis into series
try {
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);
+ epvector ser { expair(Order(_ex1), order) };
+ result = pseries(r, std::move(ser));
}
return result;
}
new_seq.push_back(it);
}
- return pseries(r, new_seq);
+ return pseries(r, std::move(new_seq));
}
} else
return convert_to_poly().series(r, order, options);
}
// Expanding lower boundary
- ex result = (new pseries(r, fexpansion))->setflag(status_flags::dynallocated);
+ ex result = dynallocate<pseries>(r, std::move(fexpansion));
ex aseries = (a-a.subs(r)).series(r, order, options);
fseries = f.series(x == (a.subs(r)), order, options);
for (size_t i=0; i<fseries.nops(); ++i) {
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