#include "pseries.h"
#include "add.h"
-#include "inifcns.h"
+#include "inifcns.h" // for Order function
#include "lst.h"
#include "mul.h"
#include "power.h"
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();
}
DEFAULT_UNARCHIVE(pseries)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
void pseries::print(const print_context & c, unsigned level) const
{
debugmsg("pseries print", LOGLEVEL_PRINT);
- if (is_of_type(c, print_tree)) {
+ if (is_a<print_tree>(c)) {
c.s << std::string(level, ' ') << class_name()
<< std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
<< std::endl;
unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
- for (unsigned i=0; i<seq.size(); ++i) {
+ unsigned num = seq.size();
+ for (unsigned i=0; i<num; ++i) {
seq[i].rest.print(c, level + delta_indent);
seq[i].coeff.print(c, level + delta_indent);
c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
if (precedence() <= level)
c.s << "(";
- std::string par_open = is_of_type(c, print_latex) ? "{(" : "(";
- std::string par_close = is_of_type(c, print_latex) ? ")}" : ")";
+ std::string par_open = is_a<print_latex>(c) ? "{(" : "(";
+ std::string par_close = is_a<print_latex>(c) ? ")}" : ")";
// objects of type pseries must not have any zero entries, so the
// trivial (zero) pseries needs a special treatment here:
- if (seq.size() == 0)
+ if (seq.empty())
c.s << '0';
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
// print a sign, if needed
if (i != seq.begin())
c.s << '+';
}
// print 'coeff', something like (x-1)^42
if (!i->coeff.is_zero()) {
- if (is_of_type(c, print_latex))
+ if (is_a<print_latex>(c))
c.s << ' ';
else
c.s << '*';
i->coeff.print(c);
c.s << par_close;
} else {
- if (is_of_type(c, print_latex)) {
+ if (is_a<print_latex>(c)) {
c.s << '{';
i->coeff.print(c);
c.s << '}';
}
} else
Order(power(var-point,i->coeff)).print(c);
+ ++i;
}
if (precedence() <= level)
if (var.is_equal(s)) {
// Return last exponent
if (seq.size())
- return ex_to_numeric((*(seq.end() - 1)).coeff).to_int();
+ return ex_to<numeric>((seq.end()-1)->coeff).to_int();
else
return 0;
} else {
if (var.is_equal(s)) {
// Return first exponent
if (seq.size())
- return ex_to_numeric((*(seq.begin())).coeff).to_int();
+ return ex_to<numeric>((seq.begin())->coeff).to_int();
else
return 0;
} else {
ex pseries::coeff(const ex &s, int n) const
{
if (var.is_equal(s)) {
- if (seq.size() == 0)
+ if (seq.empty())
return _ex0();
// Binary search in sequence for given power
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));
- int cmp = ex_to_numeric(seq[mid].coeff).compare(looking_for);
+ GINAC_ASSERT(is_exactly_a<numeric>(seq[mid].coeff));
+ int cmp = ex_to<numeric>(seq[mid].coeff).compare(looking_for);
switch (cmp) {
case -1:
lo = mid + 1;
return *this;
}
-/** Evaluate coefficients. */
+/** Perform coefficient-wise automatic term rewriting rules in this class. */
ex pseries::eval(int level) const
{
if (level == 1)
ex pseries::expand(unsigned options) const
{
epvector newseq;
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
ex restexp = i->rest.expand();
if (!restexp.is_zero())
newseq.push_back(expair(restexp, i->coeff));
+ ++i;
}
return (new pseries(relational(var,point), newseq))
- ->setflag(status_flags::dynallocated | status_flags::expanded);
+ ->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}
/** Implementation of ex::diff() for a power series. It treats the series as a
bool pseries::is_terminating(void) const
{
- return seq.size() == 0 || !is_order_function((seq.end()-1)->rest);
+ return seq.empty() || !is_order_function((seq.end()-1)->rest);
}
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)
}
break;
} else
- pow_a = ex_to_numeric((*a).coeff).to_int();
+ pow_a = ex_to<numeric>((*a).coeff).to_int();
// If b is empty, fill up with elements from a and stop
if (b == b_end) {
}
break;
} else
- pow_b = ex_to_numeric((*b).coeff).to_int();
+ pow_b = ex_to<numeric>((*b).coeff).to_int();
// a and b are non-empty, compare powers
if (pow_a < pow_b) {
else
op = it->rest.series(r, order, options);
if (!it->coeff.is_equal(_ex1()))
- op = ex_to_pseries(op).mul_const(ex_to_numeric(it->coeff));
+ op = ex_to<pseries>(op).mul_const(ex_to<numeric>(it->coeff));
// Series addition
- acc = ex_to_pseries(acc).add_series(ex_to_pseries(op));
+ acc = ex_to<pseries>(acc).add_series(ex_to<pseries>(op));
}
return acc;
}
// Series multiplication
epvector new_seq;
-
int a_max = degree(var);
int b_max = other.degree(var);
int a_min = ldegree(var);
* @see ex::series */
ex mul::series(const relational & r, int order, unsigned options) const
{
- ex acc; // Series accumulator
-
- // Get first term from overall_coeff
- acc = overall_coeff.series(r, order, options);
-
+ pseries acc; // Series accumulator
+
// Multiply with remaining terms
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- for (; it!=itend; ++it) {
- ex op = it->rest;
- if (op.info(info_flags::numeric)) {
- // series * const (special case, faster)
- ex f = power(op, it->coeff);
- acc = ex_to_pseries(acc).mul_const(ex_to_numeric(f));
- continue;
- } else 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);
+ 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 = recombine_pair_to_ex(*it).series(r, order, options);
// Series multiplication
- acc = ex_to_pseries(acc).mul_series(ex_to_pseries(op));
+ if (it==itbeg)
+ acc = ex_to<pseries>(op);
+ else
+ acc = ex_to<pseries>(acc.mul_series(ex_to<pseries>(op)));
}
- return acc;
+ return acc.mul_const(ex_to<numeric>(overall_coeff));
}
ex pseries::power_const(const numeric &p, int deg) const
{
// method:
+ // (due to Leonhard Euler)
// let A(x) be this series and for the time being let it start with a
// constant (later we'll generalize):
// A(x) = a_0 + a_1*x + a_2*x^2 + ...
// repeat the above derivation. The leading power of C2(x) = A2(x)^2 is
// then of course x^(p*m) but the recurrence formula still holds.
- if (seq.size()==0) {
- // as a spacial case, handle the empty (zero) series honoring the
+ if (seq.empty()) {
+ // as a special case, handle the empty (zero) series honoring the
// usual power laws such as implemented in power::eval()
if (p.real().is_zero())
- throw (std::domain_error("pseries::power_const(): pow(0,I) is undefined"));
+ throw std::domain_error("pseries::power_const(): pow(0,I) is undefined");
else if (p.real().is_negative())
- throw (pole_error("pseries::power_const(): division by zero",1));
+ throw pole_error("pseries::power_const(): division by zero",1);
else
return *this;
}
- int ldeg = ldegree(var);
+ 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;
}
if (!sum.is_zero())
all_sums_zero = false;
- co.push_back(sum / coeff(var, ldeg) / numeric(i));
+ co.push_back(sum / coeff(var, ldeg) / i);
}
// Construct new series (of non-zero coefficients)
bool higher_order = false;
for (int i=0; i<deg; ++i) {
if (!co[i].is_zero())
- new_seq.push_back(expair(co[i], numeric(i) + p * ldeg));
+ new_seq.push_back(expair(co[i], p * ldeg + i));
if (is_order_function(co[i])) {
higher_order = true;
break;
}
}
if (!higher_order && !all_sums_zero)
- new_seq.push_back(expair(Order(_ex1()), numeric(deg) + p * ldeg));
+ new_seq.push_back(expair(Order(_ex1()), p * ldeg + deg));
return pseries(relational(var,point), new_seq);
}
/** Return a new pseries object with the powers shifted by deg. */
pseries pseries::shift_exponents(int deg) const
{
- epvector newseq(seq);
- for (epvector::iterator i=newseq.begin(); i!=newseq.end(); ++i)
- i->coeff = i->coeff + deg;
+ epvector newseq = seq;
+ epvector::iterator i = newseq.begin(), end = newseq.end();
+ while (i != end) {
+ i->coeff += deg;
+ ++i;
+ }
return pseries(relational(var, point), newseq);
}
* @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
- return ex_to_pseries(e).power_const(ex_to_numeric(exponent), order);
+
+ // 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))
epvector new_seq;
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- int o = ex_to_numeric(it->coeff).to_int();
+ int o = ex_to<numeric>(it->coeff).to_int();
if (o >= order) {
new_seq.push_back(expair(Order(_ex1()), o));
break;
relational rel_;
if (is_ex_exactly_of_type(r,relational))
- rel_ = ex_to_relational(r);
+ rel_ = ex_to<relational>(r);
else if (is_ex_exactly_of_type(r,symbol))
rel_ = relational(r,_ex0());
else
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