#include "pseries.h"
#include "add.h"
-#include "inifcns.h"
+#include "inifcns.h" // for Order function
#include "lst.h"
#include "mul.h"
#include "power.h"
#include "relational.h"
#include "symbol.h"
+#include "print.h"
#include "archive.h"
#include "utils.h"
#include "debugmsg.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
GINAC_IMPLEMENT_REGISTERED_CLASS(pseries, basic)
+
/*
- * Default constructor, destructor, copy constructor, assignment operator and helpers
+ * Default ctor, dtor, copy ctor, assignment operator and helpers
*/
pseries::pseries() : basic(TINFO_pseries)
{
- debugmsg("pseries default constructor", LOGLEVEL_CONSTRUCT);
-}
-
-pseries::~pseries()
-{
- debugmsg("pseries destructor", LOGLEVEL_DESTRUCT);
- destroy(false);
-}
-
-pseries::pseries(const pseries &other)
-{
- debugmsg("pseries copy constructor", LOGLEVEL_CONSTRUCT);
- copy(other);
-}
-
-const pseries &pseries::operator=(const pseries & other)
-{
- debugmsg("pseries operator=", LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(true);
- copy(other);
- }
- return *this;
+ debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT);
}
void pseries::copy(const pseries &other)
point = other.point;
}
-void pseries::destroy(bool call_parent)
-{
- if (call_parent)
- inherited::destroy(call_parent);
-}
+DEFAULT_DESTROY(pseries)
/*
- * Other constructors
+ * Other ctors
*/
/** Construct pseries from a vector of coefficients and powers.
* @return newly constructed pseries */
pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_)
{
- debugmsg("pseries constructor from ex,epvector", LOGLEVEL_CONSTRUCT);
+ 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));
point = rel_.rhs();
* Archiving
*/
-/** Construct object from archive_node. */
pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("pseries constructor from archive_node", LOGLEVEL_CONSTRUCT);
+ debugmsg("pseries ctor from archive_node", LOGLEVEL_CONSTRUCT);
for (unsigned int i=0; true; ++i) {
ex rest;
ex coeff;
n.find_ex("point", point, sym_lst);
}
-/** Unarchive the object. */
-ex pseries::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new pseries(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
void pseries::archive(archive_node &n) const
{
inherited::archive(n);
n.add_ex("point", point);
}
+DEFAULT_UNARCHIVE(pseries)
+
//////////
// functions overriding virtual functions from bases classes
//////////
-basic *pseries::duplicate() const
-{
- debugmsg("pseries duplicate", LOGLEVEL_DUPLICATE);
- return new pseries(*this);
-}
-
-void pseries::print(std::ostream &os, unsigned upper_precedence) const
+void pseries::print(const print_context & c, unsigned level) const
{
debugmsg("pseries print", LOGLEVEL_PRINT);
- if (precedence<=upper_precedence) os << "(";
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
- // omit zero terms
- if (i->rest.is_zero())
- continue;
- // print a sign, if needed
- if (i!=seq.begin())
- os << '+';
- if (!is_order_function(i->rest)) {
- // print 'rest', i.e. the expansion coefficient
- if (i->rest.info(info_flags::numeric) &&
- i->rest.info(info_flags::positive)) {
- os << i->rest;
- } else
- os << "(" << i->rest << ')';
- // print 'coeff', something like (x-1)^42
- if (!i->coeff.is_zero()) {
- os << '*';
- if (!point.is_zero())
- os << '(' << var-point << ')';
- else
- os << var;
- if (i->coeff.compare(_ex1())) {
- os << '^';
- if (i->coeff.info(info_flags::negative))
- os << '(' << i->coeff << ')';
+
+ 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) {
+ 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;
+ }
+ var.print(c, level + delta_indent);
+ point.print(c, level + delta_indent);
+
+ } else {
+
+ if (precedence() <= level)
+ c.s << "(";
+
+ 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)
+ c.s << '0';
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ // print a sign, if needed
+ if (i != seq.begin())
+ c.s << '+';
+ if (!is_order_function(i->rest)) {
+ // print 'rest', i.e. the expansion coefficient
+ if (i->rest.info(info_flags::numeric) &&
+ i->rest.info(info_flags::positive)) {
+ i->rest.print(c);
+ } else {
+ c.s << par_open;
+ i->rest.print(c);
+ c.s << par_close;
+ }
+ // print 'coeff', something like (x-1)^42
+ if (!i->coeff.is_zero()) {
+ if (is_a<print_latex>(c))
+ c.s << ' ';
else
- os << i->coeff;
+ c.s << '*';
+ if (!point.is_zero()) {
+ c.s << par_open;
+ (var-point).print(c);
+ c.s << par_close;
+ } else
+ var.print(c);
+ if (i->coeff.compare(_ex1())) {
+ c.s << '^';
+ if (i->coeff.info(info_flags::negative)) {
+ c.s << par_open;
+ i->coeff.print(c);
+ c.s << par_close;
+ } else {
+ if (is_a<print_latex>(c)) {
+ c.s << '{';
+ i->coeff.print(c);
+ c.s << '}';
+ } else
+ i->coeff.print(c);
+ }
+ }
}
- }
- } else {
- os << Order(power(var-point,i->coeff));
+ } else
+ Order(power(var-point,i->coeff)).print(c);
}
- }
- if (precedence<=upper_precedence) os << ")";
-}
-
-void pseries::printraw(std::ostream &os) const
-{
- debugmsg("pseries printraw", LOGLEVEL_PRINT);
- os << "pseries(" << var << ";" << point << ";";
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
- os << "(" << (*i).rest << "," << (*i).coeff << "),";
+ if (precedence() <= level)
+ c.s << ")";
}
- os << ")";
}
-
-void pseries::printtree(std::ostream & os, unsigned indent) const
+int pseries::compare_same_type(const basic & other) const
{
- debugmsg("pseries printtree",LOGLEVEL_PRINT);
- os << std::string(indent,' ') << "pseries "
- << ", hash=" << hashvalue
- << " (0x" << std::hex << hashvalue << std::dec << ")"
- << ", flags=" << flags << std::endl;
- for (unsigned i=0; i<seq.size(); ++i) {
- seq[i].rest.printtree(os,indent+delta_indent);
- seq[i].coeff.printtree(os,indent+delta_indent);
- if (i!=seq.size()-1)
- os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
+ GINAC_ASSERT(is_of_type(other, pseries));
+ const pseries &o = static_cast<const pseries &>(other);
+
+ // first compare the lengths of the series...
+ if (seq.size()>o.seq.size())
+ return 1;
+ if (seq.size()<o.seq.size())
+ return -1;
+
+ // ...then the expansion point...
+ int cmpval = var.compare(o.var);
+ if (cmpval)
+ return cmpval;
+ cmpval = point.compare(o.point);
+ if (cmpval)
+ return cmpval;
+
+ // ...and if that failed the individual elements
+ epvector::const_iterator it = seq.begin(), o_it = o.seq.begin();
+ while (it!=seq.end() && o_it!=o.seq.end()) {
+ cmpval = it->compare(*o_it);
+ if (cmpval)
+ return cmpval;
+ ++it;
+ ++o_it;
}
- var.printtree(os, indent+delta_indent);
- point.printtree(os, indent+delta_indent);
+
+ // so they are equal.
+ return 0;
}
/** Return the number of operands including a possible order term. */
return seq.size();
}
-
/** Return the ith term in the series when represented as a sum. */
ex pseries::op(int i) const
{
return seq[i].rest * power(var - point, seq[i].coeff);
}
-
ex &pseries::let_op(int i)
{
throw (std::logic_error("let_op not defined for pseries"));
}
-
/** Return degree of highest power of the series. This is usually the exponent
* of the Order term. If s is not the expansion variable of the series, the
* series is examined termwise. */
-int pseries::degree(const symbol &s) const
+int pseries::degree(const ex &s) const
{
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 {
* series is examined termwise. If s is the expansion variable but the
* expansion point is not zero the series is not expanded to find the degree.
* I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0. */
-int pseries::ldegree(const symbol &s) const
+int pseries::ldegree(const ex &s) const
{
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 symbol &s, int n) const
+/** Return coefficient of degree n in power series if s is the expansion
+ * variable. If the expansion point is nonzero, by definition the n=1
+ * coefficient in s of a+b*(s-z)+c*(s-z)^2+Order((s-z)^3) is b (assuming
+ * the expansion took place in the s in the first place).
+ * If s is not the expansion variable, an attempt is made to convert the
+ * series to a polynomial and return the corresponding coefficient from
+ * there. */
+ex pseries::coeff(const ex &s, int n) const
{
if (var.is_equal(s)) {
if (seq.size() == 0)
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);
+ int cmp = ex_to<numeric>(seq[mid].coeff).compare(looking_for);
switch (cmp) {
case -1:
lo = mid + 1;
return convert_to_poly().coeff(s, n);
}
-
-ex pseries::collect(const symbol &s) const
+/** Does nothing. */
+ex pseries::collect(const ex &s, bool distributed) const
{
return *this;
}
-
/** Evaluate coefficients. */
ex pseries::eval(int level) const
{
return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
-
/** Evaluate coefficients numerically. */
ex pseries::evalf(int level) const
{
return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
-
-ex pseries::subs(const lst & ls, const lst & lr) const
+ex pseries::subs(const lst & ls, const lst & lr, bool no_pattern) const
{
// If expansion variable is being substituted, convert the series to a
// polynomial and do the substitution there because the result might
// no longer be a power series
if (ls.has(var))
- return convert_to_poly(true).subs(ls, lr);
+ return convert_to_poly(true).subs(ls, lr, no_pattern);
// Otherwise construct a new series with substituted coefficients and
// expansion point
newseq.reserve(seq.size());
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- newseq.push_back(expair(it->rest.subs(ls, lr), it->coeff));
+ newseq.push_back(expair(it->rest.subs(ls, lr, no_pattern), it->coeff));
++it;
}
- return (new pseries(relational(var,point.subs(ls, lr)), newseq))->setflag(status_flags::dynallocated);
+ return (new pseries(relational(var,point.subs(ls, lr, no_pattern)), newseq))->setflag(status_flags::dynallocated);
}
-
/** Implementation of ex::expand() for a power series. It expands all the
- * terms individually and returns the resulting series as a new pseries.
- * @see ex::diff */
+ * terms individually and returns the resulting series as a new pseries. */
ex pseries::expand(unsigned options) const
{
epvector newseq;
- newseq.reserve(seq.size());
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
- newseq.push_back(expair(i->rest.expand(), i->coeff));
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ ex restexp = i->rest.expand();
+ if (!restexp.is_zero())
+ newseq.push_back(expair(restexp, i->coeff));
+ }
return (new pseries(relational(var,point), newseq))
->setflag(status_flags::dynallocated | status_flags::expanded);
}
-
/** Implementation of ex::diff() for a power series. It treats the series as a
* polynomial.
* @see ex::diff */
}
}
-
-/*
- * Construct ordinary polynomial out of series
- */
-
-/** Convert a pseries object to an ordinary polynomial.
- *
- * @param no_order flag: discard higher order terms */
ex pseries::convert_to_poly(bool no_order) const
{
ex e;
return e;
}
-/** Returns true if there is no order term, i.e. the series terminates and
- * false otherwise. */
bool pseries::is_terminating(void) const
{
return seq.size() == 0 || !is_order_function((seq.end()-1)->rest);
/*
- * Implementation of series expansion
+ * Implementations of series expansion
*/
/** Default implementation of ex::series(). This performs Taylor expansion.
numeric fac(1);
ex deriv = *this;
ex coeff = deriv.subs(r);
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
+ const symbol &s = static_cast<symbol &>(*r.lhs().bp);
if (!coeff.is_zero())
- seq.push_back(expair(coeff, numeric(0)));
+ seq.push_back(expair(coeff, _ex0()));
int n;
for (n=1; n<order; ++n) {
fac = fac.mul(numeric(n));
- deriv = deriv.diff(*s).expand();
+ deriv = deriv.diff(s).expand();
if (deriv.is_zero()) {
// Series terminates
return pseries(r, seq);
}
// Higher-order terms, if present
- deriv = deriv.diff(*s);
+ deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
seq.push_back(expair(Order(_ex1()), numeric(n)));
return pseries(r, seq);
epvector seq;
const ex point = r.rhs();
GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
+ ex s = r.lhs();
- if (this->is_equal(*s)) {
+ if (this->is_equal(*s.bp)) {
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;
- const symbol *s = static_cast<symbol *>(var.bp);
- int a_max = degree(*s);
- int b_max = other.degree(*s);
- int a_min = ldegree(*s);
- int b_min = other.ldegree(*s);
+ 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;
int cdeg_max = a_max + b_max;
int higher_order_a = INT_MAX;
int higher_order_b = INT_MAX;
- if (is_order_function(coeff(*s, a_max)))
+ if (is_order_function(coeff(var, a_max)))
higher_order_a = a_max + b_min;
- if (is_order_function(other.coeff(*s, b_max)))
+ 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);
if (cdeg_max >= higher_order_c)
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(*s, i);
- ex b_coeff = other.coeff(*s, cdeg-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;
}
}
if (higher_order_c < 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), new_seq);
}
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));
+ 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);
+ op = ex_to<pseries>(op).power_const(ex_to<numeric>(it->coeff), order);
// Series multiplication
- acc = ex_to_pseries(acc).mul_series(ex_to_pseries(op));
+ acc = ex_to<pseries>(acc).mul_series(ex_to<pseries>(op));
}
return acc;
}
* @param deg truncation order of series calculation */
ex pseries::power_const(const numeric &p, int deg) const
{
- int i;
- const symbol *s = static_cast<symbol *>(var.bp);
- int ldeg = ldegree(*s);
+ // method:
+ // 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 + ...
+ // We want to compute
+ // C(x) = A(x)^p
+ // C(x) = c_0 + c_1*x + c_2*x^2 + ...
+ // Taking the derivative on both sides and multiplying with A(x) one
+ // immediately arrives at
+ // C'(x)*A(x) = p*C(x)*A'(x)
+ // Multiplying this out and comparing coefficients we get the recurrence
+ // formula
+ // c_i = (i*p*a_i*c_0 + ((i-1)*p-1)*a_{i-1}*c_1 + ...
+ // ... + (p-(i-1))*a_1*c_{i-1})/(a_0*i)
+ // which can easily be solved given the starting value c_0 = (a_0)^p.
+ // For the more general case where the leading coefficient of A(x) is not
+ // a constant, just consider A2(x) = A(x)*x^m, with some integer m and
+ // 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
+ // 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"));
+ else if (p.real().is_negative())
+ throw (pole_error("pseries::power_const(): division by zero",1));
+ else
+ return *this;
+ }
- // Calculate coefficients of powered series
+ int ldeg = ldegree(var);
+
+ // Compute coefficients of the powered series
exvector co;
co.reserve(deg);
- ex co0;
- co.push_back(co0 = power(coeff(*s, ldeg), p));
+ co.push_back(power(coeff(var, ldeg), p));
bool all_sums_zero = true;
- for (i=1; i<deg; ++i) {
+ for (int i=1; i<deg; ++i) {
ex sum = _ex0();
for (int j=1; j<=i; ++j) {
- ex c = coeff(*s, j + ldeg);
+ ex c = coeff(var, j + ldeg);
if (is_order_function(c)) {
co.push_back(Order(_ex1()));
break;
}
if (!sum.is_zero())
all_sums_zero = false;
- co.push_back(co0 * sum / numeric(i));
+ co.push_back(sum / coeff(var, ldeg) / numeric(i));
}
// Construct new series (of non-zero coefficients)
epvector new_seq;
bool higher_order = false;
- for (i=0; i<deg; ++i) {
+ for (int i=0; i<deg; ++i) {
if (!co[i].is_zero())
new_seq.push_back(expair(co[i], numeric(i) + p * ldeg));
if (is_order_function(co[i])) {
{
ex e;
if (!is_ex_exactly_of_type(basis, pseries)) {
- // Basis is not a series, may there be a singulary?
- if (!exponent.info(info_flags::negint))
+ // 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);
- // Expression is of type something^(-int), check for singularity
- if (!basis.subs(r).is_zero())
+ // Is the expression of type 0^something?
+ if (!must_expand_basis && !basis.subs(r).is_zero())
return basic::series(r, order, options);
// Singularity encountered, expand basis into series
}
// Power e
- return ex_to_pseries(e).power_const(ex_to_numeric(exponent), order);
+ return ex_to<pseries>(e).power_const(ex_to<numeric>(exponent), order);
}
{
const ex p = r.rhs();
GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
+ const symbol &s = static_cast<symbol &>(*r.lhs().bp);
- if (var.is_equal(*s) && point.is_equal(p)) {
- if (order > degree(*s))
+ if (var.is_equal(s) && point.is_equal(p)) {
+ if (order > degree(s))
return *this;
else {
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
return e;
}
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned pseries::precedence = 38; // for clarity just below add::precedence
-
-//////////
-// global constants
-//////////
-
-const pseries some_pseries;
-const std::type_info & typeid_pseries = typeid(some_pseries);
-
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC