X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=22d7b7777a19c8c5ea82eec48b2b99adfc707f2a;hp=d7f784760be6f2b43f2ccc1f0da325e1fcd55dde;hb=5ef801553eb39aed7bd2df9dd1aff9d752c3ea9d;hpb=0cf43f3096cbcfc7472ff9c8927c6eb74f2eeb8c

diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp
index d7f78476..22d7b777 100644
--- a/ginac/pseries.cpp
+++ b/ginac/pseries.cpp
@@ -4,7 +4,7 @@
  *  methods for series expansion. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -21,6 +21,7 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <stdexcept>
 
 #include "pseries.h"
@@ -30,11 +31,11 @@
 #include "mul.h"
 #include "power.h"
 #include "relational.h"
+#include "operators.h"
 #include "symbol.h"
 #include "print.h"
 #include "archive.h"
 #include "utils.h"
-#include "debugmsg.h"
 
 namespace GiNaC {
 
@@ -42,23 +43,10 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(pseries, basic)
 
 
 /*
- *  Default ctor, dtor, copy ctor, assignment operator and helpers
+ *  Default constructor
  */
 
-pseries::pseries() : basic(TINFO_pseries)
-{
-	debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT);
-}
-
-void pseries::copy(const pseries &other)
-{
-	inherited::copy(other);
-	seq = other.seq;
-	var = other.var;
-	point = other.point;
-}
-
-DEFAULT_DESTROY(pseries)
+pseries::pseries() : inherited(TINFO_pseries) { }
 
 
 /*
@@ -68,7 +56,7 @@ DEFAULT_DESTROY(pseries)
 /** Construct pseries from a vector of coefficients and powers.
  *  expair.rest holds the coefficient, expair.coeff holds the power.
  *  The powers must be integers (positive or negative) and in ascending order;
- *  the last coefficient can be Order(_ex1()) to represent a truncated,
+ *  the last coefficient can be Order(_ex1) to represent a truncated,
  *  non-terminating series.
  *
  *  @param rel_  expansion variable and point (must hold a relational)
@@ -76,11 +64,10 @@ DEFAULT_DESTROY(pseries)
  *  @return newly constructed pseries */
 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_a<relational>(rel_));
+	GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
 	point = rel_.rhs();
-	var = *static_cast<symbol *>(rel_.lhs().bp);
+	var = rel_.lhs();
 }
 
 
@@ -88,9 +75,8 @@ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), s
  *  Archiving
  */
 
-pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+pseries::pseries(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("pseries ctor from archive_node", LOGLEVEL_CONSTRUCT);
 	for (unsigned int i=0; true; ++i) {
 		ex rest;
 		ex coeff;
@@ -119,20 +105,19 @@ void pseries::archive(archive_node &n) const
 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_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) {
+		size_t num = seq.size();
+		for (size_t 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;
@@ -140,6 +125,23 @@ void pseries::print(const print_context & c, unsigned level) const
 		var.print(c, level + delta_indent);
 		point.print(c, level + delta_indent);
 
+	} else if (is_a<print_python_repr>(c)) {
+		c.s << class_name() << "(relational(";
+		var.print(c);
+		c.s << ',';
+		point.print(c);
+		c.s << "),[";
+		size_t num = seq.size();
+		for (size_t i=0; i<num; ++i) {
+			if (i)
+				c.s << ',';
+			c.s << '(';
+			seq[i].rest.print(c);
+			c.s << ',';
+			seq[i].coeff.print(c);
+			c.s << ')';
+		}
+		c.s << "])";
 	} else {
 
 		if (precedence() <= level)
@@ -150,9 +152,10 @@ void pseries::print(const print_context & c, unsigned level) const
 		
 		// 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 << '+';
@@ -178,8 +181,11 @@ void pseries::print(const print_context & c, unsigned level) const
 						c.s << par_close;
 					} else
 						var.print(c);
-					if (i->coeff.compare(_ex1())) {
-						c.s << '^';
+					if (i->coeff.compare(_ex1)) {
+						if (is_a<print_python>(c))
+							c.s << "**";
+						else
+							c.s << '^';
 						if (i->coeff.info(info_flags::negative)) {
 							c.s << par_open;
 							i->coeff.print(c);
@@ -196,6 +202,7 @@ void pseries::print(const print_context & c, unsigned level) const
 				}
 			} else
 				Order(power(var-point,i->coeff)).print(c);
+			++i;
 		}
 
 		if (precedence() <= level)
@@ -205,7 +212,7 @@ void pseries::print(const print_context & c, unsigned level) const
 
 int pseries::compare_same_type(const basic & other) const
 {
-	GINAC_ASSERT(is_of_type(other, pseries));
+	GINAC_ASSERT(is_a<pseries>(other));
 	const pseries &o = static_cast<const pseries &>(other);
 	
 	// first compare the lengths of the series...
@@ -237,22 +244,18 @@ int pseries::compare_same_type(const basic & other) const
 }
 
 /** Return the number of operands including a possible order term. */
-unsigned pseries::nops(void) const
+size_t pseries::nops() const
 {
 	return seq.size();
 }
 
 /** Return the ith term in the series when represented as a sum. */
-ex pseries::op(int i) const
+ex pseries::op(size_t i) const
 {
-	if (i < 0 || unsigned(i) >= seq.size())
+	if (i >= seq.size())
 		throw (std::out_of_range("op() out of range"));
-	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 seq[i].rest * power(var - point, seq[i].coeff);
 }
 
 /** Return degree of highest power of the series.  This is usually the exponent
@@ -263,7 +266,7 @@ 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 {
@@ -291,7 +294,7 @@ 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 {
@@ -319,16 +322,16 @@ int pseries::ldegree(const ex &s) const
 ex pseries::coeff(const ex &s, int n) const
 {
 	if (var.is_equal(s)) {
-		if (seq.size() == 0)
-			return _ex0();
+		if (seq.empty())
+			return _ex0;
 		
 		// Binary search in sequence for given power
 		numeric looking_for = numeric(n);
 		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;
@@ -342,7 +345,7 @@ ex pseries::coeff(const ex &s, int n) const
 					throw(std::logic_error("pseries::coeff: compare() didn't return -1, 0 or 1"));
 			}
 		}
-		return _ex0();
+		return _ex0;
 	} else
 		return convert_to_poly().coeff(s, n);
 }
@@ -353,7 +356,7 @@ ex pseries::collect(const ex &s, bool distributed) const
 	return *this;
 }
 
-/** Evaluate coefficients. */
+/** Perform coefficient-wise automatic term rewriting rules in this class. */
 ex pseries::eval(int level) const
 {
 	if (level == 1)
@@ -393,13 +396,13 @@ 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, bool no_pattern) const
+ex pseries::subs(const exmap & m, unsigned options) 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, no_pattern);
+	if (m.find(var) != m.end())
+		return convert_to_poly(true).subs(m, options);
 	
 	// Otherwise construct a new series with substituted coefficients and
 	// expansion point
@@ -407,10 +410,10 @@ ex pseries::subs(const lst & ls, const lst & lr, bool no_pattern) const
 	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, no_pattern), it->coeff));
+		newseq.push_back(expair(it->rest.subs(m, options), it->coeff));
 		++it;
 	}
-	return (new pseries(relational(var,point.subs(ls, lr, no_pattern)), newseq))->setflag(status_flags::dynallocated);
+	return (new pseries(relational(var,point.subs(m, options)), newseq))->setflag(status_flags::dynallocated);
 }
 
 /** Implementation of ex::expand() for a power series.  It expands all the
@@ -418,23 +421,25 @@ ex pseries::subs(const lst & ls, const lst & lr, bool no_pattern) const
 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
- *  polynomial.
+/** Implementation of ex::diff() for a power series.
  *  @see ex::diff */
 ex pseries::derivative(const symbol & s) const
 {
+	epvector new_seq;
+	epvector::const_iterator it = seq.begin(), itend = seq.end();
+
 	if (s == var) {
-		epvector new_seq;
-		epvector::const_iterator it = seq.begin(), itend = seq.end();
 		
 		// FIXME: coeff might depend on var
 		while (it != itend) {
@@ -447,10 +452,22 @@ ex pseries::derivative(const symbol & s) const
 			}
 			++it;
 		}
-		return pseries(relational(var,point), new_seq);
+
 	} else {
-		return *this;
+
+		while (it != itend) {
+			if (is_order_function(it->rest)) {
+				new_seq.push_back(*it);
+			} else {
+				ex c = it->rest.diff(s);
+				if (!c.is_zero())
+					new_seq.push_back(expair(c, it->coeff));
+			}
+			++it;
+		}
 	}
+
+	return pseries(relational(var,point), new_seq);
 }
 
 ex pseries::convert_to_poly(bool no_order) const
@@ -469,9 +486,9 @@ ex pseries::convert_to_poly(bool no_order) const
 	return e;
 }
 
-bool pseries::is_terminating(void) const
+bool pseries::is_terminating() const
 {
-	return seq.size() == 0 || !is_order_function((seq.end()-1)->rest);
+	return seq.empty() || !is_order_function((seq.end()-1)->rest);
 }
 
 
@@ -484,31 +501,33 @@ bool pseries::is_terminating(void) const
 ex basic::series(const relational & r, int order, unsigned options) const
 {
 	epvector seq;
-	numeric fac(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()));
+		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);
 }
 
@@ -519,18 +538,17 @@ ex symbol::series(const relational & r, int order, unsigned options) const
 {
 	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_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()));
+			seq.push_back(expair(point, _ex0));
 		if (order > 1)
-			seq.push_back(expair(_ex1(), _ex1()));
+			seq.push_back(expair(_ex1, _ex1));
 		else
-			seq.push_back(expair(Order(_ex1()), numeric(order)));
+			seq.push_back(expair(Order(_ex1), numeric(order)));
 	} else
-		seq.push_back(expair(*this, _ex0()));
+		seq.push_back(expair(*this, _ex0));
 	return pseries(r, seq);
 }
 
@@ -546,7 +564,7 @@ ex pseries::add_series(const pseries &other) const
 	// results in an empty (constant) series 
 	if (!is_compatible_to(other)) {
 		epvector nul;
-		nul.push_back(expair(Order(_ex1()), _ex0()));
+		nul.push_back(expair(Order(_ex1), _ex0));
 		return pseries(relational(var,point), nul);
 	}
 	
@@ -566,7 +584,7 @@ ex pseries::add_series(const pseries &other) const
 			}
 			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) {
@@ -576,7 +594,7 @@ ex pseries::add_series(const pseries &other) const
 			}
 			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) {
@@ -594,7 +612,7 @@ ex pseries::add_series(const pseries &other) const
 		} else {
 			// Add coefficient of a and b
 			if (is_order_function((*a).rest) || is_order_function((*b).rest)) {
-				new_seq.push_back(expair(Order(_ex1()), (*a).coeff));
+				new_seq.push_back(expair(Order(_ex1), (*a).coeff));
 				break;  // Order term ends the sequence
 			} else {
 				ex sum = (*a).rest + (*b).rest;
@@ -624,15 +642,15 @@ ex add::series(const relational & r, int order, unsigned options) const
 	epvector::const_iterator itend = seq.end();
 	for (; it!=itend; ++it) {
 		ex op;
-		if (is_ex_exactly_of_type(it->rest, pseries))
+		if (is_exactly_a<pseries>(it->rest))
 			op = it->rest;
 		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));
+		if (!it->coeff.is_equal(_ex1))
+			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;
 }
@@ -671,13 +689,12 @@ ex pseries::mul_series(const pseries &other) const
 	// results in an empty (constant) series 
 	if (!is_compatible_to(other)) {
 		epvector nul;
-		nul.push_back(expair(Order(_ex1()), _ex0()));
+		nul.push_back(expair(Order(_ex1), _ex0));
 		return pseries(relational(var,point), nul);
 	}
 	
 	// Series multiplication
 	epvector new_seq;
-	
 	int a_max = degree(var);
 	int b_max = other.degree(var);
 	int a_min = ldegree(var);
@@ -696,7 +713,7 @@ ex pseries::mul_series(const pseries &other) const
 		cdeg_max = higher_order_c - 1;
 	
 	for (int cdeg=cdeg_min; cdeg<=cdeg_max; ++cdeg) {
-		ex co = _ex0();
+		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);
@@ -708,7 +725,7 @@ ex pseries::mul_series(const pseries &other) const
 			new_seq.push_back(expair(co, numeric(cdeg)));
 	}
 	if (higher_order_c < INT_MAX)
-		new_seq.push_back(expair(Order(_ex1()), numeric(higher_order_c)));
+		new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c)));
 	return pseries(relational(var, point), new_seq);
 }
 
@@ -718,30 +735,21 @@ ex pseries::mul_series(const pseries &other) const
  *  @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));
 }
 
 
@@ -752,6 +760,7 @@ ex mul::series(const relational & r, int order, unsigned options) const
 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 + ...
@@ -771,18 +780,24 @@ ex pseries::power_const(const numeric &p, int deg) const
 	// 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;
@@ -790,18 +805,18 @@ ex pseries::power_const(const numeric &p, int deg) const
 	co.push_back(power(coeff(var, ldeg), p));
 	bool all_sums_zero = true;
 	for (int i=1; i<deg; ++i) {
-		ex sum = _ex0();
+		ex sum = _ex0;
 		for (int j=1; j<=i; ++j) {
 			ex c = coeff(var, j + ldeg);
 			if (is_order_function(c)) {
-				co.push_back(Order(_ex1()));
+				co.push_back(Order(_ex1));
 				break;
 			} else
 				sum += (p * j - (i - j)) * co[i - j] * c;
 		}
 		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)
@@ -809,14 +824,14 @@ ex pseries::power_const(const numeric &p, int deg) const
 	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);
 }
 
@@ -824,9 +839,12 @@ ex pseries::power_const(const numeric &p, int deg) const
 /** 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);
 }
 
@@ -836,33 +854,39 @@ pseries pseries::shift_exponents(int deg) const
  *  @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_exactly_a<pseries>(basis))
+		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);
 }
 
 
@@ -870,8 +894,8 @@ ex power::series(const relational & r, int order, unsigned options) const
 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_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))
@@ -880,9 +904,9 @@ ex pseries::series(const relational & r, int order, unsigned options) const
 			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));
+					new_seq.push_back(expair(Order(_ex1), o));
 					break;
 				}
 				new_seq.push_back(*it);
@@ -906,14 +930,13 @@ ex pseries::series(const relational & r, int order, unsigned options) const
  *  @return an expression holding a pseries object */
 ex ex::series(const ex & r, int order, unsigned options) const
 {
-	GINAC_ASSERT(bp!=0);
 	ex e;
 	relational rel_;
 	
-	if (is_ex_exactly_of_type(r,relational))
-		rel_ = ex_to_relational(r);
-	else if (is_ex_exactly_of_type(r,symbol))
-		rel_ = relational(r,_ex0());
+	if (is_a<relational>(r))
+		rel_ = ex_to<relational>(r);
+	else if (is_a<symbol>(r))
+		rel_ = relational(r,_ex0);
 	else
 		throw (std::logic_error("ex::series(): expansion point has unknown type"));