X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns.cpp;h=c6b14c6b63e768032efe0efc720a542094a65c0b;hp=c18f4c6385c8a3500dac0ca4700b88de2c64d4fa;hb=e65326821bb7f9c4054f35caef46039f1963e951;hpb=686f68ef7dc4e33d910780252cd1032ebcfc25ac

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index c18f4c63..c6b14c6b 100644
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's initially known functions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 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
@@ -44,11 +44,10 @@ namespace GiNaC {
 
 static ex abs_evalf(const ex & arg)
 {
-	BEGIN_TYPECHECK
-		TYPECHECK(arg,numeric)
-	END_TYPECHECK(abs(arg))
+	if (is_exactly_a<numeric>(arg))
+		return abs(ex_to<numeric>(arg));
 	
-	return abs(ex_to<numeric>(arg));
+	return abs(arg).hold();
 }
 
 static ex abs_eval(const ex & arg)
@@ -69,11 +68,10 @@ REGISTER_FUNCTION(abs, eval_func(abs_eval).
 
 static ex csgn_evalf(const ex & arg)
 {
-	BEGIN_TYPECHECK
-		TYPECHECK(arg,numeric)
-	END_TYPECHECK(csgn(arg))
+	if (is_exactly_a<numeric>(arg))
+		return csgn(ex_to<numeric>(arg));
 	
-	return csgn(ex_to<numeric>(arg));
+	return csgn(arg).hold();
 }
 
 static ex csgn_eval(const ex & arg)
@@ -117,7 +115,7 @@ static ex csgn_series(const ex & arg,
 		throw (std::domain_error("csgn_series(): on imaginary axis"));
 	
 	epvector seq;
-	seq.push_back(expair(csgn(arg_pt), _ex0()));
+	seq.push_back(expair(csgn(arg_pt), _ex0));
 	return pseries(rel,seq);
 }
 
@@ -128,6 +126,8 @@ REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
 
 //////////
 // Eta function: eta(x,y) == log(x*y) - log(x) - log(y).
+// This function is closely related to the unwinding number K, sometimes found
+// in modern literature: K(z) == (z-log(exp(z)))/(2*Pi*I).
 //////////
 
 static ex eta_evalf(const ex &x, const ex &y)
@@ -135,7 +135,7 @@ static ex eta_evalf(const ex &x, const ex &y)
 	// It seems like we basically have to replicate the eval function here,
 	// since the expression might not be fully evaluated yet.
 	if (x.info(info_flags::positive) || y.info(info_flags::positive))
-		return _ex0();
+		return _ex0;
 
 	if (x.info(info_flags::numeric) &&	y.info(info_flags::numeric)) {
 		const numeric nx = ex_to<numeric>(x);
@@ -159,7 +159,7 @@ static ex eta_eval(const ex &x, const ex &y)
 {
 	// trivial:  eta(x,c) -> 0  if c is real and positive
 	if (x.info(info_flags::positive) || y.info(info_flags::positive))
-		return _ex0();
+		return _ex0;
 
 	if (x.info(info_flags::numeric) &&	y.info(info_flags::numeric)) {
 		// don't call eta_evalf here because it would call Pi.evalf()!
@@ -192,13 +192,13 @@ static ex eta_series(const ex & x, const ex & y,
 	    ((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative)))
 			throw (std::domain_error("eta_series(): on discontinuity"));
 	epvector seq;
-	seq.push_back(expair(eta(x_pt,y_pt), _ex0()));
+	seq.push_back(expair(eta(x_pt,y_pt), _ex0));
 	return pseries(rel,seq);
 }
 
 REGISTER_FUNCTION(eta, eval_func(eta_eval).
                        evalf_func(eta_evalf).
-				       series_func(eta_series).
+                       series_func(eta_series).
                        latex_name("\\eta").
                        set_symmetry(sy_symm(0, 1)));
 
@@ -209,11 +209,10 @@ REGISTER_FUNCTION(eta, eval_func(eta_eval).
 
 static ex Li2_evalf(const ex & x)
 {
-	BEGIN_TYPECHECK
-		TYPECHECK(x,numeric)
-	END_TYPECHECK(Li2(x))
+	if (is_exactly_a<numeric>(x))
+		return Li2(ex_to<numeric>(x));
 	
-	return Li2(ex_to<numeric>(x));  // -> numeric Li2(numeric)
+	return Li2(x).hold();
 }
 
 static ex Li2_eval(const ex & x)
@@ -221,25 +220,25 @@ static ex Li2_eval(const ex & x)
 	if (x.info(info_flags::numeric)) {
 		// Li2(0) -> 0
 		if (x.is_zero())
-			return _ex0();
+			return _ex0;
 		// Li2(1) -> Pi^2/6
-		if (x.is_equal(_ex1()))
-			return power(Pi,_ex2())/_ex6();
+		if (x.is_equal(_ex1))
+			return power(Pi,_ex2)/_ex6;
 		// Li2(1/2) -> Pi^2/12 - log(2)^2/2
-		if (x.is_equal(_ex1_2()))
-			return power(Pi,_ex2())/_ex12() + power(log(_ex2()),_ex2())*_ex_1_2();
+		if (x.is_equal(_ex1_2))
+			return power(Pi,_ex2)/_ex12 + power(log(_ex2),_ex2)*_ex_1_2;
 		// Li2(-1) -> -Pi^2/12
-		if (x.is_equal(_ex_1()))
-			return -power(Pi,_ex2())/_ex12();
+		if (x.is_equal(_ex_1))
+			return -power(Pi,_ex2)/_ex12;
 		// Li2(I) -> -Pi^2/48+Catalan*I
 		if (x.is_equal(I))
-			return power(Pi,_ex2())/_ex_48() + Catalan*I;
+			return power(Pi,_ex2)/_ex_48 + Catalan*I;
 		// Li2(-I) -> -Pi^2/48-Catalan*I
 		if (x.is_equal(-I))
-			return power(Pi,_ex2())/_ex_48() - Catalan*I;
+			return power(Pi,_ex2)/_ex_48 - Catalan*I;
 		// Li2(float)
 		if (!x.info(info_flags::crational))
-			return Li2_evalf(x);
+			return Li2(ex_to<numeric>(x));
 	}
 	
 	return Li2(x).hold();
@@ -250,7 +249,7 @@ static ex Li2_deriv(const ex & x, unsigned deriv_param)
 	GINAC_ASSERT(deriv_param==0);
 	
 	// d/dx Li2(x) -> -log(1-x)/x
-	return -log(1-x)/x;
+	return -log(_ex1-x)/x;
 }
 
 static ex Li2_series(const ex &x, const relational &rel, int order, unsigned options)
@@ -275,12 +274,12 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 			ex ser;
 			// manually construct the primitive expansion
 			for (int i=1; i<order; ++i)
-				ser += pow(s,i) / pow(numeric(i), _num2());
+				ser += pow(s,i) / pow(numeric(i), _num2);
 			// substitute the argument's series expansion
 			ser = ser.subs(s==x.series(rel, order));
 			// maybe that was terminating, so add a proper order term
 			epvector nseq;
-			nseq.push_back(expair(Order(_ex1()), order));
+			nseq.push_back(expair(Order(_ex1), order));
 			ser += pseries(rel, nseq);
 			// reexpanding it will collapse the series again
 			return ser.series(rel, order);
@@ -293,11 +292,11 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 			// obsolete!
 		}
 		// second special case: x==1 (branch point)
-		if (x_pt == _ex1()) {
+		if (x_pt.is_equal(_ex1)) {
 			// method:
 			// construct series manually in a dummy symbol s
 			const symbol s;
-			ex ser = zeta(_ex2());
+			ex ser = zeta(_ex2);
 			// manually construct the primitive expansion
 			for (int i=1; i<order; ++i)
 				ser += pow(1-s,i) * (numeric(1,i)*(I*Pi+log(s-1)) - numeric(1,i*i));
@@ -305,7 +304,7 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 			ser = ser.subs(s==x.series(rel, order));
 			// maybe that was terminating, so add a proper order term
 			epvector nseq;
-			nseq.push_back(expair(Order(_ex1()), order));
+			nseq.push_back(expair(Order(_ex1), order));
 			ser += pseries(rel, nseq);
 			// reexpanding it will collapse the series again
 			return ser.series(rel, order);
@@ -316,18 +315,18 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 			// method:
 			// This is the branch cut: assemble the primitive series manually
 			// and then add the corresponding complex step function.
-			const symbol *s = static_cast<symbol *>(rel.lhs().bp);
+			const symbol &s = ex_to<symbol>(rel.lhs());
 			const ex point = rel.rhs();
 			const symbol foo;
 			epvector seq;
 			// zeroth order term:
-			seq.push_back(expair(Li2(x_pt), _ex0()));
+			seq.push_back(expair(Li2(x_pt), _ex0));
 			// compute the intermediate terms:
-			ex replarg = series(Li2(x), *s==foo, order);
+			ex replarg = series(Li2(x), s==foo, order);
 			for (unsigned i=1; i<replarg.nops()-1; ++i)
-				seq.push_back(expair((replarg.op(i)/power(*s-foo,i)).series(foo==point,1,options).op(0).subs(foo==*s),i));
+				seq.push_back(expair((replarg.op(i)/power(s-foo,i)).series(foo==point,1,options).op(0).subs(foo==s),i));
 			// append an order term:
-			seq.push_back(expair(Order(_ex1()), replarg.nops()-1));
+			seq.push_back(expair(Order(_ex1), replarg.nops()-1));
 			return pseries(rel, seq);
 		}
 	}
@@ -404,14 +403,14 @@ static ex Order_eval(const ex & x)
 	if (is_ex_exactly_of_type(x, numeric)) {
 		// O(c) -> O(1) or 0
 		if (!x.is_zero())
-			return Order(_ex1()).hold();
+			return Order(_ex1).hold();
 		else
-			return _ex0();
+			return _ex0;
 	} else if (is_ex_exactly_of_type(x, mul)) {
-		mul *m = static_cast<mul *>(x.bp);
+		const mul &m = ex_to<mul>(x);
 		// O(c*expr) -> O(expr)
-		if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric))
-			return Order(x / m->op(m->nops() - 1)).hold();
+		if (is_ex_exactly_of_type(m.op(m.nops() - 1), numeric))
+			return Order(x / m.op(m.nops() - 1)).hold();
 	}
 	return Order(x).hold();
 }
@@ -420,9 +419,9 @@ static ex Order_series(const ex & x, const relational & r, int order, unsigned o
 {
 	// Just wrap the function into a pseries object
 	epvector new_seq;
-	GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
-	const symbol *s = static_cast<symbol *>(r.lhs().bp);
-	new_seq.push_back(expair(Order(_ex1()), numeric(std::min(x.ldegree(*s), order))));
+	GINAC_ASSERT(is_exactly_a<symbol>(r.lhs()));
+	const symbol &s = ex_to<symbol>(r.lhs());
+	new_seq.push_back(expair(Order(_ex1), numeric(std::min(x.ldegree(s), order))));
 	return pseries(r, new_seq);
 }
 
@@ -436,7 +435,7 @@ REGISTER_FUNCTION(Order, eval_func(Order_eval).
 // Solve linear system
 //////////
 
-ex lsolve(const ex &eqns, const ex &symbols)
+ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 {
 	// solve a system of linear equations
 	if (eqns.info(info_flags::relation_equal)) {
@@ -445,7 +444,7 @@ ex lsolve(const ex &eqns, const ex &symbols)
 		const ex sol = lsolve(lst(eqns),lst(symbols));
 		
 		GINAC_ASSERT(sol.nops()==1);
-		GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
+		GINAC_ASSERT(is_exactly_a<relational>(sol.op(0)));
 		
 		return sol.op(0).op(1); // return rhs of first solution
 	}
@@ -496,12 +495,12 @@ ex lsolve(const ex &eqns, const ex &symbols)
 	
 	matrix solution;
 	try {
-		solution = sys.solve(vars,rhs);
+		solution = sys.solve(vars,rhs,options);
 	} catch (const std::runtime_error & e) {
 		// Probably singular matrix or otherwise overdetermined system:
 		// It is consistent to return an empty list
 		return lst();
-	}    
+	}
 	GINAC_ASSERT(solution.cols()==1);
 	GINAC_ASSERT(solution.rows()==symbols.nops());