X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns.cpp;h=33582acb1f3c2672371cdba1742d5dfb19161559;hp=e211442406f30989197cf322a37ed6282c5866f8;hb=8dc09f48182574d792a2ed7c37b66831d9267a6c;hpb=27d6204effdef95a00af461fff98024e290dbaa7;ds=sidebyside

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index e2114424..33582acb 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) 1999-2004 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
@@ -30,6 +30,7 @@
 #include "matrix.h"
 #include "mul.h"
 #include "power.h"
+#include "operators.h"
 #include "relational.h"
 #include "pseries.h"
 #include "symbol.h"
@@ -38,6 +39,38 @@
 
 namespace GiNaC {
 
+//////////
+// complex conjugate
+//////////
+
+static ex conjugate_evalf(const ex & arg)
+{
+	if (is_exactly_a<numeric>(arg)) {
+		return ex_to<numeric>(arg).conjugate();
+	}
+	return conjugate(arg).hold();
+}
+
+static ex conjugate_eval(const ex & arg)
+{
+	return arg.conjugate();
+}
+
+static void conjugate_print_latex(const ex & arg, const print_context & c)
+{
+	c.s << "\bar{"; arg.print(c); c.s << "}";
+}
+
+static ex conjugate_conjugate(const ex & arg)
+{
+	return arg;
+}
+
+REGISTER_FUNCTION(conjugate, eval_func(conjugate_eval).
+                       evalf_func(conjugate_evalf).
+                       print_func<print_latex>(conjugate_print_latex).
+                       conjugate_func(conjugate_conjugate));
+
 //////////
 // absolute value
 //////////
@@ -52,14 +85,33 @@ static ex abs_evalf(const ex & arg)
 
 static ex abs_eval(const ex & arg)
 {
-	if (is_ex_exactly_of_type(arg, numeric))
+	if (is_exactly_a<numeric>(arg))
 		return abs(ex_to<numeric>(arg));
 	else
 		return abs(arg).hold();
 }
 
+static void abs_print_latex(const ex & arg, const print_context & c)
+{
+	c.s << "{|"; arg.print(c); c.s << "|}";
+}
+
+static void abs_print_csrc_float(const ex & arg, const print_context & c)
+{
+	c.s << "fabs("; arg.print(c); c.s << ")";
+}
+
+static ex abs_conjugate(const ex & arg)
+{
+	return abs(arg);
+}
+
 REGISTER_FUNCTION(abs, eval_func(abs_eval).
-                       evalf_func(abs_evalf));
+                       evalf_func(abs_evalf).
+                       print_func<print_latex>(abs_print_latex).
+                       print_func<print_csrc_float>(abs_print_csrc_float).
+                       print_func<print_csrc_double>(abs_print_csrc_float).
+                       conjugate_func(abs_conjugate));
 
 
 //////////
@@ -76,11 +128,11 @@ static ex csgn_evalf(const ex & arg)
 
 static ex csgn_eval(const ex & arg)
 {
-	if (is_ex_exactly_of_type(arg, numeric))
+	if (is_exactly_a<numeric>(arg))
 		return csgn(ex_to<numeric>(arg));
 	
-	else if (is_ex_of_type(arg, mul) &&
-	         is_ex_of_type(arg.op(arg.nops()-1),numeric)) {
+	else if (is_exactly_a<mul>(arg) &&
+	         is_exactly_a<numeric>(arg.op(arg.nops()-1))) {
 		numeric oc = ex_to<numeric>(arg.op(arg.nops()-1));
 		if (oc.is_real()) {
 			if (oc > 0)
@@ -108,7 +160,7 @@ static ex csgn_series(const ex & arg,
                       int order,
                       unsigned options)
 {
-	const ex arg_pt = arg.subs(rel);
+	const ex arg_pt = arg.subs(rel, subs_options::no_pattern);
 	if (arg_pt.info(info_flags::numeric)
 	    && ex_to<numeric>(arg_pt).real().is_zero()
 	    && !(options & series_options::suppress_branchcut))
@@ -119,9 +171,15 @@ static ex csgn_series(const ex & arg,
 	return pseries(rel,seq);
 }
 
+static ex csgn_conjugate(const ex& arg)
+{
+	return csgn(arg);
+}
+
 REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
                         evalf_func(csgn_evalf).
-                        series_func(csgn_series));
+                        series_func(csgn_series).
+                        conjugate_func(csgn_conjugate));
 
 
 //////////
@@ -185,8 +243,8 @@ static ex eta_series(const ex & x, const ex & y,
                      int order,
                      unsigned options)
 {
-	const ex x_pt = x.subs(rel);
-	const ex y_pt = y.subs(rel);
+	const ex x_pt = x.subs(rel, subs_options::no_pattern);
+	const ex y_pt = y.subs(rel, subs_options::no_pattern);
 	if ((x_pt.info(info_flags::numeric) && x_pt.info(info_flags::negative)) ||
 	    (y_pt.info(info_flags::numeric) && y_pt.info(info_flags::negative)) ||
 	    ((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative)))
@@ -196,11 +254,17 @@ static ex eta_series(const ex & x, const ex & y,
 	return pseries(rel,seq);
 }
 
+static ex eta_conjugate(const ex & x, const ex & y)
+{
+	return -eta(x,y);
+}
+
 REGISTER_FUNCTION(eta, eval_func(eta_eval).
                        evalf_func(eta_evalf).
                        series_func(eta_series).
                        latex_name("\\eta").
-                       set_symmetry(sy_symm(0, 1)));
+                       set_symmetry(sy_symm(0, 1)).
+                       conjugate_func(eta_conjugate));
 
 
 //////////
@@ -254,7 +318,7 @@ static ex Li2_deriv(const ex & x, unsigned deriv_param)
 
 static ex Li2_series(const ex &x, const relational &rel, int order, unsigned options)
 {
-	const ex x_pt = x.subs(rel);
+	const ex x_pt = x.subs(rel, subs_options::no_pattern);
 	if (x_pt.info(info_flags::numeric)) {
 		// First special case: x==0 (derivatives have poles)
 		if (x_pt.is_zero()) {
@@ -276,7 +340,7 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 			for (int i=1; i<order; ++i)
 				ser += pow(s,i) / pow(numeric(i), _num2);
 			// substitute the argument's series expansion
-			ser = ser.subs(s==x.series(rel, order));
+			ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern);
 			// maybe that was terminating, so add a proper order term
 			epvector nseq;
 			nseq.push_back(expair(Order(_ex1), order));
@@ -301,7 +365,7 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 			for (int i=1; i<order; ++i)
 				ser += pow(1-s,i) * (numeric(1,i)*(I*Pi+log(s-1)) - numeric(1,i*i));
 			// substitute the argument's series expansion
-			ser = ser.subs(s==x.series(rel, order));
+			ser = ser.subs(s==x.series(rel, order), subs_options::no_pattern);
 			// maybe that was terminating, so add a proper order term
 			epvector nseq;
 			nseq.push_back(expair(Order(_ex1), order));
@@ -323,8 +387,8 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 			seq.push_back(expair(Li2(x_pt), _ex0));
 			// compute the intermediate terms:
 			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));
+			for (size_t 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, subs_options::no_pattern),i));
 			// append an order term:
 			seq.push_back(expair(Order(_ex1), replarg.nops()-1));
 			return pseries(rel, seq);
@@ -354,6 +418,37 @@ static ex Li3_eval(const ex & x)
 REGISTER_FUNCTION(Li3, eval_func(Li3_eval).
                        latex_name("\\mbox{Li}_3"));
 
+//////////
+// Derivatives of Riemann's Zeta-function  zetaderiv(0,x)==zeta(x)
+//////////
+
+static ex zetaderiv_eval(const ex & n, const ex & x)
+{
+	if (n.info(info_flags::numeric)) {
+		// zetaderiv(0,x) -> zeta(x)
+		if (n.is_zero())
+			return zeta(x);
+	}
+	
+	return zetaderiv(n, x).hold();
+}
+
+static ex zetaderiv_deriv(const ex & n, const ex & x, unsigned deriv_param)
+{
+	GINAC_ASSERT(deriv_param<2);
+	
+	if (deriv_param==0) {
+		// d/dn zeta(n,x)
+		throw(std::logic_error("cannot diff zetaderiv(n,x) with respect to n"));
+	}
+	// d/dx psi(n,x)
+	return zetaderiv(n+1,x);
+}
+
+REGISTER_FUNCTION(zetaderiv, eval_func(zetaderiv_eval).
+	                       	 derivative_func(zetaderiv_deriv).
+  	                         latex_name("\\zeta^\\prime"));
+
 //////////
 // factorial
 //////////
@@ -365,14 +460,20 @@ static ex factorial_evalf(const ex & x)
 
 static ex factorial_eval(const ex & x)
 {
-	if (is_ex_exactly_of_type(x, numeric))
+	if (is_exactly_a<numeric>(x))
 		return factorial(ex_to<numeric>(x));
 	else
 		return factorial(x).hold();
 }
 
+static ex factorial_conjugate(const ex & x)
+{
+	return factorial(x);
+}
+
 REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
-                             evalf_func(factorial_evalf));
+                             evalf_func(factorial_evalf).
+                             conjugate_func(factorial_conjugate));
 
 //////////
 // binomial
@@ -385,14 +486,23 @@ static ex binomial_evalf(const ex & x, const ex & y)
 
 static ex binomial_eval(const ex & x, const ex &y)
 {
-	if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
+	if (is_exactly_a<numeric>(x) && is_exactly_a<numeric>(y))
 		return binomial(ex_to<numeric>(x), ex_to<numeric>(y));
 	else
 		return binomial(x, y).hold();
 }
 
+// At the moment the numeric evaluation of a binomail function always
+// gives a real number, but if this would be implemented using the gamma
+// function, also complex conjugation should be changed (or rather, deleted).
+static ex binomial_conjugate(const ex & x, const ex & y)
+{
+	return binomial(x,y);
+}
+
 REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
-                            evalf_func(binomial_evalf));
+                            evalf_func(binomial_evalf).
+                            conjugate_func(binomial_conjugate));
 
 //////////
 // Order term function (for truncated power series)
@@ -400,16 +510,16 @@ REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
 
 static ex Order_eval(const ex & x)
 {
-	if (is_ex_exactly_of_type(x, numeric)) {
+	if (is_exactly_a<numeric>(x)) {
 		// O(c) -> O(1) or 0
 		if (!x.is_zero())
 			return Order(_ex1).hold();
 		else
 			return _ex0;
-	} else if (is_ex_exactly_of_type(x, mul)) {
+	} else if (is_exactly_a<mul>(x)) {
 		const mul &m = ex_to<mul>(x);
 		// O(c*expr) -> O(expr)
-		if (is_ex_exactly_of_type(m.op(m.nops() - 1), numeric))
+		if (is_exactly_a<numeric>(m.op(m.nops() - 1)))
 			return Order(x / m.op(m.nops() - 1)).hold();
 	}
 	return Order(x).hold();
@@ -419,17 +529,23 @@ 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_exactly_a<symbol>(r.lhs()));
+	GINAC_ASSERT(is_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);
 }
 
+static ex Order_conjugate(const ex & x)
+{
+	return Order(x);
+}
+
 // Differentiation is handled in function::derivative because of its special requirements
 
 REGISTER_FUNCTION(Order, eval_func(Order_eval).
                          series_func(Order_series).
-                         latex_name("\\mathcal{O}"));
+                         latex_name("\\mathcal{O}").
+                         conjugate_func(Order_conjugate));
 
 //////////
 // Solve linear system
@@ -453,7 +569,7 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 	if (!eqns.info(info_flags::list)) {
 		throw(std::invalid_argument("lsolve(): 1st argument must be a list"));
 	}
-	for (unsigned i=0; i<eqns.nops(); i++) {
+	for (size_t i=0; i<eqns.nops(); i++) {
 		if (!eqns.op(i).info(info_flags::relation_equal)) {
 			throw(std::invalid_argument("lsolve(): 1st argument must be a list of equations"));
 		}
@@ -461,7 +577,7 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 	if (!symbols.info(info_flags::list)) {
 		throw(std::invalid_argument("lsolve(): 2nd argument must be a list"));
 	}
-	for (unsigned i=0; i<symbols.nops(); i++) {
+	for (size_t i=0; i<symbols.nops(); i++) {
 		if (!symbols.op(i).info(info_flags::symbol)) {
 			throw(std::invalid_argument("lsolve(): 2nd argument must be a list of symbols"));
 		}
@@ -472,10 +588,10 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 	matrix rhs(eqns.nops(),1);
 	matrix vars(symbols.nops(),1);
 	
-	for (unsigned r=0; r<eqns.nops(); r++) {
+	for (size_t r=0; r<eqns.nops(); r++) {
 		const ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
 		ex linpart = eq;
-		for (unsigned c=0; c<symbols.nops(); c++) {
+		for (size_t c=0; c<symbols.nops(); c++) {
 			const ex co = eq.coeff(ex_to<symbol>(symbols.op(c)),1);
 			linpart -= co*symbols.op(c);
 			sys(r,c) = co;
@@ -485,7 +601,7 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 	}
 	
 	// test if system is linear and fill vars matrix
-	for (unsigned i=0; i<symbols.nops(); i++) {
+	for (size_t i=0; i<symbols.nops(); i++) {
 		vars(i,0) = symbols.op(i);
 		if (sys.has(symbols.op(i)))
 			throw(std::logic_error("lsolve: system is not linear"));
@@ -506,7 +622,7 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 	
 	// return list of equations of the form lst(var1==sol1,var2==sol2,...)
 	lst sollist;
-	for (unsigned i=0; i<symbols.nops(); i++)
+	for (size_t i=0; i<symbols.nops(); i++)
 		sollist.append(symbols.op(i)==solution(i,0));
 	
 	return sollist;
@@ -514,7 +630,7 @@ ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
 
 /* Force inclusion of functions from inifcns_gamma and inifcns_zeta
  * for static lib (so ginsh will see them). */
-unsigned force_include_tgamma = function_index_tgamma;
-unsigned force_include_zeta1 = function_index_zeta1;
+unsigned force_include_tgamma = tgamma_SERIAL::serial;
+unsigned force_include_zeta1 = zeta1_SERIAL::serial;
 
 } // namespace GiNaC