X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns.cpp;h=745223062a70a0f0ba9332942bdeece970f7a05f;hp=2667215416129be392b21891aa2d16ed6bf89139;hb=bf82f5b1d41738936afe763e1fa6aa347c81ba2c;hpb=0117bd6ef4af029934703940d59e1c70866937b0

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index 26672154..74522306 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
@@ -29,12 +29,11 @@
 #include "lst.h"
 #include "matrix.h"
 #include "mul.h"
-#include "ncmul.h"
-#include "numeric.h"
 #include "power.h"
 #include "relational.h"
 #include "pseries.h"
 #include "symbol.h"
+#include "symmetry.h"
 #include "utils.h"
 
 namespace GiNaC {
@@ -45,17 +44,16 @@ 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)
 {
 	if (is_ex_exactly_of_type(arg, numeric))
-		return abs(ex_to_numeric(arg));
+		return abs(ex_to<numeric>(arg));
 	else
 		return abs(arg).hold();
 }
@@ -70,21 +68,20 @@ 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)
 {
 	if (is_ex_exactly_of_type(arg, numeric))
-		return csgn(ex_to_numeric(arg));
+		return csgn(ex_to<numeric>(arg));
 	
-	else if (is_ex_of_type(arg, mul) &&
+	else if (is_ex_exactly_of_type(arg, mul) &&
 	         is_ex_of_type(arg.op(arg.nops()-1),numeric)) {
-		numeric oc = ex_to_numeric(arg.op(arg.nops()-1));
+		numeric oc = ex_to<numeric>(arg.op(arg.nops()-1));
 		if (oc.is_real()) {
 			if (oc > 0)
 				// csgn(42*x) -> csgn(x)
@@ -113,12 +110,12 @@ static ex csgn_series(const ex & arg,
 {
 	const ex arg_pt = arg.subs(rel);
 	if (arg_pt.info(info_flags::numeric)
-	    && ex_to_numeric(arg_pt).real().is_zero()
+	    && ex_to<numeric>(arg_pt).real().is_zero()
 	    && !(options & series_options::suppress_branchcut))
 		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);
 }
 
@@ -128,58 +125,82 @@ REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
 
 
 //////////
-// Eta function: log(x*y) == log(x) + log(y) + eta(x,y).
+// 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)
+static ex eta_evalf(const ex &x, const ex &y)
 {
-	BEGIN_TYPECHECK
-		TYPECHECK(x,numeric)
-		TYPECHECK(y,numeric)
-	END_TYPECHECK(eta(x,y))
-		
-	numeric xim = imag(ex_to_numeric(x));
-	numeric yim = imag(ex_to_numeric(y));
-	numeric xyim = imag(ex_to_numeric(x*y));
-	return evalf(I/4*Pi)*((csgn(-xim)+1)*(csgn(-yim)+1)*(csgn(xyim)+1)-(csgn(xim)+1)*(csgn(yim)+1)*(csgn(-xyim)+1));
+	// 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;
+
+	if (x.info(info_flags::numeric) &&	y.info(info_flags::numeric)) {
+		const numeric nx = ex_to<numeric>(x);
+		const numeric ny = ex_to<numeric>(y);
+		const numeric nxy = ex_to<numeric>(x*y);
+		int cut = 0;
+		if (nx.is_real() && nx.is_negative())
+			cut -= 4;
+		if (ny.is_real() && ny.is_negative())
+			cut -= 4;
+		if (nxy.is_real() && nxy.is_negative())
+			cut += 4;
+		return evalf(I/4*Pi)*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
+		                      (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
+	}
+
+	return eta(x,y).hold();
 }
 
-static ex eta_eval(const ex & x, const ex & y)
+static ex eta_eval(const ex &x, const ex &y)
 {
-	if (is_ex_exactly_of_type(x, numeric) &&
-		is_ex_exactly_of_type(y, numeric)) {
+	// trivial:  eta(x,c) -> 0  if c is real and positive
+	if (x.info(info_flags::positive) || y.info(info_flags::positive))
+		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()!
-		numeric xim = imag(ex_to_numeric(x));
-		numeric yim = imag(ex_to_numeric(y));
-		numeric xyim = imag(ex_to_numeric(x*y));
-		return (I/4)*Pi*((csgn(-xim)+1)*(csgn(-yim)+1)*(csgn(xyim)+1)-(csgn(xim)+1)*(csgn(yim)+1)*(csgn(-xyim)+1));
+		const numeric nx = ex_to<numeric>(x);
+		const numeric ny = ex_to<numeric>(y);
+		const numeric nxy = ex_to<numeric>(x*y);
+		int cut = 0;
+		if (nx.is_real() && nx.is_negative())
+			cut -= 4;
+		if (ny.is_real() && ny.is_negative())
+			cut -= 4;
+		if (nxy.is_real() && nxy.is_negative())
+			cut += 4;
+		return (I/4)*Pi*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
+		                 (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
 	}
 	
 	return eta(x,y).hold();
 }
 
-static ex eta_series(const ex & arg1,
-                     const ex & arg2,
+static ex eta_series(const ex & x, const ex & y,
                      const relational & rel,
                      int order,
                      unsigned options)
 {
-	const ex arg1_pt = arg1.subs(rel);
-	const ex arg2_pt = arg2.subs(rel);
-	if (ex_to_numeric(arg1_pt).imag().is_zero() ||
-		ex_to_numeric(arg2_pt).imag().is_zero() ||
-		ex_to_numeric(arg1_pt*arg2_pt).imag().is_zero()) {
-		throw (std::domain_error("eta_series(): on discontinuity"));
-	}
+	const ex x_pt = x.subs(rel);
+	const ex y_pt = y.subs(rel);
+	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)))
+			throw (std::domain_error("eta_series(): on discontinuity"));
 	epvector seq;
-	seq.push_back(expair(eta(arg1_pt,arg2_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).
-                       latex_name("\\eta"));
+                       latex_name("\\eta").
+                       set_symmetry(sy_symm(0, 1)));
 
 
 //////////
@@ -188,11 +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)
@@ -200,25 +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();
@@ -229,7 +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)
@@ -254,12 +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);
@@ -272,11 +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(2);
+			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));
@@ -284,29 +304,29 @@ 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);
 		}
 		// third special case: x real, >=1 (branch cut)
 		if (!(options & series_options::suppress_branchcut) &&
-			ex_to_numeric(x_pt).is_real() && ex_to_numeric(x_pt)>1) {
+			ex_to<numeric>(x_pt).is_real() && ex_to<numeric>(x_pt)>1) {
 			// 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);
 		}
 	}
@@ -346,7 +366,7 @@ static ex factorial_evalf(const ex & x)
 static ex factorial_eval(const ex & x)
 {
 	if (is_ex_exactly_of_type(x, numeric))
-		return factorial(ex_to_numeric(x));
+		return factorial(ex_to<numeric>(x));
 	else
 		return factorial(x).hold();
 }
@@ -366,7 +386,7 @@ 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))
-		return binomial(ex_to_numeric(x), ex_to_numeric(y));
+		return binomial(ex_to<numeric>(x), ex_to<numeric>(y));
 	else
 		return binomial(x, y).hold();
 }
@@ -383,14 +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();
 }
@@ -399,9 +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_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);
 }
 
@@ -411,37 +431,20 @@ REGISTER_FUNCTION(Order, eval_func(Order_eval).
                          series_func(Order_series).
                          latex_name("\\mathcal{O}"));
 
-//////////
-// Inert partial differentiation operator
-//////////
-
-static ex Derivative_eval(const ex & f, const ex & l)
-{
-	if (!is_ex_exactly_of_type(f, function)) {
-		throw(std::invalid_argument("Derivative(): 1st argument must be a function"));
-	}
-	if (!is_ex_exactly_of_type(l, lst)) {
-		throw(std::invalid_argument("Derivative(): 2nd argument must be a list"));
-	}
-	return Derivative(f, l).hold();
-}
-
-REGISTER_FUNCTION(Derivative, eval_func(Derivative_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)) {
 		if (!symbols.info(info_flags::symbol))
 			throw(std::invalid_argument("lsolve(): 2nd argument must be a symbol"));
-		ex sol=lsolve(lst(eqns),lst(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
 	}
@@ -470,20 +473,20 @@ ex lsolve(const ex &eqns, const ex &symbols)
 	matrix vars(symbols.nops(),1);
 	
 	for (unsigned r=0; r<eqns.nops(); r++) {
-		ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
+		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++) {
-			ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
+			const ex co = eq.coeff(ex_to<symbol>(symbols.op(c)),1);
 			linpart -= co*symbols.op(c);
-			sys.set(r,c,co);
+			sys(r,c) = co;
 		}
 		linpart = linpart.expand();
-		rhs.set(r,0,-linpart);
+		rhs(r,0) = -linpart;
 	}
 	
 	// test if system is linear and fill vars matrix
 	for (unsigned i=0; i<symbols.nops(); i++) {
-		vars.set(i,0,symbols.op(i));
+		vars(i,0) = symbols.op(i);
 		if (sys.has(symbols.op(i)))
 			throw(std::logic_error("lsolve: system is not linear"));
 		if (rhs.has(symbols.op(i)))
@@ -492,12 +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());
 	
@@ -509,87 +512,8 @@ ex lsolve(const ex &eqns, const ex &symbols)
 	return sollist;
 }
 
-/** non-commutative power. */
-ex ncpow(const ex & basis, unsigned exponent)
-{
-	if (exponent == 0)
-		return _ex1();
-
-	exvector v;
-	v.reserve(exponent);
-	for (unsigned i=0; i<exponent; ++i)
-		v.push_back(basis);
-
-	return ncmul(v, true);
-}
-
-// Symmetrize/antisymmetrize over a vector of objects
-static ex symm(const ex & e, exvector::const_iterator first, exvector::const_iterator last, bool asymmetric)
-{
-	// Need at least 2 objects for this operation
-	int num = last - first;
-	if (num < 2)
-		return e;
-
-	// Sort object vector, transform it into a list, and make a copy so we
-	// will know which objects get substituted for which
-	exvector iv(first, last);
-	sort(iv.begin(), iv.end(), ex_is_less());
-	exlist iv_lst;
-	iv_lst.insert(iv_lst.begin(), iv.begin(), iv.end());
-	lst orig_lst(iv_lst);
-
-	// With n objects there are n! possible permutations
-	int num_perms = factorial(numeric(num)).to_int();
-
-	// Loop over all permutations (the first permutation, which is the
-	// identity, is unrolled)
-	ex sum = e;
-	int i = 1;
-	do {
-		next_permutation(iv_lst.begin(), iv_lst.end(), ex_is_less());
-		ex term = e.subs(orig_lst, lst(iv_lst));
-		if (asymmetric) {
-			exlist test_lst = iv_lst;
-			term *= permutation_sign(test_lst.begin(), test_lst.end(), ex_is_less());
-		}
-		sum += term;
-		i++;
-	} while (i < num_perms);
-
-	return sum / num_perms;
-}
-
-ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
-{
-	return symm(e, first, last, false);
-}
-
-ex antisymmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
-{
-	return symm(e, first, last, true);
-}
-
-ex symmetrize(const ex & e, const lst & l)
-{
-	exvector v;
-	v.reserve(l.nops());
-	for (unsigned i=0; i<l.nops(); i++)
-		v.push_back(l.op(i));
-	return symm(e, v.begin(), v.end(), false);
-}
-
-ex antisymmetrize(const ex & e, const lst & l)
-{
-	exvector v;
-	v.reserve(l.nops());
-	for (unsigned i=0; i<l.nops(); i++)
-		v.push_back(l.op(i));
-	return symm(e, v.begin(), v.end(), true);
-}
-
-/** Force inclusion of functions from initcns_gamma and inifcns_zeta
- *  for static lib (so ginsh will see them). */
+/* 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;