X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns.cpp;h=677d92f61925a47a10599375a72ae16e0f7be817;hp=e0d1e91edcaa0520ce5f94c017dff93e3e67a8a2;hb=db5765dc91202851739e196ba11bfccb0b3fe7bc;hpb=fe9dbfb9947b24149b3ce7dd9285f27ab286cbd7

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index e0d1e91e..677d92f6 100644
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -45,21 +45,21 @@ namespace GiNaC {
 // absolute value
 //////////
 
-static ex abs_evalf(const ex & x)
+static ex abs_evalf(const ex & arg)
 {
     BEGIN_TYPECHECK
-        TYPECHECK(x,numeric)
-    END_TYPECHECK(abs(x))
+        TYPECHECK(arg,numeric)
+    END_TYPECHECK(abs(arg))
     
-    return abs(ex_to_numeric(x));
+    return abs(ex_to_numeric(arg));
 }
 
-static ex abs_eval(const ex & x)
+static ex abs_eval(const ex & arg)
 {
-    if (is_ex_exactly_of_type(x, numeric))
-        return abs(ex_to_numeric(x));
+    if (is_ex_exactly_of_type(arg, numeric))
+        return abs(ex_to_numeric(arg));
     else
-        return abs(x).hold();
+        return abs(arg).hold();
 }
 
 REGISTER_FUNCTION(abs, eval_func(abs_eval).
@@ -70,41 +70,41 @@ REGISTER_FUNCTION(abs, eval_func(abs_eval).
 // Complex sign
 //////////
 
-static ex csgn_evalf(const ex & x)
+static ex csgn_evalf(const ex & arg)
 {
     BEGIN_TYPECHECK
-        TYPECHECK(x,numeric)
-    END_TYPECHECK(csgn(x))
+        TYPECHECK(arg,numeric)
+    END_TYPECHECK(csgn(arg))
     
-    return csgn(ex_to_numeric(x));
+    return csgn(ex_to_numeric(arg));
 }
 
-static ex csgn_eval(const ex & x)
+static ex csgn_eval(const ex & arg)
 {
-    if (is_ex_exactly_of_type(x, numeric))
-        return csgn(ex_to_numeric(x));
+    if (is_ex_exactly_of_type(arg, numeric))
+        return csgn(ex_to_numeric(arg));
     
-    else if (is_ex_exactly_of_type(x, mul)) {
-        numeric oc = ex_to_numeric(x.op(x.nops()-1));
+    else if (is_ex_exactly_of_type(arg, mul)) {
+        numeric oc = ex_to_numeric(arg.op(arg.nops()-1));
         if (oc.is_real()) {
             if (oc > 0)
                 // csgn(42*x) -> csgn(x)
-                return csgn(x/oc).hold();
+                return csgn(arg/oc).hold();
             else
                 // csgn(-42*x) -> -csgn(x)
-                return -csgn(x/oc).hold();
+                return -csgn(arg/oc).hold();
         }
         if (oc.real().is_zero()) {
             if (oc.imag() > 0)
                 // csgn(42*I*x) -> csgn(I*x)
-                return csgn(I*x/oc).hold();
+                return csgn(I*arg/oc).hold();
             else
                 // csgn(-42*I*x) -> -csgn(I*x)
-                return -csgn(I*x/oc).hold();
+                return -csgn(I*arg/oc).hold();
         }
 	}
    
-    return csgn(x).hold();
+    return csgn(arg).hold();
 }
 
 static ex csgn_series(const ex & arg,
@@ -113,13 +113,10 @@ static ex csgn_series(const ex & arg,
                       unsigned options)
 {
     const ex arg_pt = arg.subs(rel);
-    if (arg_pt.info(info_flags::numeric)) {
-        if (ex_to_numeric(arg_pt).real().is_zero())
-            throw (std::domain_error("csgn_series(): on imaginary axis"));
-        epvector seq;
-        seq.push_back(expair(csgn(arg_pt), _ex0()));
-        return pseries(rel,seq);
-    }
+    if (arg_pt.info(info_flags::numeric) &&
+        ex_to_numeric(arg_pt).real().is_zero())
+        throw (std::domain_error("csgn_series(): on imaginary axis"));
+    
     epvector seq;
     seq.push_back(expair(csgn(arg_pt), _ex0()));
     return pseries(rel,seq);
@@ -129,6 +126,61 @@ REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
                         evalf_func(csgn_evalf).
                         series_func(csgn_series));
 
+
+//////////
+// Eta function: log(x*y) == log(x) + log(y) + eta(x,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));
+}
+
+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)) {
+        // 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));
+    }
+    
+    return eta(x,y).hold();
+}
+
+static ex eta_series(const ex & arg1,
+                     const ex & arg2,
+                     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"));
+    }
+    epvector seq;
+    seq.push_back(expair(eta(arg1_pt,arg2_pt), _ex0()));
+    return pseries(rel,seq);
+}
+
+REGISTER_FUNCTION(eta, eval_func(eta_eval).
+                       evalf_func(eta_evalf).
+                       series_func(eta_series));
+
+
 //////////
 // dilogarithm
 //////////
@@ -325,21 +377,19 @@ REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
 
 static ex Order_eval(const ex & x)
 {
-	if (is_ex_exactly_of_type(x, numeric)) {
-
-		// O(c)=O(1)
-		return Order(_ex1()).hold();
-
-	} else if (is_ex_exactly_of_type(x, mul)) {
-
-	 	mul *m = static_cast<mul *>(x.bp);
-		if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric)) {
-
-			// O(c*expr)=O(expr)
-			return Order(x / m->op(m->nops() - 1)).hold();
-		}
-	}
-	return Order(x).hold();
+    if (is_ex_exactly_of_type(x, numeric)) {
+        // 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)) {
+        mul *m = static_cast<mul *>(x.bp);
+        // 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();
+    }
+    return Order(x).hold();
 }
 
 static ex Order_series(const ex & x, const relational & r, int order, unsigned options)
@@ -383,7 +433,7 @@ ex lsolve(const ex &eqns, const ex &symbols)
     // 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"));
+            throw(std::invalid_argument("lsolve(): 2nd argument must be a symbol"));
         ex sol=lsolve(lst(eqns),lst(symbols));
         
         GINAC_ASSERT(sol.nops()==1);
@@ -394,19 +444,19 @@ ex lsolve(const ex &eqns, const ex &symbols)
     
     // syntax checks
     if (!eqns.info(info_flags::list)) {
-        throw(std::invalid_argument("lsolve: 1st argument must be a list"));
+        throw(std::invalid_argument("lsolve(): 1st argument must be a list"));
     }
     for (unsigned 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"));
+            throw(std::invalid_argument("lsolve(): 1st argument must be a list of equations"));
         }
     }
     if (!symbols.info(info_flags::list)) {
-        throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
+        throw(std::invalid_argument("lsolve(): 2nd argument must be a list"));
     }
     for (unsigned 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"));
+            throw(std::invalid_argument("lsolve(): 2nd argument must be a list of symbols"));
         }
     }
     
@@ -423,7 +473,7 @@ ex lsolve(const ex &eqns, const ex &symbols)
             linpart -= co*symbols.op(c);
             sys.set(r,c,co);
         }
-        linpart=linpart.expand();
+        linpart = linpart.expand();
         rhs.set(r,0,-linpart);
     }
     
@@ -436,32 +486,21 @@ ex lsolve(const ex &eqns, const ex &symbols)
             throw(std::logic_error("lsolve: system is not linear"));
     }
     
-    //matrix solution=sys.solve(rhs);
     matrix solution;
     try {
-        solution = sys.fraction_free_elim(vars,rhs);
+        solution = sys.solve(vars,rhs);
     } catch (const runtime_error & e) {
-        // probably singular matrix (or other error)
-        // return empty solution list
-        // cerr << e.what() << endl;
+        // 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());
     
-    // return a list of equations
-    if (solution.cols()!=1) {
-        throw(std::runtime_error("lsolve: strange number of columns returned from matrix::solve"));
-    }
-    if (solution.rows()!=symbols.nops()) {
-        cout << "symbols.nops()=" << symbols.nops() << endl;
-        cout << "solution.rows()=" << solution.rows() << endl;
-        throw(std::runtime_error("lsolve: strange number of rows returned from matrix::solve"));
-    }
-    
-    // return list of the form lst(var1==sol1,var2==sol2,...)
+    // return list of equations of the form lst(var1==sol1,var2==sol2,...)
     lst sollist;
-    for (unsigned i=0; i<symbols.nops(); i++) {
+    for (unsigned i=0; i<symbols.nops(); i++)
         sollist.append(symbols.op(i)==solution(i,0));
-    }
     
     return sollist;
 }