- expairseq.cpp: moved expairseq::to_rational to...
[ginac.git] / ginac / inifcns.cpp
index bc401f47266272789b371d9bdced87464ddc3ba7..f7d2864ef9ae64035eae269d140b6c36b6d41169 100644 (file)
@@ -65,6 +65,67 @@ static ex abs_eval(const ex & x)
 REGISTER_FUNCTION(abs, eval_func(abs_eval).
                        evalf_func(abs_evalf));
 
+
+//////////
+// Complex sign
+//////////
+
+static ex csgn_evalf(const ex & x)
+{
+    BEGIN_TYPECHECK
+        TYPECHECK(x,numeric)
+    END_TYPECHECK(csgn(x))
+    
+    return csgn(ex_to_numeric(x));
+}
+
+static ex csgn_eval(const ex & x)
+{
+    if (is_ex_exactly_of_type(x, numeric))
+        return csgn(ex_to_numeric(x));
+    
+    if (is_ex_exactly_of_type(x, mul)) {
+        numeric oc = ex_to_numeric(x.op(x.nops()-1));
+        if (oc.is_real()) {
+            if (oc > 0)
+                // csgn(42*x) -> csgn(x)
+                return csgn(x/oc).hold();
+            else
+                // csgn(-42*x) -> -csgn(x)
+                return -csgn(x/oc).hold();
+        }
+        if (oc.real().is_zero()) {
+            if (oc.imag() > 0)
+                // csgn(42*I*x) -> csgn(I*x)
+                return csgn(I*x/oc).hold();
+            else
+                // csgn(-42*I*x) -> -csgn(I*x)
+                return -csgn(I*x/oc).hold();
+        }
+    }
+    
+    return csgn(x).hold();
+}
+
+static ex csgn_series(const ex & x, const relational & rel, int order)
+{
+    const ex x_pt = x.subs(rel);
+    if (x_pt.info(info_flags::numeric)) {
+        if (ex_to_numeric(x_pt).real().is_zero())
+            throw (std::domain_error("csgn_series(): on imaginary axis"));
+        epvector seq;
+        seq.push_back(expair(csgn(x_pt), _ex0()));
+        return pseries(rel,seq);
+    }
+    epvector seq;
+    seq.push_back(expair(csgn(x_pt), _ex0()));
+    return pseries(rel,seq);
+}
+
+REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
+                        evalf_func(csgn_evalf).
+                        series_func(csgn_series));
+
 //////////
 // dilogarithm
 //////////
@@ -158,17 +219,38 @@ static ex Order_eval(const ex & x)
        return Order(x).hold();
 }
 
-static ex Order_series(const ex & x, const symbol & s, const ex & point, int order)
+static ex Order_series(const ex & x, const relational & r, int order)
 {
        // Just wrap the function into a pseries object
        epvector new_seq;
-       new_seq.push_back(expair(Order(_ex1()), numeric(min(x.ldegree(s), order))));
-       return pseries(s, point, 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(min(x.ldegree(*s), order))));
+       return pseries(r, new_seq);
 }
 
+// Differentiation is handled in function::derivative because of its special requirements
+
 REGISTER_FUNCTION(Order, eval_func(Order_eval).
                          series_func(Order_series));
 
+//////////
+// 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
 //////////
@@ -212,10 +294,10 @@ 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
-        ex linpart=eq;
+        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);
+            ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
             linpart -= co*symbols.op(c);
             sys.set(r,c,co);
         }
@@ -226,18 +308,16 @@ ex lsolve(const ex &eqns, const ex &symbols)
     // test if system is linear and fill vars matrix
     for (unsigned i=0; i<symbols.nops(); i++) {
         vars.set(i,0,symbols.op(i));
-        if (sys.has(symbols.op(i))) {
+        if (sys.has(symbols.op(i)))
             throw(std::logic_error("lsolve: system is not linear"));
-        }
-        if (rhs.has(symbols.op(i))) {
+        if (rhs.has(symbols.op(i)))
             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.fraction_free_elim(vars,rhs);
     } catch (const runtime_error & e) {
         // probably singular matrix (or other error)
         // return empty solution list
@@ -282,7 +362,7 @@ ex ncpower(const ex &basis, unsigned exponent)
 
 /** Force inclusion of functions from initcns_gamma and inifcns_zeta
  *  for static lib (so ginsh will see them). */
-unsigned force_include_gamma = function_index_gamma;
+unsigned force_include_tgamma = function_index_tgamma;
 unsigned force_include_zeta1 = function_index_zeta1;
 
 #ifndef NO_NAMESPACE_GINAC