added example for namespace bracing

[ginac.git] / ginac / inifcns.cpp

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index 73f9c22111d13cead3d7f4082e83691695e49863..443022a556da6c9f48e062e2381b4be05b0e0ae3 100644 (file)
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -59,8 +59,21 @@ static ex abs_eval(const ex & arg)
                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 << ")";
+}
+
 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));
 
 
 //////////
@@ -109,7 +122,7 @@ 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))
@@ -186,8 +199,8 @@ 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)))
@@ -255,7 +268,7 @@ 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()) {
@@ -277,7 +290,7 @@ 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));
@@ -302,7 +315,7 @@ 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));
@@ -325,7 +338,7 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
                        // compute the intermediate terms:
                        ex replarg = series(Li2(x), s==foo, order);
                        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),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);
@@ -355,6 +368,37 @@ 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
 //////////