Vlamirs patch for automatically simplifying e.g., csgn(x)^3 -> csgn(x).

[ginac.git] / ginac / inifcns.cpp

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index 26ebd937466c2d31a029c306dc225d5a1f417f9e..a8f82d8ea0413efaa02e63ea29d9a9919759f793 100644 (file)
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -107,13 +107,88 @@ static ex abs_conjugate(const ex & arg)
        return abs(arg);
 }
 
+static ex abs_power(const ex & arg, const ex & exp)
+{
+       if (arg.is_equal(arg.conjugate()) && is_a<numeric>(exp) && ex_to<numeric>(exp).is_even())
+               return power(arg, exp);
+       else
+               return power(abs(arg), exp).hold();
+}
+
 REGISTER_FUNCTION(abs, eval_func(abs_eval).
                        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));
+                       conjugate_func(abs_conjugate).
+                       power_func(abs_power));
+
+//////////
+// Step function
+//////////
+
+static ex step_evalf(const ex & arg)
+{
+       if (is_exactly_a<numeric>(arg))
+               return step(ex_to<numeric>(arg));
+       
+       return step(arg).hold();
+}
+
+static ex step_eval(const ex & arg)
+{
+       if (is_exactly_a<numeric>(arg))
+               return step(ex_to<numeric>(arg));
+       
+       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)
+                               // step(42*x) -> step(x)
+                               return step(arg/oc).hold();
+                       else
+                               // step(-42*x) -> step(-x)
+                               return step(-arg/oc).hold();
+               }
+               if (oc.real().is_zero()) {
+                       if (oc.imag() > 0)
+                               // step(42*I*x) -> step(I*x)
+                               return step(I*arg/oc).hold();
+                       else
+                               // step(-42*I*x) -> step(-I*x)
+                               return step(-I*arg/oc).hold();
+               }
+       }
+       
+       return step(arg).hold();
+}
+
+static ex step_series(const ex & arg,
+                      const relational & rel,
+                      int order,
+                      unsigned options)
+{
+       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))
+               throw (std::domain_error("step_series(): on imaginary axis"));
+       
+       epvector seq;
+       seq.push_back(expair(step(arg_pt), _ex0));
+       return pseries(rel,seq);
+}
+
+static ex step_conjugate(const ex& arg)
+{
+       return step(arg);
+}
 
+REGISTER_FUNCTION(step, eval_func(step_eval).
+                        evalf_func(step_evalf).
+                        series_func(step_series).
+                        conjugate_func(step_conjugate));
 
 //////////
 // Complex sign
@@ -177,10 +252,23 @@ static ex csgn_conjugate(const ex& arg)
        return csgn(arg);
 }
 
+static ex csgn_power(const ex & arg, const ex & exp)
+{
+       if (is_a<numeric>(exp) && exp.info(info_flags::positive) && ex_to<numeric>(exp).is_integer()) {
+               if (ex_to<numeric>(exp).is_odd())
+                       return csgn(arg);
+               else
+                       return power(csgn(arg), _ex2).hold();
+       } else
+               return power(csgn(arg), exp).hold();
+}
+
+
 REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
                         evalf_func(csgn_evalf).
                         series_func(csgn_series).
-                        conjugate_func(csgn_conjugate));
+                        conjugate_func(csgn_conjugate).
+                        power_func(csgn_power));
 
 
 //////////