Evaluate abs(z)^(2n) -> z^n * conjugate(z)^n.

[ginac.git] / ginac / inifcns.cpp

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index 0cb2abbd744798bdc61b38348ad71e84e836bc8c..d4087e22b5003fd837d278f552e799fb765a1a97 100644 (file)
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's initially known functions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2014 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
@@ -76,8 +76,46 @@ static ex conjugate_imag_part(const ex & arg)
        return -arg.imag_part();
 }
 
+static bool func_arg_info(const ex & arg, unsigned inf)
+{
+       // for some functions we can return the info() of its argument
+       // (think of conjugate())
+       switch (inf) {
+               case info_flags::polynomial:
+               case info_flags::integer_polynomial:
+               case info_flags::cinteger_polynomial:
+               case info_flags::rational_polynomial:
+               case info_flags::real:
+               case info_flags::rational:
+               case info_flags::integer:
+               case info_flags::crational:
+               case info_flags::cinteger:
+               case info_flags::even:
+               case info_flags::odd:
+               case info_flags::prime:
+               case info_flags::crational_polynomial:
+               case info_flags::rational_function:
+               case info_flags::algebraic:
+               case info_flags::positive:
+               case info_flags::negative:
+               case info_flags::nonnegative:
+               case info_flags::posint:
+               case info_flags::negint:
+               case info_flags::nonnegint:
+               case info_flags::has_indices:
+                       return arg.info(inf);
+       }
+       return false;
+}
+
+static bool conjugate_info(const ex & arg, unsigned inf)
+{
+       return func_arg_info(arg, inf);
+}
+
 REGISTER_FUNCTION(conjugate_function, eval_func(conjugate_eval).
                                       evalf_func(conjugate_evalf).
+                                      info_func(conjugate_info).
                                       print_func<print_latex>(conjugate_print_latex).
                                       conjugate_func(conjugate_conjugate).
                                       real_part_func(conjugate_real_part).
@@ -207,9 +245,36 @@ static ex abs_eval(const ex & arg)
                        return pow(abs(base), exponent.real_part());
        }
 
+       if (is_ex_the_function(arg, conjugate_function))
+               return abs(arg.op(0));
+
+       if (is_ex_the_function(arg, step))
+               return arg;
+
        return abs(arg).hold();
 }
 
+static ex abs_expand(const ex & arg, unsigned options)
+{
+       if ((options & expand_options::expand_transcendental)
+               && is_exactly_a<mul>(arg)) {
+               exvector prodseq;
+               prodseq.reserve(arg.nops());
+               for (const_iterator i = arg.begin(); i != arg.end(); ++i) {
+                       if (options & expand_options::expand_function_args)
+                               prodseq.push_back(abs(i->expand(options)));
+                       else
+                               prodseq.push_back(abs(*i));
+               }
+               return (new mul(prodseq))->setflag(status_flags::dynallocated | status_flags::expanded);
+       }
+
+       if (options & expand_options::expand_function_args)
+               return abs(arg.expand(options)).hold();
+       else
+               return abs(arg).hold();
+}
+
 static void abs_print_latex(const ex & arg, const print_context & c)
 {
        c.s << "{|"; arg.print(c); c.s << "|}";
@@ -237,15 +302,46 @@ static ex abs_imag_part(const ex& 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())
-                                               || exp.info(info_flags::even)))
-               return power(arg, exp);
-       else
+       if ((is_a<numeric>(exp) && ex_to<numeric>(exp).is_even()) || exp.info(info_flags::even)) {
+               if (arg.info(info_flags::real) || arg.is_equal(arg.conjugate()))
+                       return power(arg, exp);
+               else
+                       return power(arg, exp/2)*power(arg.conjugate(), exp/2);
+       } else
                return power(abs(arg), exp).hold();
 }
 
+bool abs_info(const ex & arg, unsigned inf)
+{
+       switch (inf) {
+               case info_flags::integer:
+               case info_flags::even:
+               case info_flags::odd:
+               case info_flags::prime:
+                       return arg.info(inf);
+               case info_flags::nonnegint:
+                       return arg.info(info_flags::integer);
+               case info_flags::nonnegative:
+               case info_flags::real:
+                       return true;
+               case info_flags::negative:
+                       return false;
+               case info_flags::positive:
+                       return arg.info(info_flags::positive) || arg.info(info_flags::negative);
+               case info_flags::has_indices: {
+                       if (arg.info(info_flags::has_indices))
+                               return true;
+                       else
+                               return false;
+               }
+       }
+       return false;
+}
+
 REGISTER_FUNCTION(abs, eval_func(abs_eval).
                        evalf_func(abs_evalf).
+                       expand_func(abs_expand).
+                       info_func(abs_info).
                        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).