Transform abs(x)^n => x^n if x is real and n is even.

[ginac.git] / ginac / inifcns.cpp

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index f366e779e70fbdb18a64e0447b8b21263f3704ee..8103cd86bf3ec12ad02a2ebec48aff1b122b0c49 100644 (file)
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's initially known functions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2011 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
@@ -212,7 +212,7 @@ static void abs_print_csrc_float(const ex & arg, const print_context & c)
 
 static ex abs_conjugate(const ex & arg)
 {
-       return abs(arg);
+       return abs(arg).hold();
 }
 
 static ex abs_real_part(const ex & arg)
@@ -227,7 +227,8 @@ 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())
+       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
                return power(abs(arg), exp).hold();
@@ -398,7 +399,7 @@ 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);
+                       return csgn(arg).hold();
                else
                        return power(csgn(arg), _ex2).hold();
        } else
@@ -489,7 +490,7 @@ static ex eta_series(const ex & x, const ex & y,
 
 static ex eta_conjugate(const ex & x, const ex & y)
 {
-       return -eta(x, y);
+       return -eta(x, y).hold();
 }
 
 static ex eta_real_part(const ex & x, const ex & y)
@@ -648,7 +649,7 @@ static ex Li2_conjugate(const ex & x)
        // conjugate(Li2(x))==Li2(conjugate(x)) unless on the branch cuts which
        // run along the positive real axis beginning at 1.
        if (x.info(info_flags::negative)) {
-               return Li2(x);
+               return Li2(x).hold();
        }
        if (is_exactly_a<numeric>(x) &&
            (!x.imag_part().is_zero() || x < *_num1_p)) {
@@ -687,7 +688,7 @@ 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 zeta(x).hold();
        }
        
        return zetaderiv(n, x).hold();
@@ -1011,13 +1012,20 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
                if (!is_a<numeric>(dx_))
                        throw std::runtime_error("fsolve(): function derivative does not evaluate numerically");
                xx[side] += ex_to<numeric>(dx_);
-
-               ex f_x = f.subs(x == xx[side]).evalf();
-               if (!is_a<numeric>(f_x))
-                       throw std::runtime_error("fsolve(): function does not evaluate numerically");
-               fx[side] = ex_to<numeric>(f_x);
-
-               if ((side==0 && xx[0]<xxprev) || (side==1 && xx[1]>xxprev) || xx[0]>xx[1]) {
+               // Now check if Newton-Raphson method shot out of the interval 
+               bool bad_shot = (side == 0 && xx[0] < xxprev) || 
+                               (side == 1 && xx[1] > xxprev) || xx[0] > xx[1];
+               if (!bad_shot) {
+                       // Compute f(x) only if new x is inside the interval.
+                       // The function might be difficult to compute numerically
+                       // or even ill defined outside the interval. Also it's
+                       // a small optimization. 
+                       ex f_x = f.subs(x == xx[side]).evalf();
+                       if (!is_a<numeric>(f_x))
+                               throw std::runtime_error("fsolve(): function does not evaluate numerically");
+                       fx[side] = ex_to<numeric>(f_x);
+               }
+               if (bad_shot) {
                        // Oops, Newton-Raphson method shot out of the interval.
                        // Restore, and try again with the other side instead!
                        xx[side] = xxprev;