From 4a05a42695e4974078a0b3734e9224c246739715 Mon Sep 17 00:00:00 2001
From: oldk1331 <oldk1331@gmail.com>
Date: Wed, 12 Apr 2017 14:48:49 +0800
Subject: [PATCH] improve tantrick

---
 src/algebra/irexpand.spad | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/src/algebra/irexpand.spad b/src/algebra/irexpand.spad
index 68984ef8d..fa77a8500 100644
--- a/src/algebra/irexpand.spad
+++ b/src/algebra/irexpand.spad
@@ -102,13 +102,17 @@ IntegrationResultToFunction(R, F) : Exports == Implementation where
 -- returns 2 atan(a/b) or 2 atan(-b/a) whichever looks better
 -- they differ by a constant so it's ok to do it from an IR
     tantrick(a, b) ==
-      retractIfCan(a)@Union(Q, "failed") case Q => 2 * atan(-b/a)
-      sb := sign b
-      if sb case Z then return 2 * atan(a/b)
-      sa := sign a
-      if sa case Z then return 2 * atan(-b/a)
-      -- print("potentially noncontinuous"::OutputForm)
-      2 * atan(a/b)
+        f := a/b
+        a := numerator(f)
+        b := denominator(f)
+        AN ==> AlgebraicNumber
+        TryRetract x ==> retractIfCan(x)@Union(Q, "failed") case Q or
+                             retractIfCan(x)@Union(AN, "failed") case AN
+        TryRetract(b) => 2 * atan(f)
+        TryRetract(a) => 2 * atan(-b/a)
+        sign(a) case Z => 2 * atan(-b/a)
+        -- print("potentially noncontinuous"::OutputForm)
+        2 * atan(f)
 
     var_kers(p : P, x : Symbol) : List(K) ==
         [k for k in variables(p) | D(k::F, x) ~= 0]