From d5c58d9f8241974e15bf507af7309655f8cb1f68 Mon Sep 17 00:00:00 2001
From: Mike Sperber <sperber@deinprogramm.de>
Date: Sun, 26 Dec 2010 09:03:10 +0100
Subject: [PATCH] Extends =~ to complex numbers

This is a (variation of a) fix from David van Horn.

Closes PR 11547.
---
 collects/lang/private/beginner-funs.rkt | 6 +++---
 collects/lang/private/teachprims.rkt    | 8 ++++----
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/collects/lang/private/beginner-funs.rkt b/collects/lang/private/beginner-funs.rkt
index be8a2dc9bc..6771444f05 100644
--- a/collects/lang/private/beginner-funs.rkt
+++ b/collects/lang/private/beginner-funs.rkt
@@ -484,10 +484,10 @@
       (eqv? (any any -> boolean)
 	"to determine whether two values are equivalent from the"
 	"  perspective of all functions that can be applied to it (extensional)")
-      ((beginner-=~ =~) (real real non-negative-real -> boolean)
-	"to check whether two real numbers are within some amount (the third argument) of either other")
+      ((beginner-=~ =~) (number number non-negative-real -> boolean)
+	"to check whether two numbers are within some amount (the third argument) of either other")
       ((beginner-equal~? equal~?) (any any non-negative-real -> boolean)
-	"to compare like equal? on the first two arguments, except using =~ in the case of real numbers")
+	"to compare like equal? on the first two arguments, except using =~ in the case of numbers")
       (eof eof
 	"the end-of-file value")
       (eof-object? (any -> boolean)
diff --git a/collects/lang/private/teachprims.rkt b/collects/lang/private/teachprims.rkt
index 39f6225d49..3e3df3adba 100644
--- a/collects/lang/private/teachprims.rkt
+++ b/collects/lang/private/teachprims.rkt
@@ -276,8 +276,8 @@ namespace.
 					       (current-continuation-marks))))])
     (let ? ([a x][b y])
       (cond
-        [(real? a)
-         (and (real? b)
+        [(number? a)
+         (and (number? b)
               (beginner-=~ a b epsilon))]
 	[(procedure? a)
 	 (fail "first argument of equality cannot be a procedure, given ~e" a)]
@@ -318,8 +318,8 @@ namespace.
 
 (define-teach beginner =~
   (lambda (a b c)
-    (check-three a b c '=~ real? 'real real? 'real positive-real? 'non-negative-real)
-    (<= (- a c) b (+ a c))))
+    (check-three a b c '=~ number? 'number number? 'number positive-real? 'non-negative-real)
+    (<= (magnitude (- a b)) c)))
 
 (define-teach beginner equal~?
   (lambda (a b c)