From 38982ebf4d9b23fe336bd4880ef0f4d59dbc7684 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Sun, 18 May 2008 16:05:33 +0000
Subject: 	Fix AW/313 	* algebra/reclos.spad.pamphlet
 (sqrt$RealClosedField): Fix signature.

---
 src/algebra/reclos.spad.pamphlet | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

(limited to 'src/algebra')

diff --git a/src/algebra/reclos.spad.pamphlet b/src/algebra/reclos.spad.pamphlet
index ff396d16..e5d2ece2 100644
--- a/src/algebra/reclos.spad.pamphlet
+++ b/src/algebra/reclos.spad.pamphlet
@@ -350,7 +350,7 @@ RealClosedField : Category == PUB where
              ++ \axiom{allRootsOf(pol)} creates all the roots
              ++ of \axiom{pol} naming each uniquely
 
-        sqrt:            ($,N)                ->     $
+        sqrt:            ($,PI)                ->     $
              ++ \axiom{sqrt(x,n)} is \axiom{x ** (1/n)}
 
         sqrt:              $                  ->     $
@@ -394,7 +394,6 @@ RealClosedField : Category == PUB where
 
 
         sqrt(x,n) ==
-          n = 0 => 1
           n = 1 => x
           zero?(x) => 0
           one?(x) => 1 
@@ -407,12 +406,12 @@ RealClosedField : Category == PUB where
           n = 2 => rename(r,root(x::E)$E)
           rename(r,root(x :: E, n :: E)$E)
 
-        (x : $) ** (rn : RN) == sqrt(x**numer(rn),denom(rn)::N)
+        (x : $) ** (rn : RN) == sqrt(x**numer(rn),denom(rn)::PI)
 
         nthRoot(x, n) == 
           zero?(n) => x
-          negative?(n) => inv(sqrt(x,(-n) :: N))
-          sqrt(x,n :: N)
+          negative?(n) => inv(sqrt(x,(-n) :: PI))
+          sqrt(x,n :: PI)
 
         allRootsOf(p:SUP(RN)) == allRootsOf(map(#1 :: $ ,p)$PACK(RN,$))
 
-- 
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