@@ -1,146 +1,146 @@
-REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
-
-
-I_setting(x,y,z);
-
-
-
-torder revgradlex;
-
-
-{{},lex}
-
-
-u := I(x*z-y**2, x**3-y*z);
-
-
-              2  3
-u := i(x*z - y ,x  - y*z)
-
-y member I(x,y^2);
-
-
-0
-
-x member I(x,y^2);
-
-
-1
-
-I(x,y^2) subset I(x,y);
-
-
-1
-         % yes
-I(x,y) subset I(x,y^2);
-
-
-0
-         % no
-
-% examples taken from Cox, Little, O'Shea: "Ideals, Varieties and Algorithms"
-
-
-
-
-q1 := u .: I(x);
-
-
-         3        2      2           2
-q1 := i(x  - y*z,x *y - z , - x*z + y )
-                        % quotient ideal
-
-q2 := u .+ I(x^2 * y - z^2);
-
-
-         3        2      2           2
-q2 := i(x  - y*z,x *y - z , - x*z + y )
-            % sum ideal
-
-if q1 .= q2 then write "same ideal";
-
-
-same ideal
-    % test equality
-
-intersection(u,I(y));
-
-
-   3      2    2  2      2             3
-i(x *y - y *z,x *y  - y*z , - x*y*z + y )
-                   % ideal intersection
-
-u .: I(y);
-
-
-   3        2      2           2
-i(x  - y*z,x *y - z , - x*z + y )
-
-
-u .: I(x,y);
-
-
-   3        2      2           2
-i(x  - y*z,x *y - z , - x*z + y )
-
-
-%-----------------------------------------------------
-
-u1 := I(x,y^2);
-
-
-           2
-u1 := i(x,y )
-
-u1u1:= u1 .* u1;
-
-
-           4    2  2
-u1u1 := i(y ,x*y ,x )
-                       % square ideal
-u0 :=I(x,y);
-
-
-u0 := i(x,y)
-
-
-% test equality/inclusion for u1,u1u1,u0
-
-u1 .= u1u1;
-
-
-0
-     % no
-
-u1 subset u1u1;
-
-
-0
- % no
-
-u1u1 subset u1;
-
-
-1
- % yes
-
-u1 .= u0;
-
-
-0
-       % no
-
-u1 subset u0;
-
-
-1
-   % yes
-
-intersection (I(x) , I(x^2,x*y,y^2)) .= intersection(I(x) , I(x^2,y));
-
-
-1
- 
-
-end;
-(TIME:  ideals 330 330)
+REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
+
+
+I_setting(x,y,z);
+
+
+
+torder revgradlex;
+
+
+{{},lex}
+
+
+u := I(x*z-y**2, x**3-y*z);
+
+
+              2  3
+u := i(x*z - y ,x  - y*z)
+
+y member I(x,y^2);
+
+
+0
+
+x member I(x,y^2);
+
+
+1
+
+I(x,y^2) subset I(x,y);
+
+
+1
+         % yes
+I(x,y) subset I(x,y^2);
+
+
+0
+         % no
+
+% examples taken from Cox, Little, O'Shea: "Ideals, Varieties and Algorithms"
+
+
+
+
+q1 := u .: I(x);
+
+
+         3        2      2           2
+q1 := i(x  - y*z,x *y - z , - x*z + y )
+                        % quotient ideal
+
+q2 := u .+ I(x^2 * y - z^2);
+
+
+         3        2      2           2
+q2 := i(x  - y*z,x *y - z , - x*z + y )
+            % sum ideal
+
+if q1 .= q2 then write "same ideal";
+
+
+same ideal
+    % test equality
+
+intersection(u,I(y));
+
+
+   3      2    2  2      2             3
+i(x *y - y *z,x *y  - y*z , - x*y*z + y )
+                   % ideal intersection
+
+u .: I(y);
+
+
+   3        2      2           2
+i(x  - y*z,x *y - z , - x*z + y )
+
+
+u .: I(x,y);
+
+
+   3        2      2           2
+i(x  - y*z,x *y - z , - x*z + y )
+
+
+%-----------------------------------------------------
+
+u1 := I(x,y^2);
+
+
+           2
+u1 := i(x,y )
+
+u1u1:= u1 .* u1;
+
+
+           4    2  2
+u1u1 := i(y ,x*y ,x )
+                       % square ideal
+u0 :=I(x,y);
+
+
+u0 := i(x,y)
+
+
+% test equality/inclusion for u1,u1u1,u0
+
+u1 .= u1u1;
+
+
+0
+     % no
+
+u1 subset u1u1;
+
+
+0
+ % no
+
+u1u1 subset u1;
+
+
+1
+ % yes
+
+u1 .= u0;
+
+
+0
+       % no
+
+u1 subset u0;
+
+
+1
+   % yes
+
+intersection (I(x) , I(x^2,x*y,y^2)) .= intersection(I(x) , I(x^2,y));
+
+
+1
+ 
+
+end;
+(TIME:  ideals 330 330)