@@ -1,257 +1,257 @@
-REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
-
-
-%% sets.tst
-
-%% Author: F.J.Wright@Maths.QMW.ac.uk
-%% Date: 20 Feb 1994
-
-%% Test of REDUCE sets package, based on the examples on page 51 of
-%% the "Maple V Language Reference Manual"
-%% by Char, Geddes, Gonnet, Leong, Monagan and Watt (Springer, 1991).
-
-%% The output (especially of symbolic set expressions) looks better
-%% using PSL-REDUCE under MS-Windows or X in graphics mode.
-
-%% Note that REDUCE supports n-ary symbolic infix operators,
-%% does not require any special quoting to use an infix operator
-%% as a prefix operator, and supports member as an infix operator.
-%% However, REDUCE ALWAYS requires  evalb  to explicitly evaluate a
-%% Boolean expression outside of a conditional statement.
-%% Maple 5.2 does not provide any subset predicates.
-
-clear a, b, c, x, y, z;
-
-
-
-s := {x,y} union {y,z};
-
-
-s := {x,y,z}
-
-% s := {x,y,z}
-
-t := union({x,y},{y,z});
-
-
-t := {x,y,z}
-
-% t := {x,y,z}
-
-evalb(s = t);
-
-
-true
-
-% true
-
-evalb(s set_eq t);
-
-
-true
-
-% true
-
-evalb(member(y, s));
-
-
-true
-
-% true
-
-evalb(y member s);
-
-
-true
-
-% true
-
-evalb(y member {x*y, y*z});
-
-
-false
-
-% false
-
-evalb(x*y member {x*y, y*z});
-
-
-true
-
-% true
-
-{3,4} union a union {3,7} union b;
-
-
-{3,4,7} union a union b
-
-% {3,4,7} union a union b
-
-{x,y,z} minus {y,z,w};
-
-
-{x}
-
-% {x}
-
-a minus b;
-
-
-a\b
-
-% a\b
-
-a\b;
-
-
-a\b
-
-% a\b
-
-minus(a,a);
-
-
-{}
-
-% {}
-
-{x,y,z} intersect {y,z,w};
-
-
-{y,z}
-
-% {y,z}
-
-intersect(a,c,b,a);
-
-
-a intersection b intersection c
-
-% a intersection b intersection c
-
-%% End of Maple examples.
-
-(a union b) intersect c where set_distribution_rule;
-
-
-a intersection c union b intersection c
-
-% a intersection c union b intersection c
-
-algebraic procedure power_set s;
-   %% Power set of a set as an algebraic list (inefficiently):
-   if s = {} then {{}} else
-      {s} union for each el in s join power_set(s\{el});
-
-
-power_set
-
-
-power_set{};
-
-
-{{}}
-
-power_set{1};
-
-
-{{1},{}}
-
-power_set{1,2};
-
-
-{{2},{1,2},{1},{}}
-
-power_set{1,2,3};
-
-
-{{3},{2,3},{2},{1,3},{1,2,3},{1,2},{1},{}}
-
-
-
-evalb 1;
-
-
-true
-
-% true
-
-evalb 0;
-
-
-false
-
-% false
-
-evalb(a = a);
-
-
-true
-
-% true
-
-evalb(a = b);
-
-
-false
-
-% false
-
-evalb(2 member {1,2} union {2,3});
-
-
-true
-
-% true
-
-evalb({2} member {1,2} union {2,3});
-
-
-false
-
-% false
-
-evalb({1,3} subset {1,2} union {2,3});
-
-
-true
-
-% true
-
-evalb(a subset a union b);
-
-
-true
-
-% true
-
-evalb(a subset_eq a union b);
-
-
-true
-
-% true
-
-evalb(a set_eq a union b);
-
-
-false
-
-% false
-
-evalb(a\b subset a union c);
-
-
-true
-
-% true
-
-mkset{1,2,1};
-
-
-{1,2}
-
-% {1,2}
-
-end;
-(TIME:  sets 120 120)
+REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
+
+
+%% sets.tst
+
+%% Author: F.J.Wright@Maths.QMW.ac.uk
+%% Date: 20 Feb 1994
+
+%% Test of REDUCE sets package, based on the examples on page 51 of
+%% the "Maple V Language Reference Manual"
+%% by Char, Geddes, Gonnet, Leong, Monagan and Watt (Springer, 1991).
+
+%% The output (especially of symbolic set expressions) looks better
+%% using PSL-REDUCE under MS-Windows or X in graphics mode.
+
+%% Note that REDUCE supports n-ary symbolic infix operators,
+%% does not require any special quoting to use an infix operator
+%% as a prefix operator, and supports member as an infix operator.
+%% However, REDUCE ALWAYS requires  evalb  to explicitly evaluate a
+%% Boolean expression outside of a conditional statement.
+%% Maple 5.2 does not provide any subset predicates.
+
+clear a, b, c, x, y, z;
+
+
+
+s := {x,y} union {y,z};
+
+
+s := {x,y,z}
+
+% s := {x,y,z}
+
+t := union({x,y},{y,z});
+
+
+t := {x,y,z}
+
+% t := {x,y,z}
+
+evalb(s = t);
+
+
+true
+
+% true
+
+evalb(s set_eq t);
+
+
+true
+
+% true
+
+evalb(member(y, s));
+
+
+true
+
+% true
+
+evalb(y member s);
+
+
+true
+
+% true
+
+evalb(y member {x*y, y*z});
+
+
+false
+
+% false
+
+evalb(x*y member {x*y, y*z});
+
+
+true
+
+% true
+
+{3,4} union a union {3,7} union b;
+
+
+{3,4,7} union a union b
+
+% {3,4,7} union a union b
+
+{x,y,z} minus {y,z,w};
+
+
+{x}
+
+% {x}
+
+a minus b;
+
+
+a\b
+
+% a\b
+
+a\b;
+
+
+a\b
+
+% a\b
+
+minus(a,a);
+
+
+{}
+
+% {}
+
+{x,y,z} intersect {y,z,w};
+
+
+{y,z}
+
+% {y,z}
+
+intersect(a,c,b,a);
+
+
+a intersection b intersection c
+
+% a intersection b intersection c
+
+%% End of Maple examples.
+
+(a union b) intersect c where set_distribution_rule;
+
+
+a intersection c union b intersection c
+
+% a intersection c union b intersection c
+
+algebraic procedure power_set s;
+   %% Power set of a set as an algebraic list (inefficiently):
+   if s = {} then {{}} else
+      {s} union for each el in s join power_set(s\{el});
+
+
+power_set
+
+
+power_set{};
+
+
+{{}}
+
+power_set{1};
+
+
+{{1},{}}
+
+power_set{1,2};
+
+
+{{2},{1,2},{1},{}}
+
+power_set{1,2,3};
+
+
+{{3},{2,3},{2},{1,3},{1,2,3},{1,2},{1},{}}
+
+
+
+evalb 1;
+
+
+true
+
+% true
+
+evalb 0;
+
+
+false
+
+% false
+
+evalb(a = a);
+
+
+true
+
+% true
+
+evalb(a = b);
+
+
+false
+
+% false
+
+evalb(2 member {1,2} union {2,3});
+
+
+true
+
+% true
+
+evalb({2} member {1,2} union {2,3});
+
+
+false
+
+% false
+
+evalb({1,3} subset {1,2} union {2,3});
+
+
+true
+
+% true
+
+evalb(a subset a union b);
+
+
+true
+
+% true
+
+evalb(a subset_eq a union b);
+
+
+true
+
+% true
+
+evalb(a set_eq a union b);
+
+
+false
+
+% false
+
+evalb(a\b subset a union c);
+
+
+true
+
+% true
+
+mkset{1,2,1};
+
+
+{1,2}
+
+% {1,2}
+
+end;
+(TIME:  sets 120 120)