@@ -1,100 +1,100 @@
-REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
-
-
-% polynomial Inequality (Example where another system returned {1 <= x})
-
-ineq_solve(  (2*x^2+x-1)/(x-1) >=  (x+1/2)^2 ,x);
-
-
-{x=( - 0.894358 .. 0.326583),x=(1 .. 2.56777)}
-
-
-ineq_solve({(2*x^2+x-1)/(x-1) >=  (x+1/2)^2, x>0});
-
-
-{x=(0 .. 0.326583),x=(1 .. 2.56777)}
-
-
-ineq_solve({(2*x^2+x-1)/(x-1) >=  (x+1/2)^2, x<-1});
-
-
-{}
-
-
-
-% Systems for determining indices of Jacobi polynomials (Winfried Neun).
-
-reg := 
-{2*a - 3>=0, 3>=0, 3>=0, 1>=0, 1>=0, 5>=0, 4>=0, 2*a - 4>=0, 2>=0,
- 2>=0, 0>=0, 2*a - 2>=0, k + 1>=0, - 2*a + k - 3>=0, - 2*a + k - 2>=0,
-  - 2*a + k>=0, k - 7>=0, 2*a - k + 4>=0, 2*a - k + 5>=0, 2*a - k + 3>=0}$
-
-
-
-ineq_solve(reg,{k,a});
-
-
-{a=(2 .. infinity),k=2*a + 3}
-
-
-reg:=
-{a + b - c>=0, a - b + c>=0, - a + b + c>=0, 0>=0, 2>=0,
- 2*c - 2>=0, a - b + c>=0, a + b - c>=0, - a + b + c - 2>=0,
- 2>=0, 0>=0, 2*b - 2>=0, k + 1>=0, - a - b - c + k>=0,
-  - a - b - c + k + 2>=0, - 2*b + k>=0, - 2*c + k>=0, a + b + c - k>=0,
- 2*b + 2*c - k - 2>=0, a + b + c - k>=0}$
-
-
-
-ineq_solve (reg,{k,a,b,c});
-
-
-{c=(1 .. infinity),
-
- b=(1 .. infinity),
-
- a=(max( - b + c,b - c) .. b + c - 2),
-
- k=a + b + c}
-
-
-clear reg;
-
-
-
-% Example from Richard Liska.
-
-lvars:={a,b,d}$
-
-
-lfcond := {d>=0,
-           b + d>=0,
-           2 a - b + d + 2>=0,
-            - a + 2 d + 1>=0,
-           b>=0,
-           2 a - b>=0,
-            - a + 2 d>=0,
-           b - d>=0,
-           2 a - b - d - 2>=0,
-            - a + 2 d - 1>=0}$
-
-
-
-ineq_solve(lfcond,lvars);
-
-
-{d=(2 .. infinity),
-
- b=(d .. 3*d - 4),
-
-     b + d + 2
- a=(----------- .. 2*d - 1)}
-         2
-
-
-clear lfcond,lvars;
-
-
-
-end;
-(TIME:  ineq 510 610)
+REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
+
+
+% polynomial Inequality (Example where another system returned {1 <= x})
+
+ineq_solve(  (2*x^2+x-1)/(x-1) >=  (x+1/2)^2 ,x);
+
+
+{x=( - 0.894358 .. 0.326583),x=(1 .. 2.56777)}
+
+
+ineq_solve({(2*x^2+x-1)/(x-1) >=  (x+1/2)^2, x>0});
+
+
+{x=(0 .. 0.326583),x=(1 .. 2.56777)}
+
+
+ineq_solve({(2*x^2+x-1)/(x-1) >=  (x+1/2)^2, x<-1});
+
+
+{}
+
+
+
+% Systems for determining indices of Jacobi polynomials (Winfried Neun).
+
+reg := 
+{2*a - 3>=0, 3>=0, 3>=0, 1>=0, 1>=0, 5>=0, 4>=0, 2*a - 4>=0, 2>=0,
+ 2>=0, 0>=0, 2*a - 2>=0, k + 1>=0, - 2*a + k - 3>=0, - 2*a + k - 2>=0,
+  - 2*a + k>=0, k - 7>=0, 2*a - k + 4>=0, 2*a - k + 5>=0, 2*a - k + 3>=0}$
+
+
+
+ineq_solve(reg,{k,a});
+
+
+{a=(2 .. infinity),k=2*a + 3}
+
+
+reg:=
+{a + b - c>=0, a - b + c>=0, - a + b + c>=0, 0>=0, 2>=0,
+ 2*c - 2>=0, a - b + c>=0, a + b - c>=0, - a + b + c - 2>=0,
+ 2>=0, 0>=0, 2*b - 2>=0, k + 1>=0, - a - b - c + k>=0,
+  - a - b - c + k + 2>=0, - 2*b + k>=0, - 2*c + k>=0, a + b + c - k>=0,
+ 2*b + 2*c - k - 2>=0, a + b + c - k>=0}$
+
+
+
+ineq_solve (reg,{k,a,b,c});
+
+
+{c=(1 .. infinity),
+
+ b=(1 .. infinity),
+
+ a=(max( - b + c,b - c) .. b + c - 2),
+
+ k=a + b + c}
+
+
+clear reg;
+
+
+
+% Example from Richard Liska.
+
+lvars:={a,b,d}$
+
+
+lfcond := {d>=0,
+           b + d>=0,
+           2 a - b + d + 2>=0,
+            - a + 2 d + 1>=0,
+           b>=0,
+           2 a - b>=0,
+            - a + 2 d>=0,
+           b - d>=0,
+           2 a - b - d - 2>=0,
+            - a + 2 d - 1>=0}$
+
+
+
+ineq_solve(lfcond,lvars);
+
+
+{d=(2 .. infinity),
+
+ b=(d .. 3*d - 4),
+
+     b + d + 2
+ a=(----------- .. 2*d - 1)}
+         2
+
+
+clear lfcond,lvars;
+
+
+
+end;
+(TIME:  ineq 510 610)