File r37/packages/solve/ineq.rlg artifact 89172c89d6 part of check-in ab67b20f90

Sun Jan  3 23:47:32 MET 1999
REDUCE 3.7, 15-Jan-99 ...

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3: 3: % 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;

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Time for test: 240 ms
5: 5: 
Quitting
Sun Jan  3 23:47:42 MET 1999