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Sun Aug 18 16:08:43 2002 run on Windows % 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 for test: 802 ms, plus GC time: 461 ms