Mon Jan 19 21:53:23 MST 1998 aquarius% reduce REDUCE 3.6, 15-Jul-95, patched to 15 Apr 96 ... 1: % ----------[ R e d u c e ]---------- % ---------- Initialization ---------- on multiplicities; on time; Time: 0 ms % ---------- Inequalities ---------- % => True e^pi > pi^e; ***** > invalid as algebraic operator Cont? (Y or N) ?y Time: 10 ms % => [True, False] {x^4 - x + 1 > 0, x^4 - x + 1 > 1}; ***** > invalid as algebraic operator Cont? (Y or N) ?y Time: 0 ms % => True %assume(abs(x) < 1); %-1 < x and x < 1; % x > y > 0 and k, n > 0 => k x^n > k y^n %assume(x > y, y > 0); %is(2*x^2 > 2*y^2); %assume(k > 0); %is(k*x^2 > k*y^2); %assume(n > 0); %is(k*x^n > k*y^n); %forget(x > y, y > 0, k > 0, n > 0)$ % x > 1 and y >= x - 1 => y > 0 %assume(x > 1, y >= x - 1); %is(y > 0); %forget(y > 1, y >= x - 1)$ % x >= y, y >= z, z >= x => x = y = z %assume(x >= y, y >= z, z >= x); %{is(x = y), is(x = z), is(y = z)}; load_package(ineq)$ Time: 190 ms % x < -1 or x > 3 ineq_solve(abs(x - 1) > 2, x); ***** wrong arguments for polynomial inequality solver Cont? (Y or N) ?y Time: 0 ms ineq_solve({-(x - 1) > 2, x - 1 > 2}, x); { - (x - 1)>2,x - 1>2} Time: 10 ms % x < 1 or 2 < x < 3 or 4 < x < 5 ineq_solve((x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5) < 0, x); {x<1,x=(2 .. 3),x=(4 .. 5)} Time: 170 ms % x < 3 or x >= 5 ineq_solve(6/(x - 3) <= 3, x); 6 -------<=3 x - 3 Time: 0 ms ineq_solve((x - 3)/6 >= 1/3, x); x - 3 1 ***** ------->=--- invalid as list 6 3 Cont? (Y or N) ?y Time: 10 ms % => 0 <= x < 4 ineq_solve(sqrt(x) < 2, x); ***** wrong arguments for polynomial inequality solver Cont? (Y or N) ?y Time: 0 ms % => x is real ineq_solve(sin(x) < 2, x); ***** wrong arguments for polynomial inequality solver Cont? (Y or N) ?y Time: 0 ms % => x != pi/2 + n 2 pi ineq_solve(sin(x) < 1, x); ***** wrong arguments for polynomial inequality solver Cont? (Y or N) ?y Time: 10 ms % The next two examples come from Abdubrahim Muhammad Farhat, _Stability % Analysis of Finite Difference Schemes_, Ph.D. dissertation, University of % New Mexico, Albuquerque, New Mexico, December 1993 => 0 <= A <= 1/2 ineq_solve(abs(2*A*(cos(t) - 1) + 1) <= 1, A); abs(2*a*(cos(t) - 1) + 1)<=1 Time: 10 ms % => 125 A^4 + 24 A^2 - 48 < 0 or |A| < 2/5 sqrt([8 sqrt(6) - 3]/5) ineq_solve(A^2*(cos(t) - 4)^2*sin(t)^2 < 9, A); 2 2 2 a *(cos(t) - 4) *sin(t) <9 Time: 10 ms % => |x| < y ineq_solve({x + y > 0, x - y < 0}, {x, y}); {x + y>0,x - y<0} Time: 10 ms % ---------- Quit ---------- quit; Quitting real 14.23 user 0.55 sys 1.26