Thu Feb 25 19:33:16 MST 1999 aquarius% maple |\^/| Maple V Release 5.1 (WMI Campus Wide License) ._|\| |/|_. Copyright (c) 1981-1998 by Waterloo Maple Inc. All rights \ MAPLE / reserved. Maple and Maple V are registered trademarks of <____ ____> Waterloo Maple Inc. | Type ? for help. # ----------[ M a p l e ]---------- #interface(echo = 3); # ---------- Initialization ---------- > readlib(showtime): > _Envadditionally:= true: > _EnvAllSolutions:= true: > on; # ---------- Inequalities ---------- # => True O1 := is(exp(Pi) > Pi^exp(1)); true time = 0.24, bytes = 413650 # => [True, False] O2 := assume(x, real): time = 0.02, bytes = 11586 O3 := [is(x^4 - x + 1 > 0), is(x^4 - x + 1 > 1)]; bytes used=1125752, alloc=917336, time=0.61 [FAIL, false] time = 0.80, bytes = 1089594 O4 := x:= 'x': time = 0.01, bytes = 4242 # => True O5 := assume(abs(x) < 1): time = 0.03, bytes = 29614 O6 := is(-1 < x and x < 1); false time = 0.10, bytes = 77310 O7 := x:= 'x': time = 0.01, bytes = 3658 # x > y > 0 and k, n > 0 => k x^n > k y^n O8 := assume(x > y, y > 0): time = 0.03, bytes = 23786 O9 := is(2*x^2 > 2*y^2); true time = 0.08, bytes = 82798 O10 := assume(k > 0): time = 0.01, bytes = 8106 O11 := is(k*x^2 > k*y^2); true time = 0.10, bytes = 77110 O12 := assume(n > 0): time = 0.01, bytes = 7578 O13 := is(k*x^n > k*y^n); bytes used=2126692, alloc=1572576, time=1.78 FAIL time = 0.62, bytes = 376506 O14 := x:= 'x': time = 0.00, bytes = 3870 O15 := y:= 'y': time = 0.01, bytes = 4186 O16 := k:= 'k': time = 0.00, bytes = 3678 O17 := n:= 'n': time = 0.00, bytes = 3822 # x > 1 and y >= x - 1 => y > 0 O18 := assume(x > 1, y >= x - 1): time = 0.03, bytes = 16722 O19 := is(y > 0); true time = 0.03, bytes = 32278 O20 := x:= 'x': time = 0.01, bytes = 3326 O21 := y:= 'y': time = 0.01, bytes = 3498 # x >= y, y >= z, z >= x => x = y = z O22 := assume(x >= y, y >= z, z >= x): time = 0.03, bytes = 26190 O23 := [is(x = y), is(x = z), is(y = z)]; [true, true, true] time = 0.10, bytes = 91550 O24 := x:= 'x': time = 0.01, bytes = 3694 O25 := y:= 'y': time = 0.00, bytes = 3518 O26 := z:= 'z': time = 0.01, bytes = 4158 # x < -1 or x > 3 O27 := solve(abs(x - 1) > 2, x); RealRange(Open(3), infinity), RealRange(-infinity, Open(-1)) time = 0.20, bytes = 115758 # x < 1 or 2 < x < 3 or 4 < x < 5 O28 := solve(expand((x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5)) < 0, x); RealRange(-infinity, Open(1)), RealRange(Open(2), Open(3)), RealRange(Open(4), Open(5)) time = 0.28, bytes = 222282 # x < 3 or x >= 5 O29 := solve(6/(x - 3) <= 3, x); RealRange(-infinity, Open(3)), RealRange(5, infinity) time = 0.07, bytes = 44114 # => 0 <= x < 4 O30 := solve(sqrt(x) < 2, x); bytes used=3127528, alloc=1900196, time=3.30 RealRange(0, Open(4)) time = 0.48, bytes = 169482 # => x is real O31 := solve(sin(x) < 2, x); x time = 0.18, bytes = 153418 # => x != pi/2 + n 2 pi O32 := solve(sin(x) < 1, x); time = 0.07, bytes = 41078 # 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 O33 := solve(abs(2*A*(cos(t) - 1) + 1) <= 1, A); time = 0.54, bytes = 384154 O34 := assume(c >= -1): time = 0.01, bytes = 7142 O35 := assume(c <= 1): time = 0.02, bytes = 10246 O36 := solve(abs(2*A*(c - 1) + 1) <= 1, A); bytes used=4128352, alloc=2031244, time=4.95 Error, cannot handle intervals, use solve over name sets time = 0.90, bytes = 459786 # => 125 A^4 + 24 A^2 - 48 < 0 or |A| < 2/5 sqrt([8 sqrt(6) - 3]/5) O37 := solve(A^2*(cos(t) - 4)^2*sin(t)^2 < 9, A); time = 0.99, bytes = 835886 O38 := assume(s >= -1): time = 0.01, bytes = 7082 O39 := assume(s <= 1): time = 0.01, bytes = 7526 O40 := solve(A^2*(c - 4)^2*s^2 < 9, A); bytes used=5128616, alloc=2162292, time=6.43 time = 0.81, bytes = 465062 O41 := c:= 'c': time = 0.00, bytes = 3522 O42 := s:= 's': time = 0.01, bytes = 3334 # => |x| < y O43 := solve({x + y > 0, x - y < 0}, {x, y}); {x - y < 0, -x - y < 0, 0 < y} time = 0.04, bytes = 40858 # ---------- Quit ---------- O44 := quit bytes used=5627008, alloc=2162292, time=7.01 real 7.98 user 7.06 sys 0.88