Mon Feb 22 22:02:07 MST 1999 aquarius% macsyma Starting Macsyma math engine with no window system... /opt/local/macsyma_422/macsyma.422 local This is Macsyma 422.0 for Sparc (Solaris 2.x) computers. Copyright (c) 1982 - 1998 Macsyma Inc. All rights reserved. Portions copyright (c) 1982 Massachusetts Institute of Technology. All rights reserved. Type "DESCRIBE(TRADE_SECRET);" to see important legal notices. Type "HELP();" for more information. /aquarius/data2/opt/local/macsyma_422/system/init.lsp being loaded. /aquarius/home/wester/macsyma-init.lsp being loaded. (c1) (c2) /* ----------[ M a c s y m a ]---------- */ /* ---------- Initialization ---------- */ symbol_display_case: lower_case$ Time= 0 msecs (c3) showtime: all$ Time= 0 msecs (c4) prederror: false$ Time= 0 msecs (c5) /* ---------- Inequalities ---------- */ /* => True */ is(%e^%pi > %pi^%e); Time= 90 msecs (d5) true (c6) /* => [True, False] */ [is(x^4 - x + 1 > 0), is(x^4 - x + 1 > 1)]; Time= 20 msecs (d6) [true, unknown] (c7) /* => True */ assume(abs(x) < 1)$ Warning: ASSUME cannot handle ABS in general. Time= 10 msecs (c8) is(-1 < x and x < 1); Time= 0 msecs (d8) unknown (c9) forget(abs(x) < 1)$ Time= 10 msecs (c10) /* x > y > 0 and k, n > 0 => k x^n > k y^n */ assume(x > y, y > 0); Time= 30 msecs (d10) [x > y, y > 0] (c11) is(2*x^2 > 2*y^2); Time= 380 msecs (d11) true (c12) assume(k > 0); Time= 0 msecs (d12) [k > 0] (c13) is(k*x^2 > k*y^2); Time= 400 msecs (d13) true (c14) assume(n > 0); Time= 10 msecs (d14) [n > 0] (c15) is(k*x^n > k*y^n); Time= 120 msecs (d15) unknown (c16) forget(x > y, y > 0, k > 0, n > 0)$ Time= 10 msecs (c17) /* x > 1 and y >= x - 1 => y > 0 */ assume(x > 1, y >= x - 1); Time= 230 msecs (d17) [x > 1, y - x + 1 >= 0] (c18) is(y > 0); Time= 0 msecs (d18) unknown (c19) forget(y > 1, y >= x - 1)$ Time= 20 msecs (c20) /* x >= y, y >= z, z >= x => x = y = z */ assume(x >= y, y >= z, z >= x); Time= 90 msecs (d20) [x >= y, y >= z, z >= x] (c21) [is(equal(x, y)), is(equal(x, z)), is(equal(y, z))]; Time= 20 msecs (d21) [true, true, true] (c22) forget(x >= y, y >= z, z >= x)$ Time= 270 msecs (c23) /* x < -1 or x > 3 */ ineq_linsolve(abs(x - 1) > 2, x); /aquarius/data2/opt/local/macsyma_422/share/ineqsol.so being loaded. /aquarius/data2/opt/local/macsyma_422/share/functs.so being loaded. Time= 250 msecs (d23) [[x = %pos1 + 3], []] (c24) ineq_linsolve([-(x - 1) > 2, x - 1 > 2], x); Time= 30 msecs (d24) [[], []] (c25) /* x < 1 or 2 < x < 3 or 4 < x < 5 */ ineq_linsolve(expand((x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5)) < 0, x); Time= 40 msecs 60 %pos4 (d25) [[x = --- - -----], []] 137 274 (c26) /* x < 3 or x >= 5 */ ineq_linsolve(6/(x - 3) <= 3, x); Time= 230 msecs 3 %pz1 15 (d26) [[x = -------- - --------], []] %pz1 - 3 %pz1 - 3 (c27) ratsimp(%); Time= 10 msecs 3 %pz1 - 15 (d27) [[x = -----------], []] %pz1 - 3 (c28) ineq_linsolve((x - 3)/6 >= 1/3, x); Time= 20 msecs (d28) [[x = 6 %pz2 + 5], []] (c29) /* => 0 <= x < 4 */ assume(sqrt(%r6) < 2)$ Time= 0 msecs (c30) /* This is stupid, but does automate the demo. */ ineq_linsolve(sqrt(x) < 2, x); Time= 50 msecs (d30) [[x = %r6], []] (c31) forget(sqrt(%r6) < 2)$ Time= 10 msecs (c32) /* => x is real */ assume(sin(%r7) < 2)$ Time= 10 msecs (c33) ineq_linsolve(sin(x) < 2, x); /aquarius/data2/opt/local/macsyma_422/library1/triangsy.so being loaded. Time= 380 msecs %n1 (d33) [[x = %pi %n1 - (- 1) asin(%pos6 - 2)], []] (c34) forget(sin(%r7) < 2)$ Time= 10 msecs (c35) /* => x != pi/2 + n 2 pi */ assume(sin(%r8) < 1)$ Time= 10 msecs (c36) ineq_linsolve(sin(x) < 1, x); Time= 80 msecs %n3 (d36) [[x = %pi %n3 - (- 1) asin(%pos7 - 1)], []] (c37) forget(sin(%r8) < 1)$ Time= 10 msecs (c38) /* 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 */ assume(abs(2*%r9*cos(t) - 2*%r9 + 1) - 1 < 0)$ Warning: ASSUME cannot handle ABS in general. Time= 390 msecs (c39) errcatch(ineq_linsolve(abs(2*A*(cos(t) - 1) + 1) <= 1, A)); Inconsistent equations: (1) Time= 150 msecs (d39) [] (c40) forget(abs(2*%r9*(cos(t) - 1) + 1) <= 1)$ Time= 160 msecs (c41) /* => 125 A^4 + 24 A^2 - 48 < 0 or |A| < 2/5 sqrt([8 sqrt(6) - 3]/5) */ ineq_linsolve(A^2*(cos(t) - 4)^2*sin(t)^2 < 9, A); Dependent equations eliminated: (1) Time= 40 msecs (d41) [[a = %r11], []] (c42) /* => |x| < y */ ineq_linsolve([x + y > 0, x - y < 0], [x, y]); Time= 260 msecs %pos9 %pos10 %pos9 %pos10 (d42) [[x = ----- - ------, y = ----- + ------], []] 2 2 2 2 (c43) /* ---------- Quit ---------- */ quit(); Bye. real 7.88 user 4.41 sys 1.12