Mon Feb 22 21:59:32 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) /* ---------- Determining Zero Equivalence ---------- */ /* The following expressions are all equal to zero */ sqrt(997) - (997^3)^(1/6); Time= 20 msecs (d5) 0 (c6) sqrt(999983) - (999983^3)^(1/6); Time= 30 msecs 1/6 (d6) sqrt(999983) - 999949000866995087 (c7) radcan(%); Time= 490 msecs (d7) 0 (c8) (2^(1/3) + 4^(1/3))^3 - 6*(2^(1/3) + 4^(1/3)) - 6; Time= 10 msecs 1/3 1/3 3 1/3 1/3 (d8) (4 + 2 ) - 6 (4 + 2 ) - 6 (c9) radcan(%); Time= 300 msecs (d9) 0 (c10) cos(x)^3 + cos(x)*sin(x)^2 - cos(x); Time= 0 msecs 2 3 (d10) cos(x) sin (x) + cos (x) - cos(x) (c11) trigsimp(%); /aquarius/data2/opt/local/macsyma_422/share/trigsimp.so being loaded. Time= 70 msecs (d11) 0 (c12) /* See Joel Moses, ``Algebraic Simplification: A Guide for the Perplexed'', _Communications of the Association of Computing Machinery_, Volume 14, Number 8, August 1971, 527--537. This expression is zero if Re(x) is contained in the interval ((4 n - 1)/2 pi, (4 n + 1)/2 pi) for n an integer: ..., (-5/2 pi, -3/2 pi), (-pi/2, pi/2), (3/2 pi, 5/2 pi), ... */ expr: log(tan(1/2*x + %pi/4)) - asinh(tan(x)); Time= 80 msecs x %pi (d12) log(tan(- + ---)) - asinh(tan(x)) 2 4 (c13) radcan(exponentialize(logcontract(logarc(expr)))); Time= 1070 msecs (d13) 0 (c14) q: logcontract(trigsimp(halfangles(trigexpand(logarc(expr))))); Time= 3000 msecs 2 (d14) log((cos(x) sin(x) - cos (x) + cos(x)) abs(cos(x)) 2 2 /((sin (x) + (cos(x) - 1) sin(x)) abs(cos(x)) + cos(x) sin(x) + cos (x) - cos(x))) (c15) assume(-%pi/2 < x, x < %pi/2)$ Time= 340 msecs (c16) trigsimp(q); Time= 480 msecs (d16) 0 (c17) forget(-%pi/2 < x, x < %pi/2)$ Time= 20 msecs (c18) /* Use a roundabout method---show that expr is a constant equal to zero */ dexpr: diff(expr, x); Time= 10 msecs 2 x %pi sec (- + ---) 2 2 4 sec (x) (d18) -------------- - ----------------- x %pi 2 2 tan(- + ---) sqrt(tan (x) + 1) 2 4 (c19) radcan(exponentialize(dexpr)); Time= 750 msecs (d19) 0 (c20) q: factor(trigreduce(dexpr)); /aquarius/data2/opt/local/macsyma_422/library1/trgred.so being loaded. Time= 370 msecs sec(x) (abs(sec(x)) - sec(x)) (d20) ----------------------------- abs(sec(x)) (c21) assume(-%pi/2 < x, x < %pi/2)$ Time= 130 msecs (c22) ratsimp(q); Time= 20 msecs (d22) 0 (c23) forget(-%pi/2 < x, x < %pi/2)$ Time= 10 msecs (c24) ev(expr, x = 0); Time= 0 msecs (d24) 0 (c25) remvalue(expr, dexpr, q)$ Time= 0 msecs (c26) log((2*sqrt(r) + 1)/sqrt(4*r + 4*sqrt(r) + 1)); Time= 120 msecs log(4 r + 4 sqrt(r) + 1) (d26) log(2 sqrt(r) + 1) - ------------------------ 2 (c27) logcontract(radcan(%)); Time= 230 msecs (d27) 0 (c28) (4*r + 4*sqrt(r) + 1)^(sqrt(r)/(2*sqrt(r) + 1)) * (2*sqrt(r) + 1)^(1/(2*sqrt(r) + 1)) - 2*sqrt(r) - 1; Time= 0 msecs 1 sqrt(r) ------------- ------------- 2 sqrt(r) + 1 2 sqrt(r) + 1 (d28) (2 sqrt(r) + 1) (4 r + 4 sqrt(r) + 1) - 2 sqrt(r) - 1 (c29) radcan(%); Time= 420 msecs 1 sqrt(r) ------------- ------------- 2 sqrt(r) + 1 2 sqrt(r) + 1 (d29) (2 sqrt(r) + 1) (4 r + 4 sqrt(r) + 1) - 2 sqrt(r) - 1 (c30) /* [Gradshteyn and Ryzhik 9.535(3)] */ 2^(1 - z)*gamma(z)*zeta(z)*cos(z*%pi/2) - %pi^z*zeta(1 - z); /aquarius/data2/opt/local/macsyma_422/library1/combin.so being loaded. Time= 240 msecs %pi z zeta(z) gamma(z) cos(-----) 2 z (d30) --------------------------- - zeta(1 - z) %pi z - 1 2 (c31) ratsimp(%); Time= 10 msecs %pi z z z 2 zeta(z) gamma(z) cos(-----) - zeta(1 - z) 2 %pi 2 (d31) --------------------------------------------------- z 2 (c32) /* ---------- Quit ---------- */ quit(); Bye. real 12.46 user 9.23 sys 1.03