Mon Feb 22 21:51:46 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) /* ---------- Combinatorial Theory ---------- */ /* Pochhammer symbol (a)_n = a (a + 1) ... (a + n - 1) => a (a + 1) (a + 2) */ pochhammer(a, 3); /aquarius/data2/opt/local/macsyma_422/library1/combin.so being loaded. Time= 270 msecs (d5) a (a + 1) (a + 2) (c6) /* Binomial coefficient => n (n - 1) (n - 2)/6 */ binomial(n, 3); /aquarius/data2/opt/local/macsyma_422/library1/binoml.so being loaded. Time= 50 msecs (n - 2) (n - 1) n (d6) ----------------- 6 (c7) /* 2^n n! (2 n - 1)!! => (2 n)! */ declare(n, integer)$ Time= 0 msecs (c8) 2^n * n! * (2*n - 1)!!; Time= 0 msecs n 2 n - 1 (d8) 2 n! genfact(2 n - 1, -------, 2) 2 (c9) makefact(%); Time= 0 msecs 2 n - 1 ceiling(-------) + n 2 2 n - 1 n! 2 (-------)! 2 (d9) ----------------------------------- 2 n - 1 2 n - 1 (------- - ceiling(-------))! 2 2 (c10) ratsimp(subst(ceiling((2*n - 1)/2) = n, %)); Time= 20 msecs 2 n 2 n - 1 2 n! (-------)! 2 (d10) ------------------ sqrt(%pi) (c11) remove(n, integer)$ Time= 10 msecs (c12) /* 2^n n! product(2 k - 1, k = 1..n) => (2 n)! */ 2^n * n! * product(2*k - 1, k, 1, n); Time= 330 msecs n /===\ | | n (d12) ( | | (2 k - 1)) 2 n! | | k = 1 (c13) closedform(%); /aquarius/data2/opt/local/macsyma_422/share/nusum1.so being loaded. Time= 1230 msecs 2 n 2 n - 1 2 n! (-------)! 2 (d13) ------------------ sqrt(%pi) (c14) /* => (2 n)!/[2^(2 n) (n!)^2] or (2 n - 1)!!/[2^n n!] */ gamma(n + 1/2)/(sqrt(%pi) * n!); Time= 0 msecs 1 gamma(n + -) 2 (d14) ------------ sqrt(%pi) n! (c15) makegamma(%); Time= 0 msecs 1 gamma(n + -) 2 (d15) ---------------------- sqrt(%pi) gamma(n + 1) (c16) /* Partitions of an integer => {1+1+1+1, 1+1+2, 1+3, 2+2, 4} (5 in all) */ numpartitions(4); /aquarius/data2/opt/local/macsyma_422/share/algfuncs.so being loaded. Time= 280 msecs (d16) 5 (c17) /* Stirling numbers of the first kind: S_1(5, 2) => -50 */ /*stirling1(5, 2);*/ /* Euler's totient function => 576 */ totient(1776); /aquarius/data2/opt/local/macsyma_422/library1/numth.so being loaded. Time= 60 msecs (d17) 576 (c18) /* ---------- Quit ---------- */ quit(); Bye. real 7.29 user 2.58 sys 1.74