mbmonagan@watmum.UUCP (Michael B. Monagan) (08/17/85)
(c1) integrate( exp(-t)/(1+t), t, 0, infinity ); INTEGRAL IS DIVERGENT /* This is wrong. Have I input the problem incorrectly ? */ /* Also, after 10 minutes on the following problem. */ (c2) integrate( exp(-t)/(1+t^(3/2)), t, 0, infinity ); NAME STACK OVERFLOW /* Am using the latest version on a VAX running Berkely UNIX BSD 4.2 */
matt@oddjob.UUCP (Matt Crawford) (08/20/85)
In article <256@watmum.UUCP> mbmonagan@watmum.UUCP (Michael B. Monagan) writes: >(c1) integrate( exp(-t)/(1+t), t, 0, infinity ); >INTEGRAL IS DIVERGENT > >/* This is wrong. Have I input the problem incorrectly ? */ The word "infinity" denotes a complex infinity of arbitrary phase. Use "inf" for positive real infinity. (Although macsyma still can't solve the integral analytically, it won't claim that it is divergent.) _____________________________________________________ Matt University crawford@anl-mcs.arpa Crawford of Chicago ihnp4!oddjob!matt
Bob Caviness <caviness@UDel-Dewey.ARPA> (08/21/85)
> (c1) integrate( exp(-t)/(1+t), t, 0, infinity ); > INTEGRAL IS DIVERGENT > > /* This is wrong. Have I input the problem incorrectly ? */ > /* Also, after 10 minutes on the following problem. */ > > (c2) integrate( exp(-t)/(1+t^(3/2)), t, 0, infinity ); > NAME STACK OVERFLOW > > /* Am using the latest version on a VAX running Berkely UNIX BSD 4.2 */ ----forwarded message--- Received: from UDel-Dewey.ARPA by rand-unix.ARPA; Tue, 20 Aug 85 14:00:50 pdt Message-Id: <8508202100.AA21766@rand-unix.ARPA> Received: from localhost by .UDel-Dewey.ARPA id a027015; 20 Aug 85 16:53 EDT Subject: Reply to message re bug in Macsyma's definite integration Date: 20 Aug 85 16:53:16 EDT (Tue) From: Bob Caviness <caviness@UDel-Dewey.ARPA> In response to Michael B. Monagan's message I tried his integrals and got the following using macsyma version 309 on a Vax 785. It's not very helpful, but at least it's not incorrect. Script started on Tue Aug 20 13:12:03 1985 % macsyma This is UNIX MACSYMA Release 309.1. (c) 1976,1984 Massachusetts Institute of Technology. All Rights Reserved. Enhancements (c) 1984 Symbolics, Inc. All Rights Reserved. Type describe(trade_secret); to see Trade Secret notice. Type exec("man macsyma"); for help. /usr/macsyma.309/macsyma.l being loaded. Batching the file /users/2125/13772/macsyma.mac Batching done. (c1) %e exp(-t)/(t+1); Time= 50 msec. - t %e (d1) ----- t + 1 (c2) integrate(%,t,0,inf); Totaltime= 16233 msec. GCtime= 4666 msec. inf / - t [ %e (d2) I ----- dt ] t + 1 / 0 (c3) exp(-t)/(1+(t) t^^(3/2)); Time= 50 msec. - t %e (d3) ---------- <3/2> t + 1 (c4) exp edit(c3); [starting edit] Time= 166 msec. - t %e (d4) -------- 3/2 t + 1 (c5) integrate(5, %,t,0,int f); Totaltime= 12033 msec. GCtime= 4700 msec. inf / - t [ %e (d5) I -------- dt ] 3/2 / t + 1 0 (c6) quit(); % ^D script done on Tue Aug 20 13:15:37 1985 ------- End of Forwarded Message
fateman%ucbdali@Berkeley (Richard Fateman) (08/21/85)
> > (c1) integrate( exp(-t)/(1+t), t, 0, infinity ); > > INTEGRAL IS DIVERGENT > > > > /* This is wrong. Have I input the problem incorrectly ? */ > > /* Also, after 10 minutes on the following problem. */ > > > > (c2) integrate( exp(-t)/(1+t^(3/2)), t, 0, infinity ); > > NAME STACK OVERFLOW > > > > /* Am using the latest version on a VAX running Berkely UNIX BSD 4.2 */ > > ----forwarded message--- Received: from UCB-VAX.ARPA by rand-unix.ARPA; Tue, 20 Aug 85 14:45:37 pdt Received: from ucbdali.ARPA by UCB-VAX.ARPA (4.24/5.3) id AA01855; Tue, 20 Aug 85 14:43:16 pdt Received: by ucbdali.ARPA (5.5/4.48) id AA01115; Tue, 20 Aug 85 14:43:09 PDT Date: Tue, 20 Aug 85 14:43:09 PDT From: fateman%ucbdali@Berkeley (Richard Fateman) Message-Id: <8508202143.AA01115@ucbdali.ARPA> To: caviness@UDel-Dewey.ARPA Subject: Macsyma bugs? Cc: lseward@rand-unix.ARPA I got the same answers on a sun 2/50. It took only 35% longer to compute I think Monagan's problem was that he used "infinity", not "inf". "infinity" is complex infinity, not real positive infinity. If you want a simple bug, try Int[1/x^2,{x,-1,1}] in SMP. you get -2. Note the integrand is non-negative. The integral is divergent, as Macsyma is able to figure out. It seems to me that this is not the right place for bug reports, though. macsyma bugs can be mailed to macsym@mit-mc.arpa. Dunno about SMP, though.
igor@fisher.UUCP (Igor Rivin) (08/22/85)
> (c1) integrate( exp(-t)/(1+t), t, 0, infinity ); > INTEGRAL IS DIVERGENT > > /* This is wrong. Have I input the problem incorrectly ? */ > /* Also, after 10 minutes on the following problem. */ > > (c2) integrate( exp(-t)/(1+t^(3/2)), t, 0, infinity ); > NAME STACK OVERFLOW > > /* Am using the latest version on a VAX running Berkely UNIX BSD 4.2 */ I suspect that if you use "inf" instead of "infinity" your problems will go away; MACSYMA denotes complex infinity by "infinity" and real positive infinity by "inf". This should be better documented. Igor.