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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

> (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 */

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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

> > (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---
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	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.

> (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.