Discussion:
Maxima 5.1.40 cannot integrate A&S integral 5.1.42
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Soegtrop, Michael
2017-06-19 14:10:57 UTC
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Dear Maxima Team,

current Maxima cannot integrate Abramowitz and Stegun integral 5.1.42:

(%i44) integrate(x*%e^(%i*x)/(a^2+x^2),x);
(%o44) integrate(((x^2-a^2)*%e^(%i*x))/(%i*x^4+2*%i*a^2*x^2+%i*a^4),x)+(x*%e^(%i*x))/(%i*x^2+%i*a^2)

(%o44) [cid:***@01D2E916.A2087020]

of cause being not able to integrate this and that is not really a bug, but should I report a bug for failing Abramowitz and Stegun integrals?

Best regards,

Michael

Intel Deutschland GmbH
Registered Address: Am Campeon 10-12, 85579 Neubiberg, Germany
Tel: +49 89 99 8853-0, www.intel.de
Managing Directors: Christin Eisenschmid, Christian Lamprechter
Chairperson of the Supervisory Board: Nicole Lau
Registered Office: Munich
Commercial Register: Amtsgericht Muenchen HRB 186928
Richard Fateman
2017-06-19 14:46:53 UTC
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(%i44) integrate(x*%e^(%i*x)/(a^2+x^2),x);
(%o44)
integrate(((x^2-a^2)*%e^(%i*x))/(%i*x^4+2*%i*a^2*x^2+%i*a^4),x)+(x*%e^(%i*x))/(%i*x^2+%i*a^2)
Maxima also does not do the simpler exp(x)/(x^2+a2) either,
but since the answer involves the exponential integral Ei (or some
other expression involving gamma or hypergeometric functions),
maybe it is not exactly a bug. An unimplemented extension
maybe.

The solution to this and many other integrals may be found by
(eventually) incorporating Albert Rich's Rubi program into Maxima.
http://www.apmaths.uwo.ca/~arich/
which would be possible when the (promised) separation of Rubi
from its current rule-based / Mathematica syntax is complete.


RJF
Soegtrop, Michael
2017-06-19 15:57:42 UTC
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Dear Richard,

but since the answer involves the exponential integral Ei (or some
other expression involving gamma or hypergeometric functions),
maybe it is not exactly a bug. An unimplemented extension
maybe.
Since Maxima has all the exponential integral functions used in A&S (expintegral_e1, expintegral_ei, ...), I was expecting that the exponential integrals in A&S are handled.

The solution to this and many other integrals may be found by
(eventually) incorporating Albert Rich's Rubi program into Maxima.
http://www.apmaths.uwo.ca/~arich/
which would be possible when the (promised) separation of Rubi
from its current rule-based / Mathematica syntax is complete.

Is someone working on doing this manually, or is someone working on an automated Mathematica to Maxima translator for specific use cases?

Best regards,

Michael
Intel Deutschland GmbH
Registered Address: Am Campeon 10-12, 85579 Neubiberg, Germany
Tel: +49 89 99 8853-0, www.intel.de
Managing Directors: Christin Eisenschmid, Christian Lamprechter
Chairperson of the Supervisory Board: Nicole Lau
Registered Office: Munich
Commercial Register: Amtsgericht Muenchen HRB 186928
Richard Fateman
2017-06-19 23:34:57 UTC
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Post by Soegtrop, Michael
Dear Richard,
but since the answer involves the exponential integral Ei (or some
other expression involving gamma or hypergeometric functions),
maybe it is not exactly a bug. An unimplemented extension
maybe.
Since Maxima has all the exponential integral functions used in A&S
(expintegral_e1, expintegral_ei, …), I was expecting that the
exponential integrals in A&S are handled.
Sorry, it is much easier to differentiate Ei than to produce it as the
result of integration.
Post by Soegtrop, Michael
The solution to this and many other integrals may be found by
(eventually) incorporating Albert Rich's Rubi program into Maxima.
http://www.apmaths.uwo.ca/~arich/ <http://www.apmaths.uwo.ca/%7Earich/>
which would be possible when the (promised) separation of Rubi
from its current rule-based / Mathematica syntax is complete.
Is someone working on doing this manually,
Albert Rich seems intent on doing this, sometime, mostly automatically
Post by Soegtrop, Michael
or is someone working on an automated Mathematica to Maxima translator
This sort of exists, at least for the syntax of expressions and
patterns. There is
no obvious "translation" between some Mathematica commands and Maxima
programs, e.g. FullSimplify[] or Reduce[]. And the pattern-matching
differs in minor ways.
Post by Soegtrop, Michael
for specific use cases?
Big chunks of the original Rubi can be loaded into lisp, but not all of it.
RJF
Post by Soegtrop, Michael
Best regards,
Michael
Intel Deutschland GmbH
Registered Address: Am Campeon 10-12, 85579 Neubiberg, Germany
Tel: +49 89 99 8853-0, www.intel.de
Managing Directors: Christin Eisenschmid, Christian Lamprechter
Chairperson of the Supervisory Board: Nicole Lau
Registered Office: Munich
Commercial Register: Amtsgericht Muenchen HRB 186928
Soegtrop, Michael
2017-06-20 07:38:52 UTC
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Dear Richard,

This sort of exists, at least for the syntax of expressions and patterns. There is
no obvious "translation" between some Mathematica commands and Maxima
programs, e.g. FullSimplify[] or Reduce[]. And the pattern-matching differs in minor ways.

Are you referring to Mixima/ribot by John Lapeyre (https://sourceforge.net/projects/ribot/) ?

Btw.: for those who want to try Albert Rich's Rubi in Mathematica: set ShowSteps=False. It fails on many integrals when this is enabled.

Best regards,

Michael
Intel Deutschland GmbH
Registered Address: Am Campeon 10-12, 85579 Neubiberg, Germany
Tel: +49 89 99 8853-0, www.intel.de
Managing Directors: Christin Eisenschmid, Christian Lamprechter
Chairperson of the Supervisory Board: Nicole Lau
Registered Office: Munich
Commercial Register: Amtsgericht Muenchen HRB 186928

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