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Bugzilla from jakubi@df.uba.ar
For integrals that depend on a parameter, and the output is a list of
expressions for different cases of this parameter, how can properties on
the parameter be included in the statement to get as output a single
expression? Namely, in this example:

integrate(1/(x^2+a),x)

         2      +---+
       (x  - a)\|- a  + 2a x         +-+
   log(---------------------)      x\|a
                2             atan(-----)
               x  + a                a
  [--------------------------,-----------]
               +---+               +-+
             2\|- a               \|a
                               Type: Union(List Expression Integer,...)

tell to 'integrate' that a>0, say, and get the 'atan' expression.

I have read a few comments on the Axiom web sites about properties, provisos,
and a command 'Assume', eg here:

http://www.axiom-developer.org/axiom-website/currentstate.html

http://axiom-wiki.newsynthesis.org/DefiniteIntegration

But I have not found yet a hint on how to do it (if possible).

Alejandro Jakubi







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Re: (no subject)

daly
>For integrals that depend on a parameter, and the output is a list of
>expressions for different cases of this parameter, how can properties on
>the parameter be included in the statement to get as output a single
>expression? Namely, in this example:
>
>integrate(1/(x^2+a),x)
>
>         2      +---+
>       (x  - a)\|- a  + 2a x         +-+
>   log(---------------------)      x\|a
>                2             atan(-----)
>               x  + a                a
>  [--------------------------,-----------]
>               +---+               +-+
>             2\|- a               \|a
>                               Type: Union(List Expression Integer,...)
>
>tell to 'integrate' that a>0, say, and get the 'atan' expression.
>
>I have read a few comments on the Axiom web sites about properties, provisos,
>and a command 'Assume', eg here:
>
>http://www.axiom-developer.org/axiom-website/currentstate.html
>
>http://axiom-wiki.newsynthesis.org/DefiniteIntegration
>
>But I have not found yet a hint on how to do it (if possible).

The proviso research will eventually allow you to do this but
this is long term research, not anything you'll see escape from
my desk anytime soon.

I don't know of any way to achieve what you want (a Maple-style
assume facility) in Axiom.

Tim


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Re: (no subject)

Bugzilla from jakubi@df.uba.ar
On Wed, 19 Nov 2008, root wrote:

> The proviso research will eventually allow you to do this but
> this is long term research, not anything you'll see escape from
> my desk anytime soon.
> I don't know of any way to achieve what you want (a Maple-style
> assume facility) in Axiom.

OK. But still I wonder how does the integration algorithm split these two
cases without knowing somehow that it is dealing with a<0 or a>0.

Alejandro



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