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Re: [Axiom-math] (no subject)


From: root
Subject: Re: [Axiom-math] (no subject)
Date: Wed, 19 Nov 2008 19:39:19 -0500

>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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