I copied this from the documentation.
"When assume_pos is true and the sign of a parameter x cannot be determined from the current context or other
considerations, sign and asksign (x) return true. This may forestall some automatically-generated asksign queries, such
as may arise from integrate or other computations. "
It seems to me that assume_pos is a patch to "fix" a much deeper problem with Maxima's asksign. It is not a very good
one. You can get into trouble even if you read the documentation.
Try
(%i9) assume_pos:true;
(%o9) true
(%i10) plot2d([(2*unit_step(x)-1)/x], [x,-3,3], [plot_format, gnuplot])$
(%i11) assume_pos:false;
(%o11) false
(%i12) plot2d((2*unit_step(x)-1)/x,[x,-3,3],[plot_format, gnuplot])$
These two plots are not the same and one is really wrong even given the context obtained from the help.
That
----- Original Message -----
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: "'Richard Hennessy'" <rvh2007 at comcast.net>
Sent: Friday, October 24, 2008 8:11 PM
Subject: RE: [Maxima] assume_pos bug
ratsimp does not use the "assume" data base, as far as I know.
So whatever difference there is, should not depend on ratsimp.
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Richard Hennessy
> Sent: Friday, October 24, 2008 4:39 PM
> To: Maxima List
> Subject: assume_pos bug
>
> Try this
>
> (%i15) assume_pos:true;
> (%o15) true
> (%i11) ratsimp((2*unit_step(x)-1)/x);
> (%o11) 1/x
> (%i12) assume_pos:false;
> (%o12) false
> (%i13) ratsimp((2*unit_step(x)-1)/x);
> (%o13) (2*unit_step(x)-1)/x
>
>
> In the first case the function simplifies to 1/x which is not
> correct. This function is always above the x axis for all
> x. 1/x on the other hand is negative for x<0 and positive
> for x > 0 which is totally wrong. The answer in output %o13
> is the only correct answer. This function does not simplify to 1/x.
>
> Rich
>
>
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