Re: [Maxima-discuss] integrate_use_rootsof question, was: How can I catch this error? "errcatch" doesn't do the trick.

[David S. <d.s...@go...>]

About replacing "rootsof" with "solve": That's probably not correct,
because of multiple/repeated roots.

"solve" would list each root only once, ignoring multiplicity.

We could define that "rootsof" handles a root with multiplicity "n" by
listing it "n" times.
E.g. "rootsof((x+1)*(x-1)^2,x)" would be "[x+1,x-1,x-1]".

Also, I found that Richard Fateman already suggested giving "rootsof" a
second argument, back in 2009:
https://www.ma.utexas.edu/pipermail/maxima/2009/017036.html

I agree with him.

Best,
David

Sent from my mobile phone. / Von meinem Handy aus gesendet.
Am 10.09.2015 08:49 schrieb "David Scherfgen" <d.s...@go...>:

> Hi Robert,
>
> > Is there another way to inhibit the unwanted substitution? I think it's
> > better to keep the rootsof(...) expression in terms of the variable of
> > integration -- otherwise we would need to add a notation to rootsof to
> > indicate what the variable is. Also it might (or might not) look
> > unfamiliar to users.
>
> In the SourceForge bug report, I added another suggestion, which is to use
> the same dummy variable in the "rootsof" argument. This is also how Wolfram
> Alpha does it (their "%r1" is "omega" - it appears below the summation sign
> and also in the "log" expression). In my view, it would be the same obvious
> as when using the variable of integration.
>
> But you're right, there is a mathematical ambiguity - especially when the
> integrand contains additional constants, then we'd get something like
> "rootsof(a*%r1^3+b*%r1+c)".
>
> Overall, I'd vote for giving "rootsof" a second argument, then it would be
> perfectly clear and unambiguous. "rootsof" could then theoretically even be
> replaced with a nounified "solve", since it assumes "= 0" if the expression
> given to it is not an equation.
>
> What do you think?
>
> And do you know of other places Maxima where "rootsof" is used (so those
> would have to be changed as well), or is it only used in integration?
>
> > If you have a Sourceforge user name, I will gladly add it to the list of
> > developers.
>
> Sure, it's "tomasriker". Thank you, it's a great honor!
>
> Best regards,
> David
>