Since x^7 is monotone increasing, wouldn't a better simplification be simply
signum(x-1)?
Anyway, the more basic question in this thread is: how much effort should a
simplifying function make? Earlier versions of Macsyma/Maxima were pretty
conservative about this, on the theory that simplification should be a
lightweight operation. With faster machines, we can afford to be less
conservative today, but still need to be careful about 'heavy' operations
like factorization.
-s
On Fri, Jan 29, 2010 at 6:32 PM, Richard Hennessy <rich.hennessy at verizon.net
> wrote:
>
> I do think it would be cool if signum(x^7-1) could be converted to a
> product of signum()'s but not if it is done automatically. It can be done
> by functions in pw.mac and in abs_integrate.mac, so perhaps factoring is not
> needed for the argument to signum(). Any thoughts?
>
> (%i1) (display2d:false,load(pw))$
> (%i2) factor(x^7-1);
> (out2) (x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)
> (%i3) signum(x^7-1);
> (out3) signum(x^7-1)
> (%i4) simpsignum(%);
> (out4) signum(x-1)*signum(x^6+x^5+x^4+x^3+x^2+x+1)
> (%i5)
>
> Rich
>
>
>
>
>
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