This would work. This particular simplification would be applicable only to arguments to the signum() function. I
don't know if anyone would want a different simplifier just for signum() arguments. Although the sin(), tan() and cos()
functions could also benefit from a separate simplifier just for their arguments too. Since sin(10^3000000*2*%pi+a)
could be simplified to just sin(a). Similar results apply to the other trig functions and also probably to the
unit_step() function, I think. Periodic functions created with pw.mac's periodic() function would also benefit. I
don't know how to create a Maxima function that does not simplify its arguments, so that the function could get the
arguments "as is"? I always get the result of the simplifier before my function gets started.
Rich
From: Stavros Macrakis
Sent: Saturday, January 30, 2010 2:23 PM
To: Richard Hennessy
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] signum() evaluation is too slow
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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