Re: [Maxima-discuss] "ratsimp" loops infinitely, but only after calling "ratexpand"

[Stavros M. (Σ. Μ. <mac...@al...>]

Interesting experiment.

Even more interesting might be doing arithmetic *between* expressions.
That's where I'd expect some speedup from preserving the varlist, at least
if the same variables are involved.

On Tue, Apr 14, 2015 at 4:44 PM, David Scherfgen <d.s...@go...
> wrote:

> Hi everyone,
>
> I have written a small test program and got some interesting results.
>
> What the program does is generate a number of random expressions
> (compositions of integers, a variable x, +, *, ^, log and trigonometric
> functions) and measure the time it takes to apply fullratsimp, ratexpand
> and radcan to all these expressions. Two variants are compared: Variant 2
> clears ?genvar and ?varlist after each call, while variant 1 doesn't. The
> results are also saved for comparison afterwards.
>
> Now the interesting result, which is exactly what I noticed in my larger
> program, too: Variant 2 is about 5 to 10 times FASTER than variant 1. But
> only if ratexpand is involved. If it's left out, variant 2 is slightly
> slower than variant 1. For some expressions, the results differ, but so far
> I found them to be equivalent, differing only in the ordering of terms.
>
> So, is there something wrong with ratexpand? Is it possible that it
> creates a lot of "mess" that slows down everything?
>
> I attached the program to this mail so that you can try it yourself.
> Please note that sometimes an expression might make either ratsimp,
> ratexpand or radcan crash or loop forever, so in that case just try again,
> and you will get different random expressions. This might also be a good
> way to identify more bugs in Maxima. :-)
>
> Please excuse my non-functional programming style, which is probably
> painful for you Lisp programmers. I grew up with C++.
>
> Best regards,
> David
>
> 2015-04-14 18:52 GMT+02:00 Richard Fateman <fa...@be...>:
>
>>  On 4/14/2015 9:41 AM, Stavros Macrakis (Σταῦρος Μακράκης) wrote:
>>
>>  On the other thread, I suggested using ratsimp, but I'd forgotten that
>> ratsimp in fact was having problems after a ratexpand.
>>
>>  Robert, you said:
>>
>>  The problem, as you guessed, is that ratexpand leaves some garbage behind,
>> namely one or the other of the special (global) variables VAR and/or
>> VARLIST. It's possible that these are handled or mishandled in a similar
>> way in the other examples you gave. However, in a sense we are getting
>> the intended effect of these specials -- one function is causing an
>> effect on another. I'd like to get some guidance from the old timers (the
>> really OLD old timers; I'm a n00b, I've been around for hardly more than
>> a decade) on the intended use of VAR and VARLIST before I commit this as
>> a bug fix.
>>
>>   ​ I took a look at varlist after ratexpand in a block, and it looks
>> correct, not "garbage":
>>
>>   ​ ​
>> (((MEXPT) ((MPLUS SIMP) -1 ((MEXPT SIMP) $X -1)) ((RAT) 1 2))
>>   ​
>> $X)
>> ​​
>>  ​
>>
>>
>>   But it's interesting that clearing varlist and genvar fixes the
>> problem.
>>
>>   The intent of having varlist/genvar as globals is that when the CRE
>> package (rat and company) computes with expressions, it first has to
>> convert them to have the same variables in the same order. Within a
>> calculation, you probably want to use the same variable list to avoid
>> constant conversions. So I guess that binding varlist/genvar to nil will at
>> worst make computations slower -- see example below.
>>
>>   In more detail: ​In CRE form, rat(x^2+y,x,y) is a polynomial in x
>> whose coefficients are polynomials in y; but rat(x^2+y,y,x) is a
>> ​polynomial in y whose coefficients are polynomials in x. To operate on the
>> two of them (add, multiply, etc.), they need to be converted to polynomials
>> in the same variables.
>>
>>  RJF, please correct me if I've gotten something wrong here.
>>
>>          -s
>>
>>
>>  This is exactly right.   There is a cost in emptying the genvar list --
>> new gensyms are constructed for the
>> internal names.  If you keep on doing this without ever
>> garbage-collecting these symbols, you might
>> have problems.   The initial implementation tried to re-use the gensyms,
>> and also tried to make the
>> comparison of ordering --- which gensym was more of a "main variable"
>> than others by a clever scheme
>> invented by William A. Martin.   Generate a bunch of symbols.  They can
>> be sorted by their addresses
>> in memory  [this is NOT an operation supported by Lisp, but is easily
>> done in certain implementations].
>> This becomes genvar.
>> Then you can easily test in polynomial arithmetic which variable/gensym
>> is "more main"  by one machine instruction or so.
>>
>> This is the explanation for the function  name  pointergp, (for those
>> reading the source code).  This idea was
>> abandoned quite some time ago for various reasons including portability
>> and bugginess when other
>> pieces were layered on top of the rational function package.  (Like
>> algebraic:true, I suspect).
>> So pointergp doesn't compare pointers any more.
>>
>> RJF
>>
>>
>>
>>
>>
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