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Re: [Maxima-discuss] a(b), a[b], op, args -- result of factor
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From: Stavros M. <mac...@gm...> - 2024-08-17 22:38:59
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Normally, the *translated* property means that the function was defined
using *translate*.
I have no idea why functions originally defined in Lisp have this flag.
This is intentional (defmfun/ commac.lisp):
;; I (rtoy) think we can consider all defmfun's as translated functions.
(defprop ,function t translated)
but I have no idea of the rationale. This seems wrong -- for example, (mget
'$cons 'mexpr) => nil, unlike a genuine translated function, where it is
the Maxima definition of the function.
Ray?
-s
On Sat, Aug 17, 2024 at 6:22 PM Eduardo Ochs <edu...@gm...> wrote:
> Thanks!!!
> A quick question...
> The source of taylorp in simp.lisp is very clear:
>
> (defmfun $taylorp (x)
> (and (not (atom x))
> (eq (caar x) 'mrat)
> (member 'trunc (cdar x)) t))
>
> but
>
> :lisp (describe '$taylorp)
>
> says "Symbol-plist: ... TRANSLATED -> T ...".
>
> What does the "translated" mean in this case? I took a quick look at
> all the occurences of "translate" in the info manual and I got the
> impression that translated functions come from Maxima functions, but I
> grepped the sources and I didn't find a possible Maxima source for
> this $taylorp...
>
> Cheers, TIA, etc,
> Eduardo
>
>
> On Sat, 17 Aug 2024 at 19:04, Stavros Macrakis <mac...@gm...> wrote:
>
>> taylorp(taylor(1,x,0,1)) => true
>>
>>
>> On Sat, Aug 17, 2024, 16:54 Eduardo Ochs <edu...@gm...> wrote:
>>
>>> Hi all,
>>>
>>> sorry for the delay - we're at the end of the semester here, with lots
>>> of tests to prepare and to mark... and this will be a partial answer -
>>> I haven't tried all of your suggestions yet. Anyway...
>>>
>>> My questions about the internal representation of the objects returned
>>> by "factor", "trunc" and "taylor" were not because I need to do
>>> something "practical" with these objects in the near future - I was
>>> asking them just because my mental model of Maxima objects is still
>>> very incomplete, and when I ask these questions here I usually get
>>> answers that help me a lot.
>>>
>>> The documentation for "trunc", at
>>>
>>> (info "(maxima)trunc")
>>> https://maxima.sourceforge.io/docs/manual/maxima_141.html#trunc
>>>
>>> says:
>>>
>>> Annotates the internal representation of the general expression
>>> <expr> so that it is displayed as if its sums were truncated Taylor
>>> series. <expr> is not otherwise modified.
>>>
>>> The snippet below shows some ways of exploring these annotations - I'm
>>> guessing that "annotations" is the correct term:
>>>
>>> a1 : a*b;
>>> a2 : factor(100);
>>> b1 : 23 + 45*x;
>>> b2 : trunc(b1); /* has a ... */
>>> b3 : taylor(b1, x, 0, 1); /* has a ... and a /T/ */
>>> ratp(b1); /* false */
>>> ratp(b2); /* false */
>>> ratp(b3); /* true */
>>> to_lisp();
>>> #$a*b$ ; ((MTIMES SIMP) $A $B)
>>> #$a1$ ; ((MTIMES SIMP) $A $B)
>>> #$a2$ ; ((MTIMES SIMP FACTORED) ((MEXPT SIMP) 2 2) ((MEXPT SIMP) 5
>>> 2))
>>> #$b1$ ; ((MPLUS SIMP) 23 ((MTIMES SIMP) 45 $X))
>>> #$b2$ ; ((MPLUS SIMP TRUNC) 23 ((MTIMES SIMP) 45 $X))
>>> #$b3$ ; ((MRAT SIMP ... TRUNC) PS ...)
>>> (car #$b2$) ; (MPLUS SIMP TRUNC)
>>> (cdar #$b2$) ; (SIMP TRUNC)
>>> (cddar #$b2$) ; (TRUNC)
>>> (to-maxima)
>>>
>>> There is a simple way to detect "taylorness" from Maxima - we can use
>>> "ratp" - but I couldn't find a simple way to detect "truncness", or
>>> "factoredness"... my guess is that if, and when, I decide that some of
>>> these annotations are important in my programs that represent Maxima
>>> objects as trees, then I will have write some Lisp to interpret the
>>> "cdar"s or the "cddar"s of these objects to see if they have any
>>> annotations that are worth showing... and "worth showing" is something
>>> that obviously depends on the context, and in many cases just adding a
>>> way to indicate that "this object has non-trivial annotations" would
>>> be enough.
>>>
>>> Anyway, these annotations look very important, but the only places in
>>> the manual in which I remember seeing them mentioned clearly are here,
>>>
>>> (info "(maxima)Introduction to Simplification")
>>> https://maxima.sourceforge.io/docs/manual/maxima_45.html
>>>
>>> that points to this paper, in which they are called "flags",
>>>
>>> https://people.eecs.berkeley.edu/~fateman/papers/intro5.txt
>>> https://maxima.sourceforge.io/misc/Fateman-Salz_Simplifier_Paper.pdf
>>>
>>> and here:
>>>
>>> (info "(maxima)Introduction to Lists")
>>> https://maxima.sourceforge.io/docs/manual/maxima_20.html
>>>
>>> Are there standard functions to inspect them _from Maxima_? Any
>>> pointers, comments, recommendations?
>>>
>>> Thanks in advance, and, again, sorry for not having digested all the
>>> material in your previous answers _yet_... =/
>>>
>>> Eduardo Ochs
>>> http://anggtwu.net/eev-maxima.html
>>>
>>>
>>> On Thu, 15 Aug 2024 at 14:11, Stavros Macrakis <mac...@gm...>
>>> wrote:
>>>
>>>> As I said in my post:
>>>>
>>>> The clean way to process factorizations programmatically is with
>>>> *ifactors*.
>>>>
>>>> ifactors(10!) => [[2, 8], [3, 4], [5, 2], [7, 1]]
>>>>
>>>>
>>>> No reason to call internal functions or futz around with the output of
>>>> *factor*, which is not designed for programmatic use.
>>>>
>>>> -s
>>>>
>>>>
>>>> On Thu, Aug 15, 2024 at 9:29 AM Richard Fateman <fa...@gm...>
>>>> wrote:
>>>>
>>>>>
>>>>> If you expect Maxima to continually retain a factorization like 2^3
>>>>> through various simplifications,
>>>>> you have to turn off the simplifier, which pretty much breaks the
>>>>> whole system.
>>>>>
>>>>> If you want to see the factors and multiplicities, do this:
>>>>> :lisp (trace nratfact).
>>>>>
>>>>> If you want to acquire a result that gives prime factors and
>>>>> multiplicities in some structure that
>>>>> does not disappear, that structure might look like ...
>>>>> factorlist([2,3], [3,1}) for 2^3*3^1 or 24.
>>>>> It would be quite easy to make an alternative version of nratfact, or
>>>>> consider
>>>>>
>>>>>
>>>>> *factorlist(r) := psubst([ "^"="[","*"="[" ], factor(r));*
>>>>>
>>>>> which, for factorlist(24) gives [[2,3],3].
>>>>> (sorry, if you want 3 to appear as 3^1 or [3,1] you'll have to write
>>>>> another line of code.
>>>>>
>>>>> As for the show expression task, here's a simpler piece of code for
>>>>> most of the task..
>>>>> *showit(r):=psubst(psubstlist,r);*
>>>>> where
>>>>>
>>>>>
>>>>> *psubstlist: [ "^"=Power, "*"=Times, "+"=Plus, "/"=Div]; (*etc
>>>>> etc for all operators of interest . Maybe choose other names *)*
>>>>>
>>>>> I think that the graphical tree representation of expressions may be
>>>>> of some brief explanatory use, but
>>>>> the prefix expression version is, for me, much more appealing. Thus
>>>>> *showit (rat(x+1)^2);*
>>>>> returns
>>>>> *Plus(Power(x,2),Times(2,x),1)*
>>>>>
>>>>>
>>>>> RJF
>>>>>
>>>>> On Wed, Aug 14, 2024 at 6:15 PM Stavros Macrakis <mac...@gm...>
>>>>> wrote:
>>>>>
>>>>>> One problem with integer factorizations is that they are
>>>>>> pseudo-simplified: normally, Maxima does not allow 2^3 as a simplified
>>>>>> expression, but *factor* cheats and marks the expression as
>>>>>> simplified, even though it isn't. That means that it gives strange results
>>>>>> if you try to manipulate it:
>>>>>>
>>>>>> qq:factor(24) => 2^3*3
>>>>>> qq+1 => 2^3*3 + 1
>>>>>>
>>>>>> <big snip>
>>>>>
>>>>>
>>>>
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