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Re: [Maxima-discuss] a(b), a[b], op, args -- result of factor
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From: Eduardo O. <edu...@gm...> - 2024-08-17 22:22:17
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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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