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[Axiom-developer] Re: conditionally defined functions
From: |
William Sit |
Subject: |
[Axiom-developer] Re: conditionally defined functions |
Date: |
Mon, 20 Sep 2004 10:08:53 -0400 |
Martin Rubey wrote:
>
> William Sit writes:
> > > In principle, this is not too difficult. However, there is a slight
> subtlety:
> > > Currently not all domains that contain variables provide such a
> function, in
> > > particular, FRAC does not. Instead, there is a package RF that provides
> this
> > > functionality. Well, no problem:
> > >
> > > * move the operation variables from RF and POLYCATQ to QFCAT :
> > >
> > > if S has variables: S -> List Symbol then
> > > variables: % -> List Symbol
> > > variables f ==
> > > mymerge(variables(numer(f)), variables(denom(f)))
> > >
> > > and add the following to UP and MPOLY :
> > >
> > > if R has variables: R -> List Symbol then
> > > coerce(r:R):% ==
> > > if member?(x, variables(r)) then
> > > error "coefficient contains variable"
> > > else coerce(r)$Rep
> > >
> >
> > If this works, it works wrongly, because this confuses the x in the inner
> > domain of a tower with the x in the outer domain of the tower.
>
> I don't understand what you mean with "wrongly". I'm aiming at the following:
> I
> want that UP(x, FRAC POLY INT) or UP(x, EXPR INT) would be a rational function
> (or expression) that is a polynomial in x. I tested the code above and it does
> indeed "work" (in this sense).
>
> > Remember that the compiler distinguishes these already. So the condition
>
> > member?(x, variables(r))
>
> > would always return false.
>
> No, it does not. (at least not in the tests I ran)
>
> > I don't know what you meant by "fishy". The code would not work at present
> > because I don't think you can consider a function as an attribute.
>
> Hmm, I think you can. The code above does so.
One can never argue with code that works! I am surprised that a function can be
treated as an attribute -- I tried that in the interpreter:
INT has min: (INT, INT)->Boolean
false
Of course, it has. I think the reason why the answer is false is because this
property is not in the AttributeRegistry. Another difference between interpreter
and compiler?
Martin, I did not test your code (lack of time, but probably also I do not have
the setup as well. I might even have misunderstood your question: Perhaps you
are just trying to "lift" a polynomial (or rational function) with integer
coefficient that may or may not involve x (and if it does, only polynomially)
and just want to separate the variable x and rewrite it as a polynomial in x
with all the rest as coefficients? In other words, there is never two different
x's and you just want to rewrite something like Q[a,b,...w,x] as
Q[a,b,...,w][x]? Have you tried using POLYLIFT?
As to why I think if it works, it works wrongly:
Try this:
(1) -> )clear all
(1) -> y:=3*x + 1
(1) 3x+1 Type: Polynomial Integer
(2) -> z: UP(x, POLY INT)
Type: Void
(3) -> z:=3*x + 1
(3) 3x+1 Type: UnivariatePolynomial(x,Polynomial Integer)
(4) -> t:=variables(y)
(4) [x] Type: List Symbol
(5) -> s:=variables(z)
(5) ["?"] Type: List SingletonAsOrderedSet
(6) sx:=s.1
(6) "?" Type: SingletonAsOrderedSet
(7) member?(sx,t)
(7) true Type: Boolean
Is this correct? How?
(8) sxx:=convert(sx)
(8) ? Type: Symbol
(9) tx := t.1
(9) x Type: Symbol
(10) g:Boolean:= sxx=tx
(10) false Type: Boolean
(11) g:= sx = tx
(11) true Type: Boolean
How do you explain (11) that two items of different type can be equal, and (10),
after conversion to the same type, are not?
William
---
PS:
> > Remember that the compiler distinguishes these already. So the condition
>
> > member?(x, variables(r))
>
> > would always return false.
>
> No, it does not. (at least not in the tests I ran)
I was writing based on a similar situation we discussed on June 12:
---quote from June 12
So is this a bug? I am not sure, it may be good that the interpreter caught the
ambiguity and it may be bad that the compiler does not. The compiler actually
knows how to distinguish POLY INT from EXPR POLY INT even if the SAME symbol is
used, but we (human) will get all confused. Try:
)abb package TEST Test
Test():Target==Implementation where
EXPR ==> Expression
POLY ==> Polynomial
INT ==> Integer
Target ==> with
f1: () -> EXPR POLY INT
f2: () -> POLY INT
f3: () -> EXPR POLY INT
f4: () -> EXPR POLY INT
Implementation ==> add
a:=new()$Symbol
b:=a ::EXPR POLY INT
c:=a :: POLY INT
f1()==b
f2()==c
f3()== (c*b)/b
f4()== f3()/b
Note that if you check the signature of /, the compiler "knows" it is legally
used and the answer for f4() is c/b, not 1 (which should be the case
mathematically).
---end of quote
I have not tried to replace EXPR by UP(x, ...) in Test(). Perhaps they behave
differently
- [Axiom-developer] Re: conditionally defined functions, Martin Rubey, 2004/09/17
- [Axiom-developer] Re: conditionally defined functions, Ralf HEMMECKE, 2004/09/17
- [Axiom-developer] Re: conditionally defined functions, Ralf HEMMECKE, 2004/09/17
- [Axiom-developer] Re: conditionally defined functions, William Sit, 2004/09/18
- [Axiom-developer] Re: conditionally defined functions, Martin Rubey, 2004/09/20
- [Axiom-developer] Re: conditionally defined functions,
William Sit <=
- [Axiom-developer] Re: conditionally defined functions, Martin Rubey, 2004/09/22
- [Axiom-developer] Re: conditionally defined functions, William Sit, 2004/09/22
- [Axiom-developer] Re: conditionally defined functions, Martin Rubey, 2004/09/23
- [Axiom-developer] Mixing up variables: (was Re: conditionally defined functions), William Sit, 2004/09/23
- [Axiom-developer] Re: Mixing up variables: (was Re: conditionally defined functions), Martin Rubey, 2004/09/23
- RE: [Axiom-developer] Re: Mixing up variables: (was Re: conditionallydefined functions), Bill Page, 2004/09/23
- RE: [Axiom-developer] Re: Mixing up variables: (was Re: conditionallydefined functions), Martin Rubey, 2004/09/24
- [Axiom-developer] speakerscorner, Martin Rubey, 2004/09/24
- RE: [Axiom-developer] Re: Mixing up variables: (was Re: conditionallydefined functions), Bill Page, 2004/09/24
- RE: [Axiom-developer] Re: Mixing up variables: (was Re: conditionallydefined functions), Martin Rubey, 2004/09/24