Hi,
+1, that seems to make sense, and it's a good idea to have both
semantics available.
Note that there are also complicated mixes:
sage: R.<x> = RR[]
sage: Zxy = PolynomialRing(ZZ,'x,y,z')
sage: xx,yy,zz = Zxy.gens()
sage: (xx+yy).subs(x=x).parent()
Multivariate Polynomial Ring in x, y, z over Real Field with 53 bits of
precision
sage: (xx+yy)(x=x).parent()
Multivariate Polynomial Ring in x, y, z over Real Field with 53 bits of
precision
Your proposal is that the latter should only be RR[x,y], I guess?
Best,
Johan
Jonas Jermann writes:
> Hi
>
> +1 by me.
> How is the order of variables for "call" determined?
> How would this work for SR?
>
>
> Regards
> Jonas
>
> On 06.12.2015 15:24, Vincent Delecroix wrote:
>> Hello,
>>
>> We have substitution available for various objects (e.g. matrices when
>> the base ring is a polynomial ring). I would like to fix the conventions
>> of the parent of
>>
>> my_object.subs(var1=val1, var2=val2)
>>
>> versus
>>
>> my_object(var1=val1, var2=val2)
>>
>> With .subs, univariate polynomial ring somehow chooses the "minimal ring"
>>
>> sage: R.<x> = ZZ[]
>> sage: (x+3).subs(x=2).parent()
>> Integer Ring
>> sage: (x+3).subs(x=x+4).parent()
>> Univariate Polynomial Ring in x over Integer Ring
>> sage: (x+3).subs(x=4.).parent()
>> Real Field with 53 bits of precision
>>
>> Whereas multivariate are somehow "undecided"
>>
>> sage: (x+3).subs(x=2).parent()
>> Multivariate Polynomial Ring in x, y over Integer Ring
>> sage: (x+3).subs(x=x+4).parent()
>> Multivariate Polynomial Ring in x, y over Integer Ring
>> sage: (x+3).subs(x=4.).parent()
>> Real Field with 53 bits of precision
>>
>> Whereas the symbolic ring is as always a black hole
>>
>> sage: x = SR('x')
>> sage: x.subs(x=3.).parent()
>> Symbolic Ring
>> sage: x(x=3.).parent()
>> Symbolic Ring
>>
>> My proposition is:
>>
>> - .subs should be considered as an *internal* operation. Hence, the
>> result will always be in the same parent (or the result of a pushout).
>> In particular we would have
>>
>> sage: R.<x> = ZZ[]
>> sage: x.subs(x=4).parent()
>> Univariate Polynomial Ring in x over Integer Ring
>> sage: x.subs(x=4.).parent()
>> Univariate Polynomial Ring in x over Real Double Field
>>
>> - __call__ is considered as an external operation. The result should
>> (more or less) be the smallest parent in which the result belong.
>>
>> sage: R.<x,y> = ZZ[]
>> sage: x(3,5).parent()
>> Integer Ring
>> sage: (x+y)(3., polygen(ZZ))
>> Univariate Polynomial Ring in x over Real Field with 53 bits of
>> precision
>>
>> Does it look reasonable?
>>
>> Best,
>> Vincent
>>
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