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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