Evaluation and subsitution of multi-variable polynomials

[wuthrich]

Let f be a polynomial in two variables x and y over a ring R. Consider the following three commands

i) f(2,3)

ii) f(x=2,y=3)

iii) f.subs(x=2,y=3)

They give the same results but not the same type. i) gives an element in R while ii) and iii) are constant polynomials in two variables:

sage: K.<x,y> = QQ[]
sage: f = x^2 + y^2
sage: f(2,3).parent()
Rational Field
sage: f(x=2,y=3).parent()
Multivariate Polynomial Ring in x, y over Rational Field
sage: f.subs(x=2,y=3).parent()
Multivariate Polynomial Ring in x, y over Rational Field

Following the documentation, i) and ii) should give an element in R while iii) is a polynomial.

f(x=2,y=3) is the __call__ method in sage.rings.polynomials.multi_polynomial_libsingular.pyx and there, in the first lines (currently line 1673), it jumps to execute subs.

See this thread: ​http://groups.google.com/group/sage-devel/browse_thread/thread/503d0d82307c9aa5

[wuthrich]

This came up when I tried to resolve #10888. But I found a different way of dealing with it there: I changed the troublesome occurriencies of ii) by i).