Evaluation and subsitution of multi-variable polynomials

[chriswuthrich]

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

Component: commutative algebra

Keywords: multi_polynomials, evaluation, substitution

Issue created by migration from https://trac.sagemath.org/ticket/10946

[chriswuthrich]

comment:1

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).

[mkoeppe]

Description changed:

--- 
+++ 
@@ -7,9 +7,20 @@
  
  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.
+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:
 
-Follinwg the documentation, i) and ii) should give an element in R
+```
+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.