# Pass a list of variable names as parameter to a polynomial ring

I am trying to write a function that compute a vector space basis $B$ for the quotient ring $k[x_1,\dots,x_n]/I$. I want to make the list of variables as the input parameter.

I tried this:

var("x,y")
Vlist=[x,y]
P.<Vlist>=PolynomialRing(QQ,order='degrevlex')
f=x^2+y^3
f.lm()


It gave me error message. I also tried

Vlist=['x,y']


or

Vlist=["x,y"]


None of them works. I know that

P.<x,y>=PolynomialRing(QQ,order='degrevlex')
f=x^2+y^3
f.lm()


works. So I can just type this before I run my function. But is there a way that I can make this as input of the function?

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You can get the list of strings representing your variables as follows:

sage: [str(i) for i in Vlist]
['x', 'y']


So you can define your polynomial ring directly, without the <> construction:

sage: P = PolynomialRing(QQ, [str(i) for i in Vlist], order='degrevlex')
sage: P
Multivariate Polynomial Ring in x, y over Rational Field


But now, the Python variables x and y still point to the symbols x and y (that belong to the Symbolic Ring), not the indeterminates x and y that belong to P. For this you can do:

sage: P.inject_variables()
Defining x, y


Then:

sage: f=x^2+y^3
sage: f.lm()
y^3


By the way, note that if your variables are going to be x0, x1,...,x9 (say), you can use the following construction:

sage: P = PolynomialRing(QQ, 10, 'x', order='degrevlex')
sage: P
Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5, x6, x7, x8, x9 over Rational Field
sage: P.inject_variables()
Defining x0, x1, x2, x3, x4, x5, x6, x7, x8, x9

more

Thank you! That problem is solved! Now another related question is, I have to pass a list of Groebner basis as input parameter too. Since they are defined before the polynomial ring $P$ is defined in the function, I still cannot use $f.lm()$ on them. Is there a way to make the $x,y$ in $f$ indeterminates?

I am not sure to understand your new question (perhaps could you make an explicit one with examples), but if f is already defined as a symbolic expression, you can try to do P(f) to transform it into an element of P, with correct indeterminates.