Functions in polynomials rings

edit

You want to access the generators of R as a tuple:

sage: R = PolynomialRing(QQ, 3, names='x'); R
Multivariate Polynomial Ring in x0, x1, x2 over Rational Field
sage: x = R.gens(); x
(x0, x1, x2)
sage: x[0]
x0

If you want to use some strange alternative indexing, then you can achieve it with a function.

One can produce strings and have the polynomial ring eat them.

String formatting is easy thanks to Python.

Define a polynomial ring as in the question:

R.<x1, x3, x5> = PolynomialRing(QQ)

Define a "generator power" function as follows:

def f(i, j):
    r"""
    Return the polynomial variable xi raised to the j-th power.
    """
    return R('x{}^{}'.format(i, j))

Example:

sage: f(3, 2)
x3^2