NameError when using Sage polynomials

Question

I read here how to work with polynomials. But when I try this

R = QQ['t']
poly = (t+1) * (t+2); poly

Sage gives me the following error:

NameError: name 't' is not defined

What can I do about it?

Answer 1

Right, you have to inject the variable name when using polynomial rings. The document you point to points out that

sage: R.<t> = PolynomialRing(QQ)

does do this. Or, you can do

sage: R=QQ['t']
sage: R.inject_variables()
Defining t
sage: t+1
t + 1

You wanted to know how to do it without printing the name:

sage: R.inject_variables(verbose=False)

Have fun!

Answer 2

To complement the answer by @kcrisman, another way to go is:

sage: R = PolynomialRing(QQ, 't')
sage: t = R.gen()

Then t works as expected:

sage: (t+1) * (t+2)
t^2 + 3*t + 2

Note that the Sage syntax R.<t> = ... will work in a .sage file but not in a .py file, while the above works also in a .py file.

In a .py file you would first import PolynomialRing as follows:

from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing

To find out what imports you need, you can do

sage: import_statements(PolynomialRing)
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing

Finally, if you don't need the ring R, you can define t directly with

sage: t = polygen(QQ)

and if you ever need R later you can use

sage: R = t.parent()