# Revision history [back]

### Can sage compute a basis for the graded parts of a graded ring?

We can define a graded ring

sage: T = TermOrder("wdeglex", (1,2))
sage: S = PolynomialRing(QQ, 'x,y', order=T)
sage: S
Multivariate Polynomial Ring in x, y over Rational Field
sage: x,y = S.gens()
sage: (x*y).degree()
3


I want to find all monomials in S of a given degree d. Can this be done in sage?

This can be done in Macaulay2 with

i1 : QQ[x, y, Degrees => {{1}, {2}}]

o1 = S

o1 : PolynomialRing

i2 : basis(4, S)

o2 = | x4 x2y y2 |

1      3
o2 : Matrix S <--- S