# Can I define a graded ring in sage?

I can define a custom grading on a polynomial ring in Macaulay2 with the command

```
S = QQ[x,y, Degrees => {{1},{2}}]
```

Can I define this ring in sage?

Can I define a graded ring in sage?

I can define a custom grading on a polynomial ring in Macaulay2 with the command

```
S = QQ[x,y, Degrees => {{1},{2}}]
```

Can I define this ring in sage?

add a comment

1

If I correctly understand the Macaulay2 command you provide, you can mimick the same behavior in SageMath as follows:

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

You can find more informations on term orders in the documentation [1]. Several weighted term orders are available.

Ahh great! Also, is it possible to define a bidegree? TermOrder('wdeglex', ((1,0),(2,2))) returns a TypeError

I do not think so. I urge you to propose a ticket on http://trac.sagemath.org to implement this kind of term orders.

Well, thinking a bit more about this, you can use matrix term orders:

```
sage: S = TermOrder('M(2,3,0,1)')
sage: S
Matrix term order with matrix
[2 3]
[0 1]
```

In such a way, the first variable will have weight `(2,0)`

and the second `(3,1)`

. This order is used when you compare monomials. Unfortunately, the method `degree`

only returns the degree with respect with the first weight of each variable rather than a tuple. I do not know how one can get the tuple.

Asked: **
2016-06-20 14:40:28 -0500
**

Seen: **103 times**

Last updated: **Jun 21 '16**

File imports for polynomial rings in sage

Trying to display the roots of a polynomial over a finite field

Reducing a Set of Polynomial Equations to Minimal Variables and Equations

Polynomial ring modulus integer to univariate polynomial ring over the Integers

Solving system of polynomial equation over finite field

Unhandled SIGABRT when working with polynomial rings

PolynomialRing and from __future__ import unicode_literals

Tensor product of polynomial algebras

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.