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How can I assign different degrees to the variables of a polynomial ring?

asked 2019-07-29 00:07:55 -0500

In defining a polynomial ring, is there any way to assign varying degrees to the variables?

For example I want to define the polynomial ring Q[x, y, z] but I want x to be of degree 1, y to be degree 2, and z to be degree 3. I am looking for a way to do this in general not just for a small number of variables.

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answered 2019-07-29 12:26:04 -0500

updated 2019-07-29 18:30:41 -0500

You can use "weights":

sage: P.<x,y,z> = PolynomialRing(QQ, 3, order=TermOrder('wdeglex',(1,2,3)))
sage: x.degree()
1
sage: z.degree()
3

I think this is not documented very well, or at least I didn't discover it easily. See http://doc.sagemath.org/html/en/refer... and http://doc.sagemath.org/html/en/refer....

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Was there something else you intended to include or was that third and a mistake?

Laughematician760 gravatar imageLaughematician760 ( 2019-07-29 13:41:32 -0500 )edit

A mistake. I was going to give the links in the other order and then decided that I preferred this order instead.

John Palmieri gravatar imageJohn Palmieri ( 2019-07-29 18:31:08 -0500 )edit

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Asked: 2019-07-29 00:07:55 -0500

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Last updated: Jul 29