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initial version

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/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial.html#sage.rings.polynomial.multi_polynomial.MPolynomial.weighted_degree and http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/term_order.html and

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No.2 Revision

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/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial.html#sage.rings.polynomial.multi_polynomial.MPolynomial.weighted_degree and http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/term_order.html and http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/term_order.html.