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sage: R.<x,y> = PolynomialRing(QQ, 2, order='lex')
sage: a,b=x^6+y^9,x^3-y^2-1
sage: a,b
(x^6 + y^9, x^3 - y^2 - 1)
sage: I=R.ideal(b)
sage: I.reduce(a)
y^9 + y^4 + 2*y^2 + 1
sage: R.<y,x> = PolynomialRing(QQ, 2, order='lex')
sage: a,b=x^6+y^9,x^3-y^2-1
sage: a,b
(y^9 + x^6, -y^2 + x^3 - 1)
sage: I=R.ideal(b)
sage: I.reduce(a)
y*x^12 - 4*y*x^9 + 6*y*x^6 - 4*y*x^3 + y + x^6
sage: R.<x,y>=QQ[]
sage: R.term_order()
Degree reverse lexicographic term order
sage: a,b=x^6+y^9,x^3-y^2-1
sage: a,b
(y^9 + x^6, x^3 - y^2 - 1)
sage: I=R.ideal(b)
sage: I.reduce(a)
y^9 + y^4 + 2*y^2 + 1
sage: a % b
x^12*y - 4*x^9*y + 6*x^6*y + x^6 - 4*x^3*y + y
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