Suppose Q = R[e_r,f_r]. The derived couple ring of Q will be R[e_{r+1},f_{r+1}]. The degree of f will not change, but the degree of e does transvect against the direction of f. Specifically, in our convention, the degree of f is assumed to be even, and the new degree of e is given by the formula
$deg e_{r+1} = deg(e_r) - deg(f)/2$.
i1 : Q = coupleRing(ZZ,1,e,f,Degrees=>{{-1,0},{2,-2}})
o1 = Q
o1 : PolynomialRing
|
i2 : Q' = derivedCoupleRing Q o2 = Q' o2 : PolynomialRing |
i3 : degree Q'_0
o3 = {-2, 1}
o3 : List
|
i4 : degree Q'_1
o4 = {2, -2}
o4 : List
|
The object derivedCoupleRing is a method function.