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ExactCouples :: derivedCoupleRing

derivedCoupleRing -- forms the ring that acts on a derived couple

Synopsis

Description

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

See also

Ways to use derivedCoupleRing:

For the programmer

The object derivedCoupleRing is a method function.