A name for an optional argument used with
map when creating a ring map, to specify a function that transforms degrees of elements in the source ring to degrees of elements in the target ring. The function will be used later when tensoring a module along the ring map to determine the degrees of the generators in the result, and to determine whether the map is homogeneous.
i1 : R = QQ[x,y,z];
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i2 : S = QQ[t,u];
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i3 : f = map(S,R,{t^2,t*u,u^2},DegreeMap => i -> 2*i)
2 2
o3 = map(S,R,{t , t*u, u })
o3 : RingMap S <--- R
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i4 : isHomogeneous f
o4 = true
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i5 : M = R^{1,2}
2
o5 = R
o5 : R-module, free, degrees {-1, -2}
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i6 : f M
2
o6 = S
o6 : S-module, free, degrees {-2, -4}
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i7 : f ** M
2
o7 = S
o7 : S-module, free, degrees {-2, -4}
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The default degree map function is the identity function, but when the two rings have different degree lengths, a function must be explicitly provided that transforms the lengths of the degree vectors appropriately, or else the default function which maps every degree to {0,...,0} will be provided automatically.