map(..., DegreeMap => ...)

map(..., DegreeMap => ...)

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];

i2 : S = QQ[t,u];

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

i4 : isHomogeneous f



o4 = true

i5 : M = R^{1,2}



      2

o5 = R



o5 : R-module, free, degrees {-1, -2}

i6 : f ** M



      2

o6 = S



o6 : S-module, free, degrees {-2, -4}

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.

See also:

Default value: null -- nothingness

Function: map -- make a map

Option name: DegreeMap