When calling randomCoordinateChange, or functions that call it, setting Replacement => Full will mean that coordinates are changed to a general degree 1 form. If Replacement => Binomial, the coordinates are only changed to bionomials, which can be much faster for certain applications.
i1 : R = ZZ/11[a,b,c]; |
i2 : randomCoordinateChange(R, Replacement=>Full)
ZZ
o2 = map (R, --[a..c], {3a - 4b - 3c, - 3a - b + 3c, a + 3b - 4c})
11
ZZ
o2 : RingMap R <--- --[a..c]
11
|
i3 : randomCoordinateChange(R, Replacement=>Binomial)
ZZ
o3 = map (R, --[a..c], {-5c, -3a, b + 3c})
11
ZZ
o3 : RingMap R <--- --[a..c]
11
|
If Homogeneous => false, then there will be constant terms, and we view $mx + b$ as a binomial.
i4 : S = ZZ/11[x,y]; |
i5 : randomCoordinateChange(S, Replacement => Full, Homogeneous => false)
ZZ
o5 = map (S, --[x..y], {- 5x - 2y - 1, - 4x - 5y + 3})
11
ZZ
o5 : RingMap S <--- --[x..y]
11
|
i6 : randomCoordinateChange(S, Replacement => Binomial, Homogeneous => false)
ZZ
o6 = map (S, --[x..y], {- 5x + y + 2, x - 5y + 2})
11
ZZ
o6 : RingMap S <--- --[x..y]
11
|
The object Replacement is a symbol.