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RandomRationalPoints :: Replacement

Replacement -- When changing coordinates, whether to replace variables by general degre 1 forms or binomials

Synopsis

Description

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 coordiates 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

See also

Functions with optional argument named Replacement :

For the programmer

The object Replacement is a symbol.