newCoordinateSystem -- change variables

newCoordinateSystem -- change variables

newCoordinateSystem(S,m) -- takes a one-rowed matrix m of independent linear forms over a ring R and returns a list {f,g}, where f is a ring map given by some linear change of coordinates from R to S which sends the last variables of R to the forms in m, and g is the inverse of f.

The ring S should have the same number of variables as S.

i1 : R = ZZ/101[a..d]



o1 = R



o1 : PolynomialRing

i2 : S = ZZ/101[p..s]



o2 = S



o2 : PolynomialRing

i3 : newCoordinateSystem(S,matrix{{a+2*b,3*c-d}})



o3 = {map(S,R,{q, s, p + 2q, 3r - s}), map(R,S,{- 2a + c, a, 34b + 34d, b})}



o3 : List

Ways to use newCoordinateSystem :

newCoordinateSystem(PolynomialRing,Matrix)