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newCoordinateSystem -- change variables

Description

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,{50p, 3r, p + 2q, 3r - s}), map(R,S,{-2a, a - 50c, 34b, b -
     ------------------------------------------------------------------------
     d})}

o3 : List

Ways to use `newCoordinateSystem` :

newCoordinateSystem(PolynomialRing,Matrix)