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Macaulay2Doc :: newCoordinateSystem

newCoordinateSystem -- change variables

Description

newCoordinateSystem(S,m) -- takes a one-rowed matrix m of independent linear forms over a ring R and returns a pair (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 : (f,g) = newCoordinateSystem(S,matrix{{a+2*b,3*c-d}});
i4 : f

o4 = map(S,R,{50p, 3r, p + 2q, 3r - s})

o4 : RingMap S <--- R
i5 : g

o5 = map(R,S,{-2a, a - 50c, 34b, b - d})

o5 : RingMap R <--- S

Ways to use newCoordinateSystem :

For the programmer

The object newCoordinateSystem is a method function.