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preimage -- preimage of an ideal under a ring map

Synopsis

Usage:
preimage(f,I)
Inputs:
- I, an ideal in the target ring of f
- f
Outputs:
- the preimage of I under the map f

Description

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : S = QQ[t,u]

o2 = S

o2 : PolynomialRing

i3 : f = map(R,S,{x*y,y*z})

o3 = map(R,S,{x*y, y*z})

o3 : RingMap R <--- S

i4 : preimage_f ideal(x^2,y^2)

             2        2
o4 = ideal (u , t*u, t )

o4 : Ideal of S

Ways to use `preimage` :

preimage(RingMap,Ideal)