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preimage -- preimage of a map

Description

preimage of an ideal under a ring map

  • Usage:
    preimage(f, I)
  • Inputs:
  • Outputs:
    • an ideal, the preimage of $I$ under the map $f$; 
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

preimage of a submodule under a module map

  • Usage:
    preimage(f, M)
  • Inputs:
    • f, a matrix,
    • M, a module, a submodule in the target of $f$;
  • Outputs:
    • a module, the preimage of $M$ under the map $f$;

$M$ and target of $f$ should have the same ambient module.

See also

Ways to use preimage:

  • preimage(Matrix,Module)
  • preimage(RingMap,Ideal)

For the programmer

The object preimage is a method function.

The source of this document is in Macaulay2Doc/functions/preimage-doc.m2:46:0.