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doc ///
Node
Key
preimage
(preimage, RingMap, Ideal)
(preimage, Matrix, Module)
Headline
preimage of a map
Synopsis
Heading
preimage of an ideal under a ring map
Usage
preimage(f, I)
Inputs
f:RingMap
M:Ideal -- in the target of $f$
Outputs
:Ideal -- the preimage of $I$ under the map $f$
Description
Example
R = QQ[x,y,z]
S = QQ[t,u]
f = map(R, S, {x*y, y*z})
preimage_f ideal(x^2,y^2)
Synopsis
Heading
preimage of a submodule under a module map
Usage
preimage(f, M)
Inputs
f:Matrix
M:Module -- a submodule in the target of $f$
Outputs
:Module -- the preimage of $M$ under the map $f$
Description
Text
$M$ and @TO target@ of $f$ should have the same @TO ambient@ module.
-- TODO: Example
SeeAlso
coimage
image
kernel
source
target
///
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