RingMap RingElement -- apply a ring map
Synopsis
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Operator: SPACE
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- Usage:
f X
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Inputs:
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Outputs:
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the image of X under the ring map f. The result has the same type as X, except that its ring will be S.
Description
If
X is a module then it must be either free or a submodule of a free module. If
X is a chain complex, then every module of
X must be free or a submodule of a free module.
i1 : R = QQ[x,y];
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i2 : S = QQ[t];
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i3 : f = map(S,R,{t^2,t^3})
2 3
o3 = map (S, R, {t , t })
o3 : RingMap S <-- R
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i4 : f (x+y^2)
6 2
o4 = t + t
o4 : S
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i5 : f image vars R
o5 = image | t2 t3 |
1
o5 : S-module, submodule of S
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i6 : f ideal (x^2,y^2)
4 6
o6 = ideal (t , t )
o6 : Ideal of S
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i7 : f resolution coker vars R
1 2 1
o7 = S <-- S <-- S <-- 0
0 1 2 3
o7 : ChainComplex
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Caveat
If the rings R and S have different degree monoids, then the degrees of the image might need to be changed, since Macaulay2 sometimes doesn't have enough information to determine the image degrees of elements of a free module.
Ways to use this method:
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RingMap ChainComplex
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RingMap Ideal
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RingMap Matrix
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RingMap Module
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RingMap RingElement -- apply a ring map
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RingMap Vector