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--- status: DRAFT
--- author(s): PZJ
--- notes:
undocumented {(setupLift,Function,Ring,Ring,Function), (setupLift,RingMap,Ring,Ring)}
doc ///
Key
setupLift
(setupLift,Function,Ring,Ring)
(setupLift,RingMap)
Headline
set up lift from one ring to another
Usage
setupLift (f,R,S)
setupLift g
Inputs
f: Function
R: Ring
S: Ring
g: RingMap
Description
Text
There are two possible ways of implementing @TO "lift"@ using @TT "setupLift"@. In the first one, we use a function:
Example
R=QQ[x]
S=QQ[y]
setupPromote map(R,S,{x^2})
setupLift(a->sum(listForm a, (e,c)->if odd first e then error "not liftable" else c*y^(first e//2)),R,S)
promote(y^2+2,R)
lift(oo,S)
lift(x,S,Verify=>false)
Text
In the second one, we define a ring map which is a partial inverse to the promotion map:
Example
R=QQ[x,y]
S=R[s]
setupPromote map(R,S,{x+y})
setupLift map(S,R,{s,0})
promote(s^3+2*s-1,R)
lift(oo,S)
lift(x,S,Verify=>false)
SeeAlso
setupPromote
///
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