findElementMappingToTarget -- given a ring map and an element of the target, this find an element from the source whose image is the given one

Synopsis

Usage:

x = findElementMappingToTarget(phi, y)
Inputs:
- phi, a ring map,
- y, a ring element,
Outputs:
- x, a ring element, a ring element mapping to y by phi

Description

Given a ring map $\phi : R \to S$ and $y \in S$, this finds $x \in R$ such that $\phi(x) = y$ (if it exists). If no such element exists, it throws an error.

i1 : R = QQ[u,v, w];

i2 : S = QQ[a,b];

i3 : phi = map(S, R, {a, a*b, 0});

o3 : RingMap S <-- R

i4 : findElementMappingToTarget(phi, a)

o4 = u

o4 : R

i5 : findElementMappingToTarget(phi, sub(0, S))

o5 = 0

o5 : R

Ways to use findElementMappingToTarget :

findElementMappingToTarget(RingMap,RingElement)

For the programmer

The object findElementMappingToTarget is a method function.