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D.5.1.2 invertBirMap
Procedure from library paraplanecurves.lib (see paraplanecurves_lib).
- Usage:
- invertBirMap(phi, I); phi ideal, I ideal
- Assume:
- The ideal phi in the basering R represents a birational map of the
variety given by the ideal I in R to its image in projective space
P = PP^(size(phi)-1).
- Note:
- The procedure might fail or give a wrong output if phi does
not define a birational map.
- Return:
- ring, the coordinate ring of P, with an ideal named J and an ideal
named psi.
The ideal J defines the image of phi.
The ideal psi gives the inverse of phi.
Note that the entries of psi should be considered as representatives
of classes in the quotient ring R/J.
- Theory:
- We compute the ideal I(G) in R**S of the graph G of phi.
The ideal J is given by the intersection of I(G) with S.
The map psi is given by a relation mod J of those relations
in I(G) which are linear in the variables of R.
Example:
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