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A Modified Coefficient Ideal for Use with the Strict Transform
Two main algorithmic approaches are known for making Hironaka's proof of
resolution of singularities in characteristic zero constructive. Their main
difference is the use of different notions of transforms during the resolution
process and the use of a stratification by the Hilbert-Samuel function in the
one using the strict transform. In this article, a (hybrid-type) algorithmic
approach is proposed which allows the use of the strict transform without the
full impact of the complexity of the stratification by the Hilbert-Samuel
function at each step of the desingularization process. This new approach is
not intended to always be superior to the implemented one which uses the weak
transform, instead it has its strengths precisely at the weak point of the
other one and is thus a candidate to be joined with it by an appropriate
heuristic.Comment: 15 Pages, revision clarifying details in sections 1-