Any sheaf on P1 is the direct sum of line bundles-- and cyclic skyscraper sheaves represented by modules of the form k[x,y]/(l^m) where l is an kirreducible homogeneous polynomial and m is a non-negative integer. The routine "analyze" computes the twists and the annihilators l^m that appear in the decomposition, starting from a coherent sheaf on P1 or a graded module over a polynomial ring on 2 variables.
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The script uses a linear nonzerodivisor, which would not exist over a finite field in the case where every point of P1 is the support of one of the skyscraper components.
This documentation describes version 0.1 of AnalyzeSheafOnP1.
If you have used this package in your research, please cite it as follows:
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The object AnalyzeSheafOnP1 is a package, defined in AnalyzeSheafOnP1.m2.
The source of this document is in AnalyzeSheafOnP1.m2:125:0.