This package implements procedures described in chapters 4, 5, and 14 of the book "The Practice of Curves", by David Eisenbud and Joe Harris.
If C is a (possibly singular) irreducible plane curve, it is possible to compute the complete linear series of a given divisor on the normalization C' of C by computations using data from the plane curve together with the conductor ideal $ann_C(C/C)$, which can be computed by Macaulay or supplied by the user.
The main routine of the package is linearSeries. If D0' and Dinf' are effective divisors on C' whose ideals, as schemes, are pulled back from ideals D0 and Dinf of C, then
ell = linearSeries(D0,Dinf)
returns a one-row matrix ell whose entries span a linear series with fixed point locus B on C' (including the conductor scheme) and form a basis of |D0'-Dinf'|+B.
The routine projectiveImage provides the image of the map to projective space given by |D0-Dinf|. There are special routines for the most important case, canonicalSeries and canonicalImage.
The functions addition and negative implement the group law in the case of a curve of genus 1.
This documentation describes version 1.0 of PlaneCurveLinearSeries.
The source code from which this documentation is derived is in the file PlaneCurveLinearSeries.m2.
The object PlaneCurveLinearSeries is a package.