The Miura package realizes arithmetic on the curves such as hyper-elliptic curves (e.g., y^2=x^5+x+1), C_{ab} curves (e.g., y^3=x^4+2x+1), complete intersection (e.g. {y^2-x^3-1,z^2-x*y-1}). For the Miura form, the pole orders should be specified such as 2 and 3 for x and y of an elliptic curve. Currently, only divisor class group computation is available for the package. For the elliptic curves, [(P)-(O)]+[(Q)-(O)] = [(P+Q)-(O)] for two points P, Q and the point O at infinity. For the general nonsingular curves, any divisor class is uniquely expressed by E-g(O) with E a positive divisor of degree g (genus). This package reduces the divisor class group addition to ideal class group multiplication, and utilizes Groebner basis computation. See http://arxiv.org/pdf/1512.08040v1.pdf for the detail
This documentation describes version 0.2 of Miura, released 5 October 2017.
If you have used this package in your research, please cite it as follows:
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The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/Miura.m2:90:0.