Miura expresses any nonsingular curves. For example, 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 details.

- Functions and commands
- add -- A method for computing the reduced ideal of J*K
- double -- A method for computing the squared ideal J*J
- inv -- A method for computing the reduced inverse ideal
- multi -- A method for computing the reduced ideal of an integral ideal J multimplied by integer m
- pR -- A method for specifying the underlying polynomial ring
- qR -- A method for specifying the underlying quotient ring
- reduced -- A method for computing the reduced ideal