import type { RingMin } from './Ring'

import { Ring } from './Ring'

/*
 * -------------------------------------------
 * model
 * -------------------------------------------
 */

export interface Field<A> extends Ring<A> {
  readonly degree: (a: A) => number
  readonly div_: (x: A, y: A) => A
  readonly div: (y: A) => (x: A) => A
  readonly mod_: (x: A, y: A) => A
  readonly mod: (y: A) => (x: A) => A
}

export type FieldMin<A> = RingMin<A> & {
  readonly degree: (a: A) => number
  readonly div_: (x: A, y: A) => A
  readonly mod_: (x: A, y: A) => A
}

export function Field<A>(F: FieldMin<A>): Field<A> {
  return {
    ...Ring(F),
    degree: F.degree,
    div_: F.div_,
    div: (y) => (x) => F.div_(x, y),
    mod_: F.mod_,
    mod: (y) => (x) => F.mod_(x, y)
  }
}