/**
 * @import { Point2, Point3 } from "../../index.js"
 * @import { Field, FieldWithOps, ShortProjected, ShortProjectedCurve } from "../../internal.js"
 */
/**
 * Short weierstrass in extended form.
 * If we denote the affine coordinates using apostrophes we get
 *    x' = x/z and y' = y/z
 *    z*y^2 = x^3 + b*z^3 (ignoring `a` which will be zero in all relevant cases for Cardano)
 * @template {bigint | [bigint, bigint]} T
 * @extends {CurveWithOpsImpl<Point3<T>, ShortProjectedCurve<T>>}
 * @implements {ShortProjected<T>}
 */
export class ShortProjectedImpl<T extends bigint | [bigint, bigint]> extends CurveWithOpsImpl<Point3<T>, ShortProjectedCurve<T>> {
    /**
     * @param {Field<T>} F
     * @param {T} b
     */
    constructor(F: Field<T>, b: T);
    /**
     * @param {Point2<T>} point
     * @returns {Point3<T>}
     */
    fromAffine(point: Point2<T>): Point3<T>;
    /**
     * @param {Point3<T>} point
     * @returns {Point2<T>}
     */
    toAffine(point: Point3<T>): Point2<T>;
}
import type { Point3 } from "../../index.js";
import type { ShortProjectedCurve } from "../../internal.js";
import { CurveWithOpsImpl } from "./CurveWithOps.js";
import type { Point2 } from "../../index.js";
import type { Field } from "../../internal.js";
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