Package cc.redberry.rings.poly.univar

Class UnivariateInterpolation

java.lang.Object

cc.redberry.rings.poly.univar.UnivariateInterpolation

public final class UnivariateInterpolation
extends Object

Univariate polynomial interpolation.

Since:

1.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	UnivariateInterpolation.Interpolation<E>	Updatable Newton interpolation
static class	UnivariateInterpolation.InterpolationZp64	Updatable Newton interpolation

Method Summary

Modifier and Type	Method	Description
static UnivariatePolynomialZp64	interpolateLagrange(long modulus, long[] points, long[] values)	Constructs an interpolating polynomial which values at points[i] are exactly values[i].
static <E> UnivariatePolynomial<E>	interpolateLagrange(Ring<E> ring, E[] points, E[] values)	Constructs an interpolating polynomial which values at points[i] are exactly values[i].
static UnivariatePolynomialZp64	interpolateNewton(long modulus, long[] points, long[] values)	Constructs an interpolating polynomial which values at points[i] are exactly values[i].
static UnivariatePolynomialZp64	interpolateNewton(IntegersZp64 ring, long[] points, long[] values)	Constructs an interpolating polynomial which values at points[i] are exactly values[i].
static <E> UnivariatePolynomial<E>	interpolateNewton(Ring<E> ring, E[] points, E[] values)	Constructs an interpolating polynomial which values at points[i] are exactly values[i].

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

interpolateLagrange

public static UnivariatePolynomialZp64 interpolateLagrange(long modulus,
                                                           long[] points,
                                                           long[] values)

Constructs an interpolating polynomial which values at points[i] are exactly values[i]. This method uses Lagrange's interpolation formula.

Parameters:

modulus - the modulus

points - evaluation points

values - corresponding polynomial values

Returns:

the interpolating polynomial

interpolateLagrange

public static <E> UnivariatePolynomial<E> interpolateLagrange(Ring<E> ring,
                                                              E[] points,
                                                              E[] values)

Constructs an interpolating polynomial which values at points[i] are exactly values[i]. This method uses Lagrange's interpolation formula.

Parameters:

ring - the ring

points - evaluation points

values - corresponding polynomial values

Returns:

the interpolating polynomial

interpolateNewton

public static UnivariatePolynomialZp64 interpolateNewton(long modulus,
                                                         long[] points,
                                                         long[] values)

Constructs an interpolating polynomial which values at points[i] are exactly values[i]. This method uses Newton's mixed radix iterations.

Parameters:

modulus - the modulus

points - evaluation points

values - corresponding polynomial values

Returns:

the interpolating polynomial

interpolateNewton

public static UnivariatePolynomialZp64 interpolateNewton(IntegersZp64 ring,
                                                         long[] points,
                                                         long[] values)

Constructs an interpolating polynomial which values at points[i] are exactly values[i]. This method uses Newton's mixed radix iterations.

Parameters:

ring - the ring

points - evaluation points

values - corresponding polynomial values

Returns:

the interpolating polynomial

interpolateNewton

public static <E> UnivariatePolynomial<E> interpolateNewton(Ring<E> ring,
                                                            E[] points,
                                                            E[] values)

Constructs an interpolating polynomial which values at points[i] are exactly values[i]. This method uses Newton's mixed radix iterations.

Parameters:

ring - the ring

points - evaluation points

values - corresponding polynomial values

Returns:

the interpolating polynomial