polynomials

package
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 Go to latest Published: Feb 16, 2026 License: Apache-2.0 Imports: 11 Imported by: 0

Documentation

Overview

Package polynomials provides polynomial rings and modules over algebraic structures with helpers for sampling, evaluation, and serialisation.

Index

Constants

This section is empty.

Variables

View Source 
var (
	ErrValidation            = errs.New("invalid")
	ErrDivisionByZero        = errs.New("division by zero")
	ErrOperationNotSupported = errs.New("operation not supported")
	ErrLengthMismatch        = errs.New("input length mismatch")
	ErrFailed                = errs.New("internal error")
	ErrSerialisationFailed   = errs.New("serialisation failed")
)

Functions

This section is empty.

Types

type ModuleValuedPolynomial 

type ModuleValuedPolynomial[ME algebra.ModuleElement[ME, S], S algebra.RingElement[S]] struct {
	// contains filtered or unexported fields
}

func LiftPolynomial 

func LiftPolynomial[ME algebra.ModuleElement[ME, RE], RE algebra.RingElement[RE]](poly *Polynomial[RE], baseElem algebra.ModuleElement[ME, RE]) (*ModuleValuedPolynomial[ME, RE], error)

func (*ModuleValuedPolynomial[ME, S]) Bytes 

func (p *ModuleValuedPolynomial[ME, S]) Bytes() []byte

func (*ModuleValuedPolynomial[ME, S]) Clone 

func (p *ModuleValuedPolynomial[ME, S]) Clone() *ModuleValuedPolynomial[ME, S]

func (*ModuleValuedPolynomial[ME, S]) CoefficientStructure 

func (p *ModuleValuedPolynomial[ME, S]) CoefficientStructure() algebra.FiniteModule[ME, S]

func (*ModuleValuedPolynomial[ME, S]) Coefficients 

func (p *ModuleValuedPolynomial[ME, S]) Coefficients() []ME

func (*ModuleValuedPolynomial[ME, S]) ConstantTerm 

func (p *ModuleValuedPolynomial[ME, S]) ConstantTerm() ME

func (*ModuleValuedPolynomial[ME, S]) Degree 

func (p *ModuleValuedPolynomial[ME, S]) Degree() int

func (*ModuleValuedPolynomial[ME, S]) Derivative 

func (p *ModuleValuedPolynomial[ME, S]) Derivative() *ModuleValuedPolynomial[ME, S]

func (*ModuleValuedPolynomial[ME, S]) Equal 

func (p *ModuleValuedPolynomial[ME, S]) Equal(rhs *ModuleValuedPolynomial[ME, S]) bool

func (*ModuleValuedPolynomial[ME, S]) Eval 

func (p *ModuleValuedPolynomial[ME, S]) Eval(at S) ME

func (*ModuleValuedPolynomial[ME, S]) HashCode 

func (p *ModuleValuedPolynomial[ME, S]) HashCode() base.HashCode

func (*ModuleValuedPolynomial[ME, S]) IsConstant 

func (p *ModuleValuedPolynomial[ME, S]) IsConstant() bool

func (*ModuleValuedPolynomial[ME, S]) IsOpIdentity 

func (p *ModuleValuedPolynomial[ME, S]) IsOpIdentity() bool

func (*ModuleValuedPolynomial[ME, S]) IsTorsionFree 

func (p *ModuleValuedPolynomial[ME, S]) IsTorsionFree() bool

func (*ModuleValuedPolynomial[ME, S]) LeadingCoefficient 

func (p *ModuleValuedPolynomial[ME, S]) LeadingCoefficient() ME

func (*ModuleValuedPolynomial[ME, S]) MarshalCBOR 

func (p *ModuleValuedPolynomial[ME, S]) MarshalCBOR() ([]byte, error)

func (*ModuleValuedPolynomial[ME, S]) Op 

func (p *ModuleValuedPolynomial[ME, S]) Op(e *ModuleValuedPolynomial[ME, S]) *ModuleValuedPolynomial[ME, S]

func (*ModuleValuedPolynomial[ME, S]) OpElement 

func (p *ModuleValuedPolynomial[ME, S]) OpElement(e ME) *ModuleValuedPolynomial[ME, S]

func (*ModuleValuedPolynomial[ME, S]) OpInv 

func (p *ModuleValuedPolynomial[ME, S]) OpInv() *ModuleValuedPolynomial[ME, S]

func (*ModuleValuedPolynomial[ME, S]) PolynomialOp 

func (p *ModuleValuedPolynomial[ME, S]) PolynomialOp(poly *Polynomial[S]) *ModuleValuedPolynomial[ME, S]

func (*ModuleValuedPolynomial[ME, S]) ScalarOp 

func (p *ModuleValuedPolynomial[ME, S]) ScalarOp(actor S) *ModuleValuedPolynomial[ME, S]

func (*ModuleValuedPolynomial[ME, S]) ScalarStructure 

func (p *ModuleValuedPolynomial[ME, S]) ScalarStructure() algebra.Ring[S]

func (*ModuleValuedPolynomial[ME, S]) String 

func (p *ModuleValuedPolynomial[ME, S]) String() string

func (*ModuleValuedPolynomial[ME, S]) Structure 

func (p *ModuleValuedPolynomial[ME, S]) Structure() algebra.Structure[*ModuleValuedPolynomial[ME, S]]

func (*ModuleValuedPolynomial[ME, S]) TryOpInv 

func (p *ModuleValuedPolynomial[ME, S]) TryOpInv() (*ModuleValuedPolynomial[ME, S], error)

func (*ModuleValuedPolynomial[ME, S]) UnmarshalCBOR 

func (p *ModuleValuedPolynomial[ME, S]) UnmarshalCBOR(data []byte) error

type Polynomial 

type Polynomial[RE algebra.RingElement[RE]] struct {
	// contains filtered or unexported fields
}

func (*Polynomial[RE]) Add 

func (p *Polynomial[RE]) Add(e *Polynomial[RE]) *Polynomial[RE]

func (*Polynomial[RE]) Bytes 

func (p *Polynomial[RE]) Bytes() []byte

func (*Polynomial[RE]) Clone 

func (p *Polynomial[RE]) Clone() *Polynomial[RE]

func (*Polynomial[RE]) CoefficientStructure 

func (p *Polynomial[RE]) CoefficientStructure() algebra.Ring[RE]

func (*Polynomial[RE]) Coefficients 

func (p *Polynomial[RE]) Coefficients() []RE

func (*Polynomial[RE]) ConstantTerm 

func (p *Polynomial[RE]) ConstantTerm() RE

func (*Polynomial[RE]) Degree 

func (p *Polynomial[RE]) Degree() int

func (*Polynomial[RE]) Derivative 

func (p *Polynomial[RE]) Derivative() *Polynomial[RE]

func (*Polynomial[RE]) Double 

func (p *Polynomial[RE]) Double() *Polynomial[RE]

func (*Polynomial[RE]) Equal 

func (p *Polynomial[RE]) Equal(rhs *Polynomial[RE]) bool

func (*Polynomial[RE]) EuclideanDiv 

func (p *Polynomial[RE]) EuclideanDiv(q *Polynomial[RE]) (quot, rem *Polynomial[RE], err error)

func (*Polynomial[RE]) EuclideanValuation 

func (p *Polynomial[RE]) EuclideanValuation() algebra.Cardinal

func (*Polynomial[RE]) Eval 

func (p *Polynomial[RE]) Eval(at RE) RE

func (*Polynomial[RE]) HashCode 

func (p *Polynomial[RE]) HashCode() base.HashCode

func (*Polynomial[RE]) IsConstant 

func (p *Polynomial[RE]) IsConstant() bool

func (*Polynomial[RE]) IsMonic 

func (p *Polynomial[RE]) IsMonic() bool

func (*Polynomial[RE]) IsOne 

func (p *Polynomial[RE]) IsOne() bool

func (*Polynomial[RE]) IsOpIdentity 

func (p *Polynomial[RE]) IsOpIdentity() bool

func (*Polynomial[RE]) IsTorsionFree 

func (p *Polynomial[RE]) IsTorsionFree() bool

func (*Polynomial[RE]) IsZero 

func (p *Polynomial[RE]) IsZero() bool

func (*Polynomial[RE]) LeadingCoefficient 

func (p *Polynomial[RE]) LeadingCoefficient() RE

func (*Polynomial[RE]) MarshalCBOR 

func (p *Polynomial[RE]) MarshalCBOR() ([]byte, error)

func (*Polynomial[RE]) Mul 

func (p *Polynomial[RE]) Mul(e *Polynomial[RE]) *Polynomial[RE]

func (*Polynomial[RE]) Neg 

func (p *Polynomial[RE]) Neg() *Polynomial[RE]

func (*Polynomial[RE]) Op 

func (p *Polynomial[RE]) Op(e *Polynomial[RE]) *Polynomial[RE]

func (*Polynomial[RE]) OpInv 

func (p *Polynomial[RE]) OpInv() *Polynomial[RE]

func (*Polynomial[RE]) OtherOp 

func (p *Polynomial[RE]) OtherOp(e *Polynomial[RE]) *Polynomial[RE]

func (*Polynomial[RE]) ScalarMul 

func (p *Polynomial[RE]) ScalarMul(s RE) *Polynomial[RE]

func (*Polynomial[RE]) ScalarOp 

func (p *Polynomial[RE]) ScalarOp(s RE) *Polynomial[RE]

func (*Polynomial[RE]) ScalarStructure 

func (p *Polynomial[RE]) ScalarStructure() algebra.Ring[RE]

func (*Polynomial[RE]) Square 

func (p *Polynomial[RE]) Square() *Polynomial[RE]

func (*Polynomial[RE]) String 

func (p *Polynomial[RE]) String() string

func (*Polynomial[RE]) Structure 

func (p *Polynomial[RE]) Structure() algebra.Structure[*Polynomial[RE]]

func (*Polynomial[RE]) Sub 

func (p *Polynomial[RE]) Sub(e *Polynomial[RE]) *Polynomial[RE]

func (*Polynomial[RE]) TryDiv 

func (*Polynomial[RE]) TryDiv(e *Polynomial[RE]) (*Polynomial[RE], error)

func (*Polynomial[RE]) TryInv 

func (*Polynomial[RE]) TryInv() (*Polynomial[RE], error)

func (*Polynomial[RE]) TryNeg 

func (p *Polynomial[RE]) TryNeg() (*Polynomial[RE], error)

func (*Polynomial[RE]) TryOpInv 

func (p *Polynomial[RE]) TryOpInv() (*Polynomial[RE], error)

func (*Polynomial[RE]) TrySub 

func (p *Polynomial[RE]) TrySub(e *Polynomial[RE]) (*Polynomial[RE], error)

func (*Polynomial[RE]) UnmarshalCBOR 

func (p *Polynomial[RE]) UnmarshalCBOR(data []byte) error

type PolynomialModule 

type PolynomialModule[ME algebra.ModuleElement[ME, S], S algebra.RingElement[S]] struct {
	// contains filtered or unexported fields
}

func NewPolynomialModule 

func NewPolynomialModule[ME algebra.ModuleElement[ME, S], S algebra.RingElement[S]](module algebra.FiniteModule[ME, S]) (*PolynomialModule[ME, S], error)

func (*PolynomialModule[ME, S]) ElementSize 

func (*PolynomialModule[ME, S]) ElementSize() int

func (*PolynomialModule[ME, S]) FromBytes 

func (m *PolynomialModule[ME, S]) FromBytes(bytes []byte) (*ModuleValuedPolynomial[ME, S], error)

func (*PolynomialModule[ME, S]) MultiScalarOp 

func (m *PolynomialModule[ME, S]) MultiScalarOp(scalars []S, elements []*ModuleValuedPolynomial[ME, S]) (*ModuleValuedPolynomial[ME, S], error)

func (*PolynomialModule[ME, S]) Name 

func (m *PolynomialModule[ME, S]) Name() string

func (*PolynomialModule[ME, S]) New 

func (m *PolynomialModule[ME, S]) New(coeffs ...ME) (*ModuleValuedPolynomial[ME, S], error)

func (*PolynomialModule[ME, S]) OpIdentity 

func (m *PolynomialModule[ME, S]) OpIdentity() *ModuleValuedPolynomial[ME, S]

func (*PolynomialModule[ME, S]) Order 

func (*PolynomialModule[ME, S]) Order() algebra.Cardinal

func (*PolynomialModule[ME, S]) RandomModuleValuedPolynomial 

func (m *PolynomialModule[ME, S]) RandomModuleValuedPolynomial(degree int, prng io.Reader) (*ModuleValuedPolynomial[ME, S], error)

func (*PolynomialModule[ME, S]) RandomModuleValuedPolynomialWithConstantTerm 

func (m *PolynomialModule[ME, S]) RandomModuleValuedPolynomialWithConstantTerm(degree int, constantTerm ME, prng io.Reader) (*ModuleValuedPolynomial[ME, S], error)

func (*PolynomialModule[ME, S]) ScalarStructure 

func (m *PolynomialModule[ME, S]) ScalarStructure() algebra.Structure[S]

type PolynomialRing 

type PolynomialRing[RE algebra.RingElement[RE]] struct {
	// contains filtered or unexported fields
}

func NewPolynomialRing 

func NewPolynomialRing[RE algebra.RingElement[RE]](ring algebra.FiniteRing[RE]) (*PolynomialRing[RE], error)

func (*PolynomialRing[RE]) Characteristic 

func (r *PolynomialRing[RE]) Characteristic() algebra.Cardinal

func (*PolynomialRing[RE]) ElementSize 

func (*PolynomialRing[RE]) ElementSize() int

func (*PolynomialRing[RE]) FromBytes 

func (r *PolynomialRing[RE]) FromBytes(inBytes []byte) (*Polynomial[RE], error)

func (*PolynomialRing[RE]) IsDomain 

func (r *PolynomialRing[RE]) IsDomain() bool

func (*PolynomialRing[RE]) Name 

func (r *PolynomialRing[RE]) Name() string

func (*PolynomialRing[RE]) New 

func (r *PolynomialRing[RE]) New(coeffs ...RE) (*Polynomial[RE], error)

func (*PolynomialRing[RE]) One 

func (r *PolynomialRing[RE]) One() *Polynomial[RE]

func (*PolynomialRing[RE]) OpIdentity 

func (r *PolynomialRing[RE]) OpIdentity() *Polynomial[RE]

func (*PolynomialRing[RE]) Order 

func (*PolynomialRing[RE]) Order() algebra.Cardinal

func (*PolynomialRing[RE]) RandomPolynomial 

func (r *PolynomialRing[RE]) RandomPolynomial(degree int, prng io.Reader) (*Polynomial[RE], error)

func (*PolynomialRing[RE]) RandomPolynomialWithConstantTerm 

func (r *PolynomialRing[RE]) RandomPolynomialWithConstantTerm(degree int, constantTerm RE, prng io.Reader) (*Polynomial[RE], error)

func (*PolynomialRing[RE]) ScalarStructure 

func (r *PolynomialRing[RE]) ScalarStructure() algebra.Structure[RE]

func (*PolynomialRing[RE]) Zero 

func (r *PolynomialRing[RE]) Zero() *Polynomial[RE]

Source Files

View all Source files

Directories

Path Synopsis
interpolation
lagrange
Package lagrange provides Lagrange interpolation utilities over finite fields and modules.
 Package lagrange provides Lagrange interpolation utilities over finite fields and modules.

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