ExtendedArithmetic.GenericPolynomial
2022.322.2016
dotnet add package ExtendedArithmetic.GenericPolynomial version 2022.322.2016
NuGet\InstallPackage ExtendedArithmetic.GenericPolynomial Version 2022.322.2016
<PackageReference Include="ExtendedArithmetic.GenericPolynomial" Version="2022.322.2016" />
paket add ExtendedArithmetic.GenericPolynomial version 2022.322.2016
#r "nuget: ExtendedArithmetic.GenericPolynomial, 2022.322.2016"
// Install ExtendedArithmetic.GenericPolynomial as a Cake Addin
#addin nuget:?package=ExtendedArithmetic.GenericPolynomial&version=2022.322.2016
// Install ExtendedArithmetic.GenericPolynomial as a Cake Tool
#tool nuget:?package=ExtendedArithmetic.GenericPolynomial&version=2022.322.2016
GenericMultivariatePolynomial
A multivariate, sparse, generic polynomial arithmetic library. That is, a polynomial in only one indeterminate, X, that only tracks terms with nonzero coefficients. This generic implementation has been tested and supports performing arithmetic on numeric types such as BigInteger, Complex, Decimal, Double, BigComplex, BigDecimal, BigRational, Int32, Int64 and more.
All arithmetic is done symbolically. That means the result of an arithmetic operation on two polynomials is another polynomial, not the result of evaluating those two polynomials and performing arithmetic on the results.
Generic Arithmetic Type Polynomial
All classes and methods support a generic type T, which can be any data type that has arithmetic operator overloads. Explicitly, the following types have tests exercising all the standard arithmetic operations (Addition, Subtraction, Multiplication, Division, Exponentiation, Modulus, Square Root, Equality and Comparison (where applicableComplex numbers are not orderable)) and so are well supported and come with verifiable proof that they work:
 Every .NET CLR value type (Byte, Int16, Int32, Int64, UInt16, UInt32, UInt64, Float, Double, Decimal)
 System.Numerics.BigInteger
 System.Numerics.Complex
 ExtendedNumerics.BigComplex (My arbitraryprecision complex number type library)
 ExtendedNumerics.BigDecimal (My arbitraryprecision floatingpoint number type library.)
 ExtendedNumerics.BigRational(My arbitrary precision rational number type library.)
 ExtendedNumerics.Fraction (My arbitraryprecision rational number type library.)
 Any type that has the Addition, Multiplication and Exponentiation operator overloads (at a minimum).
Supports symbolic multivariate polynomial (generic) arithmetic including:
 Addition
 Subtraction
 Multiplication
 Division
 Modulus
 Exponentiation
 GCD of polynomials
 Derivative
 Integral
 Reciprocal
 Irreducibility checking
 Polynomial evaluation by assigning to the invariant (X in this case) a value.
Polynomial Rings over a Finite Field
Polynomial.Field supports addition, multiplication, division/modulus and inverse of a polynomial ring over a finite field. These operations do not support Complex, BigComplex, BigDecimal, or BigRational types.
 What this effectively means in lesstechnical terms is that the polynomial arithmetic is performed in the usual way, but the result is then taken modulus two things:
 Modulo an integer: All coefficients are reduced modulo an integer.
 Modulo a polynomial: The whole polynomial is reduced modulo another, smaller, polynomial. This notion works much the same as regular modulus; The modulus polynomial, let's call it g, is declared to be equivalent to zero, and so every multiple of g is reduced to zero. You can think of it this way (although this is not how it's actually carried out): From a large polynomial, g is repeatedly subtracted from that polynomial until it can't subtract g anymore without crossing zero. The result is a polynomial that lies between 0 and g. Just like regular modulus, the result is always less than your modulus, or zero if the polynomial was a multiple of the modulus.
 Effectively forms a quotient ring
 What this effectively means in lesstechnical terms is that the polynomial arithmetic is performed in the usual way, but the result is then taken modulus two things:
You can instantiate a polynomial in various ways:
 From a string
 This is the most massivelyuseful way and is the quickest way to start working with a particular polynomial you had in mind.
 From its roots (Not all types supported)
 Build a polynomial that has, as its roots, all of the numbers in the supplied array. If you want multiplicity of roots, include that number in the array multiple times.
 From the basem expansion of a number
 Given a large number and a radix (base), call it m, a polynomial will be generated that is that number represented in the number base m.
 From a string
Other methods of interest that are related to, but not necessarily performed on a polynomial (Not all types supported):
 Euler's Criterion
 Legendre Symbol and Legendre Symbol Search
 TonelliShanks
 Chinese Remainder Theorem
 Polynomial evaluation by assigning to the invariant (X in this case) a value.
Product  Versions 

.NET  net5.0 net5.0windows net5.0windows7.0 net6.0 net6.0android net6.0ios net6.0maccatalyst net6.0macos net6.0tvos net6.0windows net7.0 net7.0android net7.0ios net7.0maccatalyst net7.0macos net7.0tvos net7.0windows 
.NET Core  netcoreapp3.0 netcoreapp3.1 
.NET Standard  netstandard2.1 
.NET Framework  net45 net451 net452 net46 net461 net462 net463 net47 net471 net472 net48 net481 
MonoAndroid  monoandroid 
MonoMac  monomac 
MonoTouch  monotouch 
Tizen  tizen60 
Xamarin.iOS  xamarinios 
Xamarin.Mac  xamarinmac 
Xamarin.TVOS  xamarintvos 
Xamarin.WatchOS  xamarinwatchos 

.NETCoreApp 3.1
 Newtonsoft.Json (>= 13.0.1)

.NETFramework 4.5
 Newtonsoft.Json (>= 13.0.1)

.NETFramework 4.6
 Newtonsoft.Json (>= 13.0.1)

.NETFramework 4.8
 Newtonsoft.Json (>= 13.0.1)

.NETStandard 2.1
 Newtonsoft.Json (>= 13.0.1)

net5.0windows7.0
 Newtonsoft.Json (>= 13.0.1)
NuGet packages
This package is not used by any NuGet packages.
GitHub repositories
This package is not used by any popular GitHub repositories.
Version  Downloads  Last updated 

2022.322.2016  137  11/19/2022 
2022.322.1953  133  11/19/2022 
2022.321.408  138  11/17/2022 
2022.195.1511  262  7/14/2022 
2022.187.1018  245  7/6/2022 
1.0.0  350  11/30/2020 