Class Polynom

A Polynom in multiple variables, often named x,y,z, but may be any dimension. e.g. ax³ + bx²y + cxy² +dy³ + ex² + fxy + gy² + hx + iy + j (deg(ree)==3, dim(ension)==2: (x,y))

Inheritance

System.Object

Polynom

Implements

System.Collections.Generic.IEnumerable<monom>

System.Collections.IEnumerable

Inherited Members

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

System.Object.ReferenceEquals(System.Object, System.Object)

Namespace: CADability

Assembly: CADability.dll

Syntax

public class Polynom : IEnumerable<monom>, IEnumerable

Constructors

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Polynom(Double, Int32)

Creates a constant Polynom (often 1 or 0) with the provided dimension

Declaration

public Polynom(double cv, int dim)

Parameters

Type	Name	Description
System.Double	cv
System.Int32	dim

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Polynom(Int32, Int32)

Creates an empty polynom with all coefficients set to 0, prepared to have a maximum degree of deg and a dimension of dim (number of variables)

Declaration

public Polynom(int deg, int dim)

Parameters

Type	Name	Description
System.Int32	deg	the maximum degree
System.Int32	dim	number of variables

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Polynom(Int32[], Double)

Creates a polynom with a single monom where m are the exponents and v is the facctor

Declaration

public Polynom(int[] m, double v)

Parameters

Type	Name	Description
System.Int32[]	m
System.Double	v

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Polynom(Object[])

Creates a polynom as specified by the parameters. Expects input like (3, "x2", 4, "x", 5, "", 6, "y2", 7, "z", 8, "x2y") a alternating sequence of double values and strings. The charcters in the strings are interpreted as follows: A letter, which is the name of the variable, followed by an optional digit, which is the exponent of the variable (when missing "1" is assumed). An empty string is for the constant. The number of different variable names defines the dimension. The highest degree is derived from the exponents. The indices of the variables are in alphabetical order. The variable names have no further meaning and are not conserved.

Declaration

public Polynom(params object[] def)

Parameters

Type	Name	Description
System.Object[]	def	the definition of the polynom

Properties

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Degree

Declaration

public int Degree { get; }

Property Value

Type	Description
System.Int32

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Dimension

Declaration

public int Dimension { get; }

Property Value

Type	Description
System.Int32

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LeadingTerm

Declaration

public int[] LeadingTerm { get; }

Property Value

Type	Description
System.Int32[]

Methods

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Add(Polynom)

Adds the provided Polynom to this Polynom. The degree of the provided Polynom may not exceed the degree of this Polynom.

Declaration

public void Add(Polynom b)

Parameters

Type	Name	Description
Polynom	b

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Clone()

Declaration

public Polynom Clone()

Returns

Type	Description
Polynom

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Derivate(Int32[])

Declaration

public Polynom Derivate(params int[] diff)

Parameters

Type	Name	Description
System.Int32[]	diff

Returns

Type	Description
Polynom

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Divide(Polynom, out Polynom)

Declaration

public Polynom Divide(Polynom devideBy, out Polynom remainder)

Parameters

Type	Name	Description
Polynom	devideBy
Polynom	remainder

Returns

Type	Description
Polynom

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Eval(Double[])

Inserts the values for the variables and calculates the result of the Polynom

Declaration

public double Eval(params double[] values)

Parameters

Type	Name	Description
System.Double[]	values

Returns

Type	Description
System.Double

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Get(Int32[])

Declaration

public double Get(params int[] exp)

Parameters

Type	Name	Description
System.Int32[]	exp

Returns

Type	Description
System.Double

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GetEnumerator()

Declaration

public IEnumerator<monom> GetEnumerator()

Returns

Type	Description
System.Collections.Generic.IEnumerator<monom>

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Integrate(Int32[])

Returns the integrated polynom

Declaration

public Polynom Integrate(params int[] intg)

Parameters

Type	Name	Description
System.Int32[]	intg	variables to integrate

Returns

Type	Description
Polynom

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LagrangeReduction2(Polynom)

Declaration

public static ModOp2D LagrangeReduction2(Polynom polynom)

Parameters

Type	Name	Description
Polynom	polynom

Returns

Type	Description
ModOp2D

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Modified(ModOp)

Modifies the Polynom (which must be 3-dimensional) by the provided Modop

Declaration

public Polynom Modified(ModOp m)

Parameters

Type	Name	Description
ModOp	m

Returns

Type	Description
Polynom

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Modified(ModOp2D)

Modifies the Polynom (which must be 2-dimensional) by the provided Modop

Declaration

public Polynom Modified(ModOp2D m)

Parameters

Type	Name	Description
ModOp2D	m

Returns

Type	Description
Polynom

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NormalizeLeadingTerm()

Declaration

public void NormalizeLeadingTerm()

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Offset(Double[])

Declaration

public Polynom Offset(params double[] off)

Parameters

Type	Name	Description
System.Double[]	off

Returns

Type	Description
Polynom

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reduce()

Reduces the degree of the Polynom, when the highest degree of all terms is less than the degree of this Polynom. Saves space.

Declaration

public void reduce()

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Reversed()

reverses all variables, replaces x by -x, y by -y, etc.

Declaration

public Polynom Reversed()

Returns

Type	Description
Polynom

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Roots()

Calculates the (real) roots of this Polynom. The Polynom must be 1-dimensional

Declaration

public double[] Roots()

Returns

Type	Description
System.Double[]

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Set(Double, Int32[])

Sets the factor for the term specified by the parameter

Declaration

public void Set(double v, params int[] exp)

Parameters

Type	Name	Description
System.Double	v
System.Int32[]	exp

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SingleDim(Double[])

Declaration

public static Polynom SingleDim(params double[] c)

Parameters

Type	Name	Description
System.Double[]	c

Returns

Type	Description
Polynom

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SingleDimLinear(Double, Double)

Declaration

public static Polynom SingleDimLinear(double c0, double c1)

Parameters

Type	Name	Description
System.Double	c0
System.Double	c1

Returns

Type	Description
Polynom

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SolveTwoSquared(Polynom, Polynom, Double[])

Sloves two polynoms (==0) of degree 2 and dimension 2. the optinal minmax parameter gives bounds for the first (index 0,1) and the second (indes 2,3) variable

Declaration

public static List<double[]> SolveTwoSquared(Polynom p1, Polynom p2, double[] minmax = null)

Parameters

Type	Name	Description
Polynom	p1
Polynom	p2
System.Double[]	minmax

Returns

Type	Description
System.Collections.Generic.List<System.Double[]>

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Substitute(Polynom[])

Replaces the variables by new polynomes and calculates the resulting Polynom. The number of provided polynoms must macht the number of variables of this Polynom, which is the degree.

Declaration

public Polynom Substitute(params Polynom[] substWith)

Parameters

Type	Name	Description
Polynom[]	substWith

Returns

Type	Description
Polynom

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SubstituteRational(Polynom, Polynom, Polynom, Polynom)

Declaration

public Polynom SubstituteRational(Polynom px, Polynom py, Polynom pz, Polynom pw)

Parameters

Type	Name	Description
Polynom	px
Polynom	py
Polynom	pz
Polynom	pw

Returns

Type	Description
Polynom

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Subtract(Polynom)

Declaration

public Polynom Subtract(Polynom b)

Parameters

Type	Name	Description
Polynom	b

Returns

Type	Description
Polynom

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ToString()

Declaration

public override string ToString()

Returns

Type	Description
System.String

Overrides

System.Object.ToString()

Operators

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Addition(Polynom, Polynom)

Adds two Polynoms, which must have the same dimension

Declaration

public static Polynom operator +(Polynom a, Polynom b)

Parameters

Type	Name	Description
Polynom	a
Polynom	b

Returns

Type	Description
Polynom

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Addition(Polynom, Double)

Declaration

public static Polynom operator +(Polynom a, double b)

Parameters

Type	Name	Description
Polynom	a
System.Double	b

Returns

Type	Description
Polynom

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Addition(Double, Polynom)

Declaration

public static Polynom operator +(double b, Polynom a)

Parameters

Type	Name	Description
System.Double	b
Polynom	a

Returns

Type	Description
Polynom

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Division(Polynom, Double)

Declaration

public static Polynom operator /(Polynom b, double a)

Parameters

Type	Name	Description
Polynom	b
System.Double	a

Returns

Type	Description
Polynom

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ExclusiveOr(Polynom, Int32)

Declaration

public static Polynom operator ^(Polynom b, int n)

Parameters

Type	Name	Description
Polynom	b
System.Int32	n

Returns

Type	Description
Polynom

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Multiply(Polynom, Polynom)

Multiplies two Polynoms, which must have the same dimension

Declaration

public static Polynom operator *(Polynom a, Polynom b)

Parameters

Type	Name	Description
Polynom	a
Polynom	b

Returns

Type	Description
Polynom

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Multiply(Polynom, Double)

Declaration

public static Polynom operator *(Polynom b, double a)

Parameters

Type	Name	Description
Polynom	b
System.Double	a

Returns

Type	Description
Polynom

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Multiply(Double, Polynom)

Declaration

public static Polynom operator *(double a, Polynom b)

Parameters

Type	Name	Description
System.Double	a
Polynom	b

Returns

Type	Description
Polynom

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Subtraction(Polynom, Polynom)

Declaration

public static Polynom operator -(Polynom a, Polynom b)

Parameters

Type	Name	Description
Polynom	a
Polynom	b

Returns

Type	Description
Polynom

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Subtraction(Polynom, Double)

Declaration

public static Polynom operator -(Polynom a, double b)

Parameters

Type	Name	Description
Polynom	a
System.Double	b

Returns

Type	Description
Polynom

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Subtraction(Double, Polynom)

Declaration

public static Polynom operator -(double b, Polynom a)

Parameters

Type	Name	Description
System.Double	b
Polynom	a

Returns

Type	Description
Polynom

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UnaryNegation(Polynom)

Declaration

public static Polynom operator -(Polynom a)

Parameters

Type	Name	Description
Polynom	a

Returns

Type	Description
Polynom

Explicit Interface Implementations

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IEnumerable.GetEnumerator()

Declaration

IEnumerator IEnumerable.GetEnumerator()

Returns

Type	Description
System.Collections.IEnumerator

Implements

System.Collections.Generic.IEnumerable<T>

System.Collections.IEnumerable