wytp.proof.util

Class Arithmetic.Polynomial

java.lang.Object

wytp.proof.util.Arithmetic.Polynomial

All Implemented Interfaces:

Comparable<Arithmetic.Polynomial>

Enclosing class:

Arithmetic

public static class Arithmetic.Polynomial
extends Object
implements Comparable<Arithmetic.Polynomial>

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Arithmetic.Polynomial.Term

Field Summary

Fields

Modifier and Type	Field and Description
static Arithmetic.Polynomial	ZERO

Method Summary

Modifier and Type	Method and Description
Arithmetic.Polynomial	add(Arithmetic.Polynomial.Term p)
Arithmetic.Polynomial	add(Arithmetic.Polynomial p) Add two polynomials together, producing a polynomial in normal form.
int	compareTo(Arithmetic.Polynomial p)
boolean	equals(Object o)
Arithmetic.Polynomial	factorise() Factorise a given polynomial.
Arithmetic.Polynomial.Term	getTerm(int i)
int	hashCode()
boolean	isConstant()
Arithmetic.Polynomial	multiply(Arithmetic.Polynomial.Term rhs)
Arithmetic.Polynomial	multiply(Arithmetic.Polynomial p) Multiply two polynomials together.
Arithmetic.Polynomial	multiply(BigInteger rhs)
Arithmetic.Polynomial	negate()
int	size()
Arithmetic.Polynomial	subtract(Arithmetic.Polynomial.Term p)
Arithmetic.Polynomial	subtract(Arithmetic.Polynomial p)
BigInteger	toConstant()
WyalFile.Expr	toExpression()
String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

ZERO

public static final Arithmetic.Polynomial ZERO

Method Detail

size

public int size()

isConstant

public boolean isConstant()

toConstant

public BigInteger toConstant()

getTerm

public Arithmetic.Polynomial.Term getTerm(int i)

negate

public Arithmetic.Polynomial negate()

add

public Arithmetic.Polynomial add(Arithmetic.Polynomial p)

Add two polynomials together, producing a polynomial in normal form. To do this, we must add the coefficients for terms which have the same set of atoms, whilst other terms are incorporated as is. For example, consider adding 2+2x with 1+3x+4y. In this case, we have some terms in common, so the result becomes (2+1) + (2x+3x) + 4y which is simplified to 3 + 5x + 4y.

Parameters:

poly -

Returns:

add

public Arithmetic.Polynomial add(Arithmetic.Polynomial.Term p)

subtract

public Arithmetic.Polynomial subtract(Arithmetic.Polynomial p)

subtract

public Arithmetic.Polynomial subtract(Arithmetic.Polynomial.Term p)

multiply

public Arithmetic.Polynomial multiply(Arithmetic.Polynomial p)

Multiply two polynomials together. This is done by reusing the add() function as much as possible, though this may not be the most efficient. In essence, to multiply one polynomial (e.g. 2+2x) by another (e.g.1+3x+4y) it breaks it down into a series of multiplications over terms and additions. That is, we multiply each term from the first polynomial by the second (e.g. 2*(1+3x+4y) and 2x*(1+3x+4y)). Then, we add the results together (e.g. (2+6x+8y) + (2x+6x2+8xy)).

Parameters:

p -

Returns:

multiply

public Arithmetic.Polynomial multiply(Arithmetic.Polynomial.Term rhs)

multiply

public Arithmetic.Polynomial multiply(BigInteger rhs)

factorise

public Arithmetic.Polynomial factorise()

Factorise a given polynomial. For example, 2x+2 is factorised to be x+1. Observe that this does not preseve the result of the polynomial. However, it is safe to do when simplifying equations. For example, 2x == 2y can be safely factorised to x == y.

Parameters:

p -

Returns:

compareTo

public int compareTo(Arithmetic.Polynomial p)

Specified by:

compareTo in interface Comparable<Arithmetic.Polynomial>

equals

public boolean equals(Object o)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

toExpression

public WyalFile.Expr toExpression()

toString

public String toString()

Overrides:

toString in class Object