IPolynomial (rings 2.5.7 API)

Type Parameters:

Poly - the type of polynomial (self type)

All Superinterfaces:

Comparable<Poly>, Serializable, Stringifiable<Poly>

All Known Subinterfaces:

IUnivariatePolynomial<Poly>

All Known Implementing Classes:

AMultivariatePolynomial, MultivariatePolynomial, MultivariatePolynomialZp64, UnivariatePolynomial, UnivariatePolynomialZ64, UnivariatePolynomialZp64
```
public interface IPolynomial<Poly extends IPolynomial<Poly>>
extends Comparable<Poly>, Stringifiable<Poly>, Serializable
```
Parent interface for all polynomials. All polynomial instances are mutable, so all structural operations except those where it is stated explicitly will in general modify the instance. All arithmetic operations (add(oth), multiply(oth), monic() etc.) applies to this inplace and return this reference ( so e.g. (poly == poly.add(other))).
Note: modifier operations are not synchronized.

Since:

1.0

Method Summary

All Methods Instance Methods Abstract Methods Default Methods Deprecated Methods
Modifier and Type	Method and Description
`default Poly`	`add(Poly... oth)` Adds `oth` to `this`.
`Poly`	`add(Poly oth)` Adds `oth` to `this`.
`default void`	`assertSameCoefficientRingWith(Poly oth)` Checks whether `oth` and `this` have the same coefficient ring, if not exception will be thrown
`default Poly`	`canonical()` Makes this poly monic if coefficient ring is field, otherwise makes this primitive
`Poly`	`ccAsPoly()` Returns the constant coefficient as a constant poly
`Poly`	`clone()` Deep copy of this
`BigInteger`	`coefficientRingCardinality()` Returns cardinality of the coefficient ring of this poly
`BigInteger`	`coefficientRingCharacteristic()` Returns characteristic of the coefficient ring of this poly
`BigInteger`	`coefficientRingPerfectPowerBase()` Returns `base` so that `coefficientRingCardinality() == base^exponent` or null if cardinality is not finite
`BigInteger`	`coefficientRingPerfectPowerExponent()` Returns `exponent` so that `coefficientRingCardinality() == base^exponent` or null if cardinality is not finite
`default String`	`coefficientRingToString()` String representation of the coefficient ring of this
`String`	`coefficientRingToString(IStringifier<Poly> stringifier)` String representation of the coefficient ring of this
`Poly`	`contentAsPoly()` Returns the content of this (gcd of coefficients) as a constant poly
`default Poly`	`copy()` Deep copy of this (alias for `clone()`, required for scala)
`Poly[]`	`createArray(int length)` overcome Java generics...
`default Poly[]`	`createArray(Poly a)` overcome Java generics...
`default Poly[]`	`createArray(Poly a, Poly b)` overcome Java generics...
`default Poly[]`	`createArray(Poly a, Poly b, Poly c)` overcome Java generics...
`Poly[][]`	`createArray2d(int length)` overcome Java generics...
`Poly[][]`	`createArray2d(int length1, int length2)` overcome Java generics...
`default Poly`	`createConstant(long value)` Creates constant polynomial with specified value
`Poly`	`createOne()` Returns the new instance of unit polynomial (with the same coefficient ring)
`Poly`	`createZero()` Returns the new instance of zero polynomial (with the same coefficient ring)
`Poly`	`decrement()` Subtracts 1 from this
`int`	`degree()` Returns the degree of this polynomial
`Poly`	`divideByLC(Poly other)` Divides this polynomial by the leading coefficient of `other` or returns `null` (causing loss of internal data) if some of the elements can't be exactly divided by the `other.lc()`.
`Poly`	`increment()` Adds 1 to this
`boolean`	`isConstant()` Returns `true` if this polynomial has only constant term
`boolean`	`isLinearExactly()` Returns whether this polynomial is linear (i.e.
`boolean`	`isLinearOrConstant()` Returns whether this polynomial is linear (i.e.
`boolean`	`isMonic()` Returns `true` if this polynomial is monic
`boolean`	`isMonomial()` Returns `true` if this polynomial has only one monomial term
`boolean`	`isOne()` Returns `true` if this is one
`boolean`	`isOverField()` Returns whether the coefficient ring of this polynomial is a field
`boolean`	`isOverFiniteField()` Returns whether the coefficient ring of this polynomial is a finite field
`boolean`	`isOverPerfectPower()` Returns whether the `coefficientRingCardinality()` is a perfect power
`boolean`	`isOverZ()` Returns whether the coefficient ring of this polynomial is Z
`boolean`	`isUnitCC()` Returns true if constant term is equal to one
`boolean`	`isZero()` Returns `true` if this is zero
`boolean`	`isZeroCC()` Returns true if constant term is zero
`Poly`	`lcAsPoly()` Returns the leading coefficient as a constant poly
`Poly`	`monic()` Sets `this` to its monic part (that is `this` divided by its leading coefficient), or returns `null` (causing loss of internal data) if some of the elements can't be exactly divided by the `lc()`.
`default Poly`	`monicExact()` Sets `this` to its monic part (that is `this` divided by its leading coefficient), or throws `ArithmeticException` if some of the elements can't be exactly divided by the l.c.
`Poly`	`monicWithLC(Poly other)` Sets `this` to its monic part multiplied by the leading coefficient of `other`;
`default Poly`	`multiply(Iterable<Poly> oth)` Multiplies this by `oth`
`Poly`	`multiply(long factor)` Multiplies this by `factor`
`default Poly`	`multiply(Poly... oth)` Multiplies this by `oth`
`Poly`	`multiply(Poly oth)` Multiplies this by `oth`
`Poly`	`multiplyByBigInteger(BigInteger factor)` Multiplies this by `factor`
`Poly`	`multiplyByLC(Poly other)` Multiply this by the leading coefficient of `other`
`Poly`	`negate()` Negates this and returns
`Poly`	`parsePoly(String string)` Deprecated. use `Coder` to parse polynomials
`Poly`	`primitivePart()` Reduces poly to its primitive part (primitive part will always have positive l.c.)
`Poly`	`primitivePartSameSign()` Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly
`boolean`	`sameCoefficientRingWith(Poly oth)` Returns whether `oth` and `this` have the same coefficient ring
`Poly`	`set(Poly oth)` Sets the content of this to `oth`
`Poly`	`setCoefficientRingFrom(Poly poly)` Set the coefficient ring from specified poly
`default Poly`	`setCoefficientRingFromOptional(Poly poly)`
`int`	`signumOfLC()` Gives signum of the leading coefficient
`int`	`size()` Returns the size of this polynomial
`Poly`	`square()` Squares `this`
`default Poly`	`subtract(Poly... oth)` Subtracts `oth` from `this`.
`Poly`	`subtract(Poly oth)` Subtracts `oth` from `this`.
`default Poly`	`toPositiveLC()` If signum of leading coefficient is minus one, negate this
`default String`	`toString(String... variables)` String representation of this polynomial with specified string variables
`Poly`	`toZero()` Sets this to zero

Methods inherited from interface java.lang.Comparable
compareTo

Methods inherited from interface cc.redberry.rings.io.Stringifiable
toString

- Method Detail
  - sameCoefficientRingWith
```
boolean sameCoefficientRingWith(Poly oth)
```
    Returns whether oth and this have the same coefficient ring
    
    Parameters:
    
    oth - other polynomial
    
    Returns:
    
    whether this and oth are over the same coefficient ring
  - assertSameCoefficientRingWith
```
default void assertSameCoefficientRingWith(Poly oth)
```
    Checks whether oth and this have the same coefficient ring, if not exception will be thrown
    
    Parameters:
    
    oth - other polynomial
    
    Throws:
    
    IllegalArgumentException - if this and oth have different coefficient ring
  - setCoefficientRingFrom
```
Poly setCoefficientRingFrom(Poly poly)
```
    Set the coefficient ring from specified poly
    
    Parameters:
    
    poly - the polynomial
    
    Returns:
    
    a copy of this with the coefficient ring taken from poly
  - setCoefficientRingFromOptional
```
default Poly setCoefficientRingFromOptional(Poly poly)
```
  - degree
```
int degree()
```
    Returns the degree of this polynomial
    
    Returns:
    
    the degree
  - size
```
int size()
```
    Returns the size of this polynomial
    
    Returns:
    
    the size
  - isZero
```
boolean isZero()
```
    Returns true if this is zero
    
    Returns:
    
    whether this is zero
  - isOne
```
boolean isOne()
```
    Returns true if this is one
    
    Returns:
    
    whether this is one
  - isMonic
```
boolean isMonic()
```
    Returns true if this polynomial is monic
    
    Returns:
    
    whether this is monic
  - isUnitCC
```
boolean isUnitCC()
```
    Returns true if constant term is equal to one
    
    Returns:
    
    whether constant term is 1
  - isZeroCC
```
boolean isZeroCC()
```
    Returns true if constant term is zero
    
    Returns:
    
    whether constant term is zero
  - isConstant
```
boolean isConstant()
```
    Returns true if this polynomial has only constant term
    
    Returns:
    
    whether this is constant
  - isMonomial
```
boolean isMonomial()
```
    Returns true if this polynomial has only one monomial term
    
    Returns:
    
    whether this has only one monomial term
  - isOverField
```
boolean isOverField()
```
    Returns whether the coefficient ring of this polynomial is a field
    
    Returns:
    
    whether the coefficient ring of this polynomial is a field
  - isOverZ
```
boolean isOverZ()
```
    Returns whether the coefficient ring of this polynomial is Z
    
    Returns:
    
    whether the coefficient ring of this polynomial is Z
  - isOverFiniteField
```
boolean isOverFiniteField()
```
    Returns whether the coefficient ring of this polynomial is a finite field
    
    Returns:
    
    whether the coefficient ring of this polynomial is a finite field
  - isLinearOrConstant
```
boolean isLinearOrConstant()
```
    Returns whether this polynomial is linear (i.e. of the form a * X + b)
  - isLinearExactly
```
boolean isLinearExactly()
```
    Returns whether this polynomial is linear (i.e. of the form a * X + b with nonzero a)
  - coefficientRingCardinality
```
BigInteger coefficientRingCardinality()
```
    Returns cardinality of the coefficient ring of this poly
    
    Returns:
    
    cardinality of the coefficient ring
  - coefficientRingCharacteristic
```
BigInteger coefficientRingCharacteristic()
```
    Returns characteristic of the coefficient ring of this poly
    
    Returns:
    
    characteristic of the coefficient ring
  - isOverPerfectPower
```
boolean isOverPerfectPower()
```
    Returns whether the coefficientRingCardinality() is a perfect power
    
    Returns:
    
    whether the coefficientRingCardinality() is a perfect power
  - coefficientRingPerfectPowerBase
```
BigInteger coefficientRingPerfectPowerBase()
```
    Returns base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
    
    Returns:
    
    base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
  - coefficientRingPerfectPowerExponent
```
BigInteger coefficientRingPerfectPowerExponent()
```
    Returns exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
    
    Returns:
    
    exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
  - monic
```
Poly monic()
```
    Sets this to its monic part (that is this divided by its leading coefficient), or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the lc(). NOTE: if null is returned, the content of this is destroyed.
    
    Returns:
    
    monic this or null
  - monicExact
```
default Poly monicExact()
```
    Sets this to its monic part (that is this divided by its leading coefficient), or throws ArithmeticException if some of the elements can't be exactly divided by the l.c.
    
    Returns:
    
    monic this or null
    
    Throws:
    
    ArithmeticException - if some of the elements can't be exactly divided by the l.c.
  - canonical
```
default Poly canonical()
```
    Makes this poly monic if coefficient ring is field, otherwise makes this primitive
  - signumOfLC
```
int signumOfLC()
```
    Gives signum of the leading coefficient
    
    Returns:
    
    signum of the leading coefficient
  - toPositiveLC
```
default Poly toPositiveLC()
```
    If signum of leading coefficient is minus one, negate this
  - toZero
```
Poly toZero()
```
    Sets this to zero
    
    Returns:
    
    this := zero
  - set
```
Poly set(Poly oth)
```
    Sets the content of this to oth
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this := oth
  - primitivePart
```
Poly primitivePart()
```
    Reduces poly to its primitive part (primitive part will always have positive l.c.)
    
    Returns:
    
    primitive part (poly will be modified)
  - primitivePartSameSign
```
Poly primitivePartSameSign()
```
    Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly
    
    Returns:
    
    primitive part (poly will be modified)
  - increment
```
Poly increment()
```
    Adds 1 to this
    
    Returns:
    
    this + 1
  - decrement
```
Poly decrement()
```
    Subtracts 1 from this
    
    Returns:
    
    this - 1
  - createZero
```
Poly createZero()
```
    Returns the new instance of zero polynomial (with the same coefficient ring)
    
    Returns:
    
    new instance of 0
  - createOne
```
Poly createOne()
```
    Returns the new instance of unit polynomial (with the same coefficient ring)
    
    Returns:
    
    new instance of 1
  - createConstant
```
default Poly createConstant(long value)
```
    Creates constant polynomial with specified value
    
    Parameters:
    
    value - the value
    
    Returns:
    
    constant polynomial
  - add
```
Poly add(Poly oth)
```
    Adds oth to this.
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this + oth
  - add
```
default Poly add(Poly... oth)
```
    Adds oth to this.
    
    Parameters:
    
    oth - the polynomials
    
    Returns:
    
    this + oth
  - subtract
```
Poly subtract(Poly oth)
```
    Subtracts oth from this.
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this - oth
  - subtract
```
default Poly subtract(Poly... oth)
```
    Subtracts oth from this.
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this - oth
  - negate
```
Poly negate()
```
    Negates this and returns
    
    Returns:
    
    this negated
  - multiply
```
Poly multiply(Poly oth)
```
    Multiplies this by oth
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this * oth
  - multiply
```
default Poly multiply(Poly... oth)
```
    Multiplies this by oth
    
    Parameters:
    
    oth - the polynomials
    
    Returns:
    
    this * oth
  - multiply
```
default Poly multiply(Iterable<Poly> oth)
```
    Multiplies this by oth
    
    Parameters:
    
    oth - the polynomials
    
    Returns:
    
    this * oth
  - multiply
```
Poly multiply(long factor)
```
    Multiplies this by factor
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this * factor
  - multiplyByBigInteger
```
Poly multiplyByBigInteger(BigInteger factor)
```
    Multiplies this by factor
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this * factor
  - square
```
Poly square()
```
    Squares this
    
    Returns:
    
    this * this
  - contentAsPoly
```
Poly contentAsPoly()
```
    Returns the content of this (gcd of coefficients) as a constant poly
  - lcAsPoly
```
Poly lcAsPoly()
```
    Returns the leading coefficient as a constant poly
  - ccAsPoly
```
Poly ccAsPoly()
```
    Returns the constant coefficient as a constant poly
  - divideByLC
```
Poly divideByLC(Poly other)
```
    Divides this polynomial by the leading coefficient of other or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the other.lc(). NOTE: if null is returned, the content of this is destroyed.
    
    Parameters:
    
    other - the polynomial
    
    Returns:
    
    this divided by the other.lc() or null if exact division is not possible
  - monicWithLC
```
Poly monicWithLC(Poly other)
```
    Sets this to its monic part multiplied by the leading coefficient of other;
    
    Parameters:
    
    other - other polynomial
    
    Returns:
    
    monic part multiplied by the leading coefficient of other or null if exact division by the reduced leading coefficient is not possible
  - multiplyByLC
```
Poly multiplyByLC(Poly other)
```
    Multiply this by the leading coefficient of other
    
    Parameters:
    
    other - polynomial
    
    Returns:
    
    this * lc(other)
  - clone
```
Poly clone()
```
    Deep copy of this
    
    Returns:
    
    deep copy of this
  - copy
```
default Poly copy()
```
    Deep copy of this (alias for clone(), required for scala)
    
    Returns:
    
    deep copy of this
  - createArray
```
Poly[] createArray(int length)
```
    overcome Java generics...
  - createArray2d
```
Poly[][] createArray2d(int length)
```
    overcome Java generics...
  - createArray2d
```
Poly[][] createArray2d(int length1,
                       int length2)
```
    overcome Java generics...
  - createArray
```
default Poly[] createArray(Poly a)
```
    overcome Java generics...
  - createArray
```
default Poly[] createArray(Poly a,
                           Poly b)
```
    overcome Java generics...
  - createArray
```
default Poly[] createArray(Poly a,
                           Poly b,
                           Poly c)
```
    overcome Java generics...
  - coefficientRingToString
```
String coefficientRingToString(IStringifier<Poly> stringifier)
```
    String representation of the coefficient ring of this
  - coefficientRingToString
```
default String coefficientRingToString()
```
    String representation of the coefficient ring of this
  - toString
```
default String toString(String... variables)
```
    String representation of this polynomial with specified string variables
  - parsePoly
```
@Deprecated
Poly parsePoly(String string)
```
    Deprecated. use Coder to parse polynomials

Interface IPolynomial<Poly extends IPolynomial<Poly>>

Method Summary

Methods inherited from interface java.lang.Comparable

Methods inherited from interface cc.redberry.rings.io.Stringifiable

Method Detail

sameCoefficientRingWith

assertSameCoefficientRingWith

setCoefficientRingFrom

setCoefficientRingFromOptional

degree

size

isZero

isOne

isMonic

isUnitCC

isZeroCC

isConstant

isMonomial

isOverField

isOverZ

isOverFiniteField

isLinearOrConstant

isLinearExactly

coefficientRingCardinality

coefficientRingCharacteristic

isOverPerfectPower

coefficientRingPerfectPowerBase

coefficientRingPerfectPowerExponent

monic

monicExact

canonical

signumOfLC

toPositiveLC

toZero

set

primitivePart

primitivePartSameSign

increment

decrement

createZero

createOne

createConstant

add

add

subtract

subtract

negate

multiply

multiply

multiply

multiply

multiplyByBigInteger

square

contentAsPoly

lcAsPoly

ccAsPoly

divideByLC

monicWithLC

multiplyByLC

clone

copy

createArray

createArray2d

createArray2d

createArray

createArray

createArray

coefficientRingToString

coefficientRingToString

toString

parsePoly