UnivariatePolynomialZ64 (rings 2.5.7 API)

java.lang.Object
- cc.redberry.rings.poly.univar.UnivariatePolynomialZ64

All Implemented Interfaces:

Stringifiable<UnivariatePolynomialZ64>, IPolynomial<UnivariatePolynomialZ64>, IUnivariatePolynomial<UnivariatePolynomialZ64>, Serializable, Comparable<UnivariatePolynomialZ64>
```
public final class UnivariatePolynomialZ64
extends Object
```
Univariate polynomial over machine integers in range [-2^63, 2^63]. NOTE: this class is used in internal routines for performance reasons, for usual polynomials over Z use UnivariatePolynomial over BigIntegers.
Arithmetic operations on instances of this type may cause long overflow in which case a proper ArithmeticException will be thrown.

Since:

1.0

See Also:

Serialized Form

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`lPoly`	`add(long val)` Add constant to this.
`lPoly`	`add(lPoly oth)` Adds `oth` to `this`.
`lPoly`	`addMonomial(long coefficient, int exponent)` Adds `coefficient*x^exponent` to `this`
`lPoly`	`addMul(lPoly oth, long factor)` Adds `oth * factor` to `this`
`AMultivariatePolynomial`	`asMultivariate(Comparator<DegreeVector> ordering)` Convert to multivariate polynomial
`long`	`cc()` Returns the constant coefficient of this poly
`lPoly`	`ccAsPoly()` Returns the constant coefficient as a constant poly
`UnivariatePolynomialZ64`	`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
`String`	`coefficientRingToString(IStringifier<UnivariatePolynomialZ64> stringifier)` String representation of the coefficient ring of this
`int`	`compareTo(lPoly o)`
`AMultivariatePolynomial`	`composition(AMultivariatePolynomial value)` Calculates the composition of this(oth)
`lPoly`	`composition(lPoly value)` Calculates the composition of this(oth) (new instance, so the content of this is not changed))
`static UnivariatePolynomialZ64`	`constant(long value)` Returns constant with specified value
`long`	`content()` Returns the content of this poly (gcd of its coefficients)
`lPoly`	`contentAsPoly()` Returns the content of this (gcd of coefficients) as a constant poly
`static UnivariatePolynomialZ64`	`create(long... data)` Creates Z[x] polynomial from the specified coefficients
`UnivariatePolynomialZ64[]`	`createArray(int length)` overcome Java generics...
`UnivariatePolynomialZ64[][]`	`createArray2d(int length)` overcome Java generics...
`UnivariatePolynomialZ64[][]`	`createArray2d(int length1, int length2)` overcome Java generics...
`lPoly`	`createConstant(long val)` Creates constant polynomial with specified value (with the same coefficient ring)
`UnivariatePolynomialZ64`	`createFromArray(long[] data)` Creates new poly with the specified coefficients (over the same ring)
`lPoly`	`createLinear(long cc, long lc)` Creates linear polynomial of form `cc + x * lc` (with the same coefficient ring)
`lPoly`	`createMonomial(int degree)` Creates new monomial `x^degree` (with the same coefficient ring)
`UnivariatePolynomialZ64`	`createMonomial(long coefficient, int degree)` Creates monomial `coefficient * x^degree` (with the same coefficient ring)
`lPoly`	`createOne()` Returns the new instance of unit polynomial (with the same coefficient ring)
`lPoly`	`createZero()` Returns the new instance of zero polynomial (with the same coefficient ring)
`lPoly`	`decrement()` Subtracts 1 from this
`int`	`degree()` Returns the degree of this polynomial
`UnivariatePolynomialZ64`	`derivative()` Returns the formal derivative of this poly (new instance, so the content of this is not changed)
`UnivariatePolynomialZ64`	`divideByLC(UnivariatePolynomialZ64 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()`.
`UnivariatePolynomialZ64`	`divideOrNull(long factor)` Divides this polynomial by a `factor` or returns `null` (causing loss of internal data) if some of the elements can't be exactly divided by the `factor`.
`void`	`ensureInternalCapacity(int desiredCapacity)` ensures that internal storage has enough size to store `desiredCapacity` elements
`boolean`	`equals(Object obj)`
`long`	`evaluate(long point)` Evaluates this poly at a given `point` (via Horner method).
`long`	`evaluateAtRational(long num, long den)` Evaluates this poly at a given rational point `num/den`
`int`	`firstNonZeroCoefficientPosition()` Returns position of the first non-zero coefficient, that is common monomial exponent (e.g.
`long`	`get(int i)` Returns the i-th coefficient of this poly (coefficient before x^i)
`lPoly`	`getAsPoly(int i)` Returns i-th coefficient of this as a constant polynomial
`long[]`	`getDataReferenceUnsafe()` internal API >>> direct unsafe access to internal storage
`UnivariatePolynomialZ64`	`getRange(int from, int to)` Creates polynomial formed from the coefficients of this starting from `from` (inclusive) to `to` (exclusive)
`int`	`hashCode()`
`lPoly`	`increment()` Adds 1 to this
`boolean`	`isConstant()` Returns `true` if this polynomial has only constant term
`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`	`isZeroAt(int i)` Returns whether i-th coefficient of this is zero
`long`	`lc()` Returns the leading coefficient of this poly
`lPoly`	`lcAsPoly()` Returns the leading coefficient as a constant poly
`<T> UnivariatePolynomial<T>`	`mapCoefficients(Ring<T> ring, LongFunction<T> mapper)` Applies transformation function to this and returns the result.
`long`	`maxAbsCoefficient()` Returns max coefficient (by absolute value) of this poly
`double`	`mignotteBound()` Returns Mignotte's bound (sqrt(n+1) * 2^n max \|this\|)
`UnivariatePolynomialZp64`	`modulus(IntegersZp64 ring)` Reduces (copied) polynomial modulo `modulus` and returns the result.
`UnivariatePolynomialZp64`	`modulus(IntegersZp64 ring, boolean copy)` Reduces this polynomial modulo `modulus` and returns the result.
`UnivariatePolynomialZp64`	`modulus(long modulus)` Reduces (copied) polynomial modulo `modulus` and returns the result.
`UnivariatePolynomialZp64`	`modulus(long modulus, boolean copy)` Reduces this polynomial modulo `modulus` and returns the result.
`UnivariatePolynomialZ64`	`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()`.
`UnivariatePolynomialZ64`	`monic(long factor)` Sets `this` to its monic part multiplied by the `factor`;
`lPoly`	`monicWithLC(lPoly other)` Sets `this` to its monic part multiplied by the leading coefficient of `other`;
`static UnivariatePolynomialZ64`	`monomial(long coefficient, int exponent)` Creates monomial `coefficient * x^exponent`
`lPoly`	`multiply(long factor)` Multiplies this by `factor`
`UnivariatePolynomialZ64`	`multiply(UnivariatePolynomialZ64 oth)` Multiplies this by `oth`
`UnivariatePolynomialZ64`	`multiplyByBigInteger(BigInteger factor)` Multiplies this by `factor`
`lPoly`	`multiplyByLC(lPoly other)` Multiply this by the leading coefficient of `other`
`lPoly`	`negate()` Negates this and returns
`double`	`norm1()` Returns L1 norm of this polynomial, i.e.
`double`	`norm2()` Returns L2 norm of this polynomial, i.e.
`double`	`normMax()` Returns max coefficient (by absolute value) of this poly
`static UnivariatePolynomialZ64`	`one()` Creates unit polynomial
`static UnivariatePolynomialZ64`	`parse(String string)` Parse string into polynomial
`UnivariatePolynomialZ64`	`parsePoly(String string)`
`lPoly`	`primitivePart()` Reduces poly to its primitive part (primitive part will always have positive l.c.)
`lPoly`	`primitivePartSameSign()` Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly
`lPoly`	`reverse()` Reverses the coefficients of this
`boolean`	`sameCoefficientRingWith(UnivariatePolynomialZ64 oth)` Returns whether `oth` and `this` have the same coefficient ring
`lPoly`	`set(int i, long el)` Sets i-th element of this poly with the specified value
`lPoly`	`set(lPoly oth)` Sets the content of this to `oth`
`lPoly`	`setAndDestroy(lPoly oth)` Sets the content of this with `oth` and destroys oth
`UnivariatePolynomialZ64`	`setCoefficientRingFrom(UnivariatePolynomialZ64 univariatePolynomialZ64)` Set the coefficient ring from specified poly
`lPoly`	`setFrom(int indexInThis, lPoly poly, int indexInPoly)` Sets i-th element of this by j-th element of other poly
`lPoly`	`setLC(long lc)` Sets hte leading coefficient of this poly with specified value
`lPoly`	`setZero(int i)` Fills i-th element with zero
`lPoly`	`shift(long value)` Shifts variable x -> x + value and returns the result (new instance)
`lPoly`	`shiftLeft(int offset)` Returns the quotient `this / x^offset`, it is polynomial with coefficient list formed by shifting coefficients of `this` to the left by `offset`.
`lPoly`	`shiftRight(int offset)` Multiplies `this` by the `x^offset`.
`int`	`signumOfLC()` Gives signum of the leading coefficient
`UnivariatePolynomialZ64`	`square()` Squares `this`
`LongStream`	`stream()` Returns a sequential `Stream` with coefficients of this as its source.
`Stream<lPoly>`	`streamAsPolys()` Stream polynomial coefficients as constant polynomials
`lPoly`	`subtract(long val)` Subtract constant from this.
`lPoly`	`subtract(lPoly oth)` Subtracts `oth` from `this`.
`lPoly`	`subtract(lPoly oth, long factor, int exponent)` Subtracts `factor * x^exponent * oth` from `this`
`UnivariatePolynomial<BigInteger>`	`toBigPoly()` Converts this to a polynomial over BigIntegers
`String`	`toString()`
`String`	`toString(IStringifier<lPoly> stringifier)` convert this to string with the use of stringifier
`String`	`toStringForCopy()`
`lPoly`	`toZero()` Sets this to zero
`lPoly`	`truncate(int newDegree)` Returns the remainder `this rem x^(newDegree + 1)`, it is polynomial formed by coefficients of this from zero to `newDegree` (both inclusive)
`static UnivariatePolynomialZ64`	`zero()` Creates zero polynomial

Methods inherited from class java.lang.Object
finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface cc.redberry.rings.poly.univar.IUnivariatePolynomial
asMultivariate, composition, exponents, isLinearExactly, isLinearOrConstant, isZeroCC, mapCoefficientsAsPolys, nNonZeroTerms, size

Methods inherited from interface cc.redberry.rings.poly.IPolynomial
add, assertSameCoefficientRingWith, canonical, coefficientRingToString, copy, createArray, createArray, createArray, monicExact, multiply, multiply, setCoefficientRingFromOptional, subtract, toPositiveLC, toString

- Method Detail
  - parse
```
public static UnivariatePolynomialZ64 parse(String string)
```
    Parse string into polynomial
  - create
```
public static UnivariatePolynomialZ64 create(long... data)
```
    Creates Z[x] polynomial from the specified coefficients
    
    Parameters:
    
    data - coefficients
    
    Returns:
    
    Z[x] polynomial
  - monomial
```
public static UnivariatePolynomialZ64 monomial(long coefficient,
                                               int exponent)
```
    Creates monomial coefficient * x^exponent
    
    Parameters:
    
    coefficient - monomial coefficient
    
    exponent - monomial exponent
    
    Returns:
    
    coefficient * x^exponent
  - zero
```
public static UnivariatePolynomialZ64 zero()
```
    Creates zero polynomial
    
    Returns:
    
    zero polynomial
  - one
```
public static UnivariatePolynomialZ64 one()
```
    Creates unit polynomial
    
    Returns:
    
    unit polynomial
  - constant
```
public static UnivariatePolynomialZ64 constant(long value)
```
    Returns constant with specified value
    
    Returns:
    
    constant with specified value
  - setCoefficientRingFrom
```
public UnivariatePolynomialZ64 setCoefficientRingFrom(UnivariatePolynomialZ64 univariatePolynomialZ64)
```
    Description copied from interface: IPolynomial
    
    Set the coefficient ring from specified poly
    
    Parameters:
    
    univariatePolynomialZ64 - the polynomial
    
    Returns:
    
    a copy of this with the coefficient ring taken from poly
  - modulus
```
public UnivariatePolynomialZp64 modulus(long modulus,
                                        boolean copy)
```
    Reduces this polynomial modulo modulus and returns the result.
    
    Parameters:
    
    modulus - the modulus
    
    copy - whether to copy the internal data or reduce inplace (in which case the data of this will be lost)
    
    Returns:
    
    this modulo modulus
  - modulus
```
public UnivariatePolynomialZp64 modulus(long modulus)
```
    Reduces (copied) polynomial modulo modulus and returns the result.
    
    Parameters:
    
    modulus - the modulus
    
    Returns:
    
    a copy of this modulo modulus
  - modulus
```
public UnivariatePolynomialZp64 modulus(IntegersZp64 ring,
                                        boolean copy)
```
    Reduces this polynomial modulo modulus and returns the result.
    
    Parameters:
    
    ring - the modulus
    
    copy - whether to copy the internal data or reduce inplace (in which case the data of this will be lost)
    
    Returns:
    
    this modulo modulus
  - modulus
```
public UnivariatePolynomialZp64 modulus(IntegersZp64 ring)
```
    Reduces (copied) polynomial modulo modulus and returns the result.
    
    Parameters:
    
    ring - the modulus
    
    Returns:
    
    a copy of this modulo modulus
  - toBigPoly
```
public UnivariatePolynomial<BigInteger> toBigPoly()
```
    Converts this to a polynomial over BigIntegers. The ring of the result is Rings.Z
    
    Returns:
    
    polynomial over BigIntegers
  - mignotteBound
```
public double mignotteBound()
```
    Returns Mignotte's bound (sqrt(n+1) * 2^n max |this|)
    
    Returns:
    
    Mignotte's bound
  - evaluateAtRational
```
public long evaluateAtRational(long num,
                               long den)
```
    Evaluates this poly at a given rational point num/den
    
    Parameters:
    
    num - point numerator
    
    den - point denominator
    
    Returns:
    
    value at num/den
    
    Throws:
    
    ArithmeticException - if the result is not integer
  - getRange
```
public UnivariatePolynomialZ64 getRange(int from,
                                        int to)
```
    Description copied from interface: IUnivariatePolynomial
    
    Creates polynomial formed from the coefficients of this starting from from (inclusive) to to (exclusive)
    
    Parameters:
    
    from - the initial index of the range to be copied, inclusive
    
    to - the final index of the range to be copied, exclusive.
    
    Returns:
    
    polynomial formed from the range of coefficients of this
  - createArray
```
public UnivariatePolynomialZ64[] createArray(int length)
```
    Description copied from interface: IPolynomial
    
    overcome Java generics...
  - createArray2d
```
public UnivariatePolynomialZ64[][] createArray2d(int length)
```
    Description copied from interface: IPolynomial
    
    overcome Java generics...
  - createArray2d
```
public UnivariatePolynomialZ64[][] createArray2d(int length1,
                                                 int length2)
```
    Description copied from interface: IPolynomial
    
    overcome Java generics...
  - sameCoefficientRingWith
```
public boolean sameCoefficientRingWith(UnivariatePolynomialZ64 oth)
```
    Description copied from interface: IPolynomial
    
    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
  - createFromArray
```
public UnivariatePolynomialZ64 createFromArray(long[] data)
```
    Creates new poly with the specified coefficients (over the same ring)
    
    Parameters:
    
    data - the data
    
    Returns:
    
    polynomial
  - createMonomial
```
public UnivariatePolynomialZ64 createMonomial(long coefficient,
                                              int degree)
```
    Creates monomial coefficient * x^degree (with the same coefficient ring)
    
    Parameters:
    
    coefficient - monomial coefficient
    
    degree - monomial degree
    
    Returns:
    
    coefficient * x^degree
  - isOverField
```
public boolean isOverField()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficient ring of this polynomial is a field
    
    Returns:
    
    whether the coefficient ring of this polynomial is a field
  - isOverFiniteField
```
public boolean isOverFiniteField()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficient ring of this polynomial is a finite field
    
    Returns:
    
    whether the coefficient ring of this polynomial is a finite field
  - isOverZ
```
public boolean isOverZ()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficient ring of this polynomial is Z
    
    Returns:
    
    whether the coefficient ring of this polynomial is Z
  - coefficientRingCardinality
```
public BigInteger coefficientRingCardinality()
```
    Description copied from interface: IPolynomial
    
    Returns cardinality of the coefficient ring of this poly
    
    Returns:
    
    cardinality of the coefficient ring
  - coefficientRingCharacteristic
```
public BigInteger coefficientRingCharacteristic()
```
    Description copied from interface: IPolynomial
    
    Returns characteristic of the coefficient ring of this poly
    
    Returns:
    
    characteristic of the coefficient ring
  - isOverPerfectPower
```
public boolean isOverPerfectPower()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficientRingCardinality() is a perfect power
    
    Returns:
    
    whether the coefficientRingCardinality() is a perfect power
  - coefficientRingPerfectPowerBase
```
public BigInteger coefficientRingPerfectPowerBase()
```
    Description copied from interface: IPolynomial
    
    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
```
public BigInteger coefficientRingPerfectPowerExponent()
```
    Description copied from interface: IPolynomial
    
    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
  - content
```
public long content()
```
    Returns the content of this poly (gcd of its coefficients)
    
    Returns:
    
    polynomial content
  - monic
```
public UnivariatePolynomialZ64 monic()
```
    Description copied from interface: IPolynomial
    
    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
  - monic
```
public UnivariatePolynomialZ64 monic(long factor)
```
    Sets this to its monic part multiplied by the factor;
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this
  - divideOrNull
```
public UnivariatePolynomialZ64 divideOrNull(long factor)
```
    Divides this polynomial by a factor or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the factor. NOTE: is null is returned, the content of this is destroyed.
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this divided by the factor or null
  - divideByLC
```
public UnivariatePolynomialZ64 divideByLC(UnivariatePolynomialZ64 other)
```
    Description copied from interface: IPolynomial
    
    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
  - multiplyByBigInteger
```
public UnivariatePolynomialZ64 multiplyByBigInteger(BigInteger factor)
```
    Description copied from interface: IPolynomial
    
    Multiplies this by factor
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this * factor
  - multiply
```
public UnivariatePolynomialZ64 multiply(UnivariatePolynomialZ64 oth)
```
    Description copied from interface: IPolynomial
    
    Multiplies this by oth
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this * oth
  - square
```
public UnivariatePolynomialZ64 square()
```
    Description copied from interface: IPolynomial
    
    Squares this
    
    Returns:
    
    this * this
  - derivative
```
public UnivariatePolynomialZ64 derivative()
```
    Description copied from interface: IUnivariatePolynomial
    
    Returns the formal derivative of this poly (new instance, so the content of this is not changed)
    
    Returns:
    
    the formal derivative
  - clone
```
public UnivariatePolynomialZ64 clone()
```
    Description copied from interface: IPolynomial
    
    Deep copy of this
    
    Specified by:
    
    clone in interface IPolynomial<UnivariatePolynomialZ64>
    
    Specified by:
    
    clone in interface IUnivariatePolynomial<UnivariatePolynomialZ64>
    
    Returns:
    
    deep copy of this
  - parsePoly
```
public UnivariatePolynomialZ64 parsePoly(String string)
```
  - coefficientRingToString
```
public String coefficientRingToString(IStringifier<UnivariatePolynomialZ64> stringifier)
```
    Description copied from interface: IPolynomial
    
    String representation of the coefficient ring of this
  - composition
```
public AMultivariatePolynomial composition(AMultivariatePolynomial value)
```
    Description copied from interface: IUnivariatePolynomial
    
    Calculates the composition of this(oth)
    
    Parameters:
    
    value - polynomial
    
    Returns:
    
    composition this(oth)
  - asMultivariate
```
public AMultivariatePolynomial asMultivariate(Comparator<DegreeVector> ordering)
```
    Description copied from interface: IUnivariatePolynomial
    
    Convert to multivariate polynomial
  - degree
```
public final int degree()
```
    Description copied from interface: IPolynomial
    
    Returns the degree of this polynomial
    
    Specified by:
    
    degree in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    the degree
  - get
```
public final long get(int i)
```
    Returns the i-th coefficient of this poly (coefficient before x^i)
  - set
```
public final lPoly set(int i,
                       long el)
```
    Sets i-th element of this poly with the specified value
  - setLC
```
public final lPoly setLC(long lc)
```
    Sets hte leading coefficient of this poly with specified value
  - firstNonZeroCoefficientPosition
```
public final int firstNonZeroCoefficientPosition()
```
    Description copied from interface: IUnivariatePolynomial
    
    Returns position of the first non-zero coefficient, that is common monomial exponent (e.g. 2 for x^2 + x^3 + ...). In the case of zero polynomial, -1 returned
    
    Specified by:
    
    firstNonZeroCoefficientPosition in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    position of the first non-zero coefficient or -1 if this is zero
  - lc
```
public final long lc()
```
    Returns the leading coefficient of this poly
    
    Returns:
    
    leading coefficient
  - lcAsPoly
```
public final lPoly lcAsPoly()
```
    Description copied from interface: IPolynomial
    
    Returns the leading coefficient as a constant poly
    
    Specified by:
    
    lcAsPoly in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
  - ccAsPoly
```
public final lPoly ccAsPoly()
```
    Description copied from interface: IPolynomial
    
    Returns the constant coefficient as a constant poly
    
    Specified by:
    
    ccAsPoly in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
  - getAsPoly
```
public lPoly getAsPoly(int i)
```
    Description copied from interface: IUnivariatePolynomial
    
    Returns i-th coefficient of this as a constant polynomial
    
    Specified by:
    
    getAsPoly in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    i - index in this
    
    Returns:
    
    i-th coefficient of this as a constant polynomial
  - cc
```
public final long cc()
```
    Returns the constant coefficient of this poly
    
    Returns:
    
    constant coefficient
  - ensureInternalCapacity
```
public final void ensureInternalCapacity(int desiredCapacity)
```
    Description copied from interface: IUnivariatePolynomial
    
    ensures that internal storage has enough size to store desiredCapacity elements
    
    Specified by:
    
    ensureInternalCapacity in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
  - createMonomial
```
public final lPoly createMonomial(int degree)
```
    Description copied from interface: IUnivariatePolynomial
    
    Creates new monomial x^degree (with the same coefficient ring)
    
    Specified by:
    
    createMonomial in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    degree - monomial degree
    
    Returns:
    
    new monomial coefficient * x^degree
  - createLinear
```
public final lPoly createLinear(long cc,
                                long lc)
```
    Creates linear polynomial of form cc + x * lc (with the same coefficient ring)
    
    Parameters:
    
    cc - the constant coefficient
    
    lc - the leading coefficient
    
    Returns:
    
    cc + x * lc
  - createConstant
```
public final lPoly createConstant(long val)
```
    Creates constant polynomial with specified value (with the same coefficient ring)
    
    Specified by:
    
    createConstant in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    val - the value
    
    Returns:
    
    constant polynomial with specified value
  - createZero
```
public final lPoly createZero()
```
    Description copied from interface: IPolynomial
    
    Returns the new instance of zero polynomial (with the same coefficient ring)
    
    Specified by:
    
    createZero in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    new instance of 0
  - createOne
```
public final lPoly createOne()
```
    Description copied from interface: IPolynomial
    
    Returns the new instance of unit polynomial (with the same coefficient ring)
    
    Specified by:
    
    createOne in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    new instance of 1
  - isZeroAt
```
public final boolean isZeroAt(int i)
```
    Description copied from interface: IUnivariatePolynomial
    
    Returns whether i-th coefficient of this is zero
    
    Specified by:
    
    isZeroAt in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    i - the position
    
    Returns:
    
    whether i-th coefficient of this is zero
  - setZero
```
public final lPoly setZero(int i)
```
    Description copied from interface: IUnivariatePolynomial
    
    Fills i-th element with zero
    
    Specified by:
    
    setZero in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    i - position
    
    Returns:
    
    self
  - setFrom
```
public final lPoly setFrom(int indexInThis,
                           lPoly poly,
                           int indexInPoly)
```
    Description copied from interface: IUnivariatePolynomial
    
    Sets i-th element of this by j-th element of other poly
    
    Specified by:
    
    setFrom in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    indexInThis - index in self
    
    poly - other polynomial
    
    indexInPoly - index in other polynomial
    
    Returns:
    
    self
  - isZero
```
public final boolean isZero()
```
    Description copied from interface: IPolynomial
    
    Returns true if this is zero
    
    Specified by:
    
    isZero in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    whether this is zero
  - isOne
```
public final boolean isOne()
```
    Description copied from interface: IPolynomial
    
    Returns true if this is one
    
    Specified by:
    
    isOne in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    whether this is one
  - isMonic
```
public final boolean isMonic()
```
    Description copied from interface: IPolynomial
    
    Returns true if this polynomial is monic
    
    Specified by:
    
    isMonic in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    whether this is monic
  - isUnitCC
```
public final boolean isUnitCC()
```
    Description copied from interface: IPolynomial
    
    Returns true if constant term is equal to one
    
    Specified by:
    
    isUnitCC in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    whether constant term is 1
  - isConstant
```
public final boolean isConstant()
```
    Description copied from interface: IPolynomial
    
    Returns true if this polynomial has only constant term
    
    Specified by:
    
    isConstant in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    whether this is constant
  - isMonomial
```
public final boolean isMonomial()
```
    Description copied from interface: IPolynomial
    
    Returns true if this polynomial has only one monomial term
    
    Specified by:
    
    isMonomial in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    whether this has only one monomial term
  - signumOfLC
```
public final int signumOfLC()
```
    Description copied from interface: IPolynomial
    
    Gives signum of the leading coefficient
    
    Specified by:
    
    signumOfLC in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    signum of the leading coefficient
  - norm1
```
public final double norm1()
```
    Returns L1 norm of this polynomial, i.e. sum of abs coefficients
    
    Returns:
    
    L1 norm of this
  - norm2
```
public final double norm2()
```
    Returns L2 norm of this polynomial, i.e. a square root of a sum of coefficient squares.
    
    Returns:
    
    L2 norm of this
  - normMax
```
public final double normMax()
```
    Returns max coefficient (by absolute value) of this poly
    
    Returns:
    
    max coefficient (by absolute value)
  - maxAbsCoefficient
```
public final long maxAbsCoefficient()
```
    Returns max coefficient (by absolute value) of this poly
    
    Returns:
    
    max coefficient (by absolute value)
  - toZero
```
public final lPoly toZero()
```
    Description copied from interface: IPolynomial
    
    Sets this to zero
    
    Specified by:
    
    toZero in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    this := zero
  - set
```
public final lPoly set(lPoly oth)
```
    Description copied from interface: IPolynomial
    
    Sets the content of this to oth
    
    Specified by:
    
    set in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this := oth
  - setAndDestroy
```
public final lPoly setAndDestroy(lPoly oth)
```
    Description copied from interface: IUnivariatePolynomial
    
    Sets the content of this with oth and destroys oth
    
    Specified by:
    
    setAndDestroy in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    oth - the polynomial (will be destroyed)
    
    Returns:
    
    this := oth
  - shiftLeft
```
public final lPoly shiftLeft(int offset)
```
    Description copied from interface: IUnivariatePolynomial
    
    Returns the quotient this / x^offset, it is polynomial with coefficient list formed by shifting coefficients of this to the left by offset.
    
    Specified by:
    
    shiftLeft in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    offset - shift amount
    
    Returns:
    
    the quotient this / x^offset
  - shiftRight
```
public final lPoly shiftRight(int offset)
```
    Description copied from interface: IUnivariatePolynomial
    
    Multiplies this by the x^offset.
    
    Specified by:
    
    shiftRight in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    offset - monomial exponent
    
    Returns:
    
    this * x^offset
  - truncate
```
public final lPoly truncate(int newDegree)
```
    Description copied from interface: IUnivariatePolynomial
    
    Returns the remainder this rem x^(newDegree + 1), it is polynomial formed by coefficients of this from zero to newDegree (both inclusive)
    
    Specified by:
    
    truncate in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    newDegree - new degree
    
    Returns:
    
    remainder this rem x^(newDegree + 1)
  - reverse
```
public final lPoly reverse()
```
    Description copied from interface: IUnivariatePolynomial
    
    Reverses the coefficients of this
    
    Specified by:
    
    reverse in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    reversed polynomial
  - contentAsPoly
```
public final lPoly contentAsPoly()
```
    Description copied from interface: IPolynomial
    
    Returns the content of this (gcd of coefficients) as a constant poly
    
    Specified by:
    
    contentAsPoly in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
  - primitivePart
```
public final lPoly primitivePart()
```
    Description copied from interface: IPolynomial
    
    Reduces poly to its primitive part (primitive part will always have positive l.c.)
    
    Specified by:
    
    primitivePart in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    primitive part (poly will be modified)
  - primitivePartSameSign
```
public final lPoly primitivePartSameSign()
```
    Description copied from interface: IPolynomial
    
    Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly
    
    Specified by:
    
    primitivePartSameSign in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    primitive part (poly will be modified)
  - evaluate
```
public final long evaluate(long point)
```
    Evaluates this poly at a given point (via Horner method).
    
    Parameters:
    
    point - point
    
    Returns:
    
    value at point
  - composition
```
public final lPoly composition(lPoly value)
```
    Description copied from interface: IUnivariatePolynomial
    
    Calculates the composition of this(oth) (new instance, so the content of this is not changed))
    
    Specified by:
    
    composition in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    value - polynomial
    
    Returns:
    
    composition this(oth)
  - shift
```
public final lPoly shift(long value)
```
    Shifts variable x -> x + value and returns the result (new instance)
    
    Parameters:
    
    value - shift amount
    
    Returns:
    
    a copy of this with x -> x + value
  - monicWithLC
```
public lPoly monicWithLC(lPoly other)
```
    Description copied from interface: IPolynomial
    
    Sets this to its monic part multiplied by the leading coefficient of other;
    
    Specified by:
    
    monicWithLC in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    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
  - add
```
public final lPoly add(long val)
```
    Add constant to this.
    
    Parameters:
    
    val - some number
    
    Returns:
    
    this + val
  - subtract
```
public final lPoly subtract(long val)
```
    Subtract constant from this.
    
    Parameters:
    
    val - some number
    
    Returns:
    
    this + val
  - decrement
```
public final lPoly decrement()
```
    Description copied from interface: IPolynomial
    
    Subtracts 1 from this
    
    Specified by:
    
    decrement in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    this - 1
  - increment
```
public final lPoly increment()
```
    Description copied from interface: IPolynomial
    
    Adds 1 to this
    
    Specified by:
    
    increment in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    this + 1
  - add
```
public final lPoly add(lPoly oth)
```
    Description copied from interface: IPolynomial
    
    Adds oth to this.
    
    Specified by:
    
    add in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this + oth
  - addMonomial
```
public final lPoly addMonomial(long coefficient,
                               int exponent)
```
    Adds coefficient*x^exponent to this
    
    Parameters:
    
    coefficient - monomial coefficient
    
    exponent - monomial exponent
    
    Returns:
    
    this + coefficient*x^exponent
  - addMul
```
public final lPoly addMul(lPoly oth,
                          long factor)
```
    Adds oth * factor to this
    
    Parameters:
    
    oth - the polynomial
    
    factor - the factor
    
    Returns:
    
    this + oth * factor modulo modulus
  - subtract
```
public final lPoly subtract(lPoly oth)
```
    Description copied from interface: IPolynomial
    
    Subtracts oth from this.
    
    Specified by:
    
    subtract in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this - oth
  - subtract
```
public final lPoly subtract(lPoly oth,
                            long factor,
                            int exponent)
```
    Subtracts factor * x^exponent * oth from this
    
    Parameters:
    
    oth - the polynomial
    
    factor - the factor
    
    exponent - the exponent
    
    Returns:
    
    this - factor * x^exponent * oth
  - negate
```
public final lPoly negate()
```
    Description copied from interface: IPolynomial
    
    Negates this and returns
    
    Specified by:
    
    negate in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Returns:
    
    this negated
  - multiplyByLC
```
public lPoly multiplyByLC(lPoly other)
```
    Description copied from interface: IPolynomial
    
    Multiply this by the leading coefficient of other
    
    Specified by:
    
    multiplyByLC in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    other - polynomial
    
    Returns:
    
    this * lc(other)
  - multiply
```
public final lPoly multiply(long factor)
```
    Description copied from interface: IPolynomial
    
    Multiplies this by factor
    
    Specified by:
    
    multiply in interface IPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this * factor
  - getDataReferenceUnsafe
```
public final long[] getDataReferenceUnsafe()
```
    internal API >>> direct unsafe access to internal storage
  - compareTo
```
public final int compareTo(lPoly o)
```
    Specified by:
    
    compareTo in interface Comparable<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - toString
```
public String toString(IStringifier<lPoly> stringifier)
```
    Description copied from interface: Stringifiable
    
    convert this to string with the use of stringifier
    
    Specified by:
    
    toString in interface Stringifiable<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
  - toStringForCopy
```
public String toStringForCopy()
```
  - streamAsPolys
```
public Stream<lPoly> streamAsPolys()
```
    Description copied from interface: IUnivariatePolynomial
    
    Stream polynomial coefficients as constant polynomials
    
    Specified by:
    
    streamAsPolys in interface IUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
  - stream
```
public final LongStream stream()
```
    Returns a sequential Stream with coefficients of this as its source.
    
    Returns:
    
    a sequential Stream over the coefficients in this polynomial
  - mapCoefficients
```
public final <T> UnivariatePolynomial<T> mapCoefficients(Ring<T> ring,
                                                         LongFunction<T> mapper)
```
    Applies transformation function to this and returns the result. This method is equivalent of stream().mapToObj(mapper).collect(new PolynomialCollector<>(ring)).
    
    Type Parameters:
    
    T - result elements type
    
    Parameters:
    
    ring - ring of the new polynomial
    
    mapper - function that maps coefficients of this to coefficients of the result
    
    Returns:
    
    a new polynomial with the coefficients obtained from this by applying mapper
  - equals
```
public final boolean equals(Object obj)
```
    Overrides:
    
    equals in class Object
  - hashCode
```
public final int hashCode()
```
    Overrides:
    
    hashCode in class Object

Class UnivariatePolynomialZ64

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface cc.redberry.rings.poly.univar.IUnivariatePolynomial

Methods inherited from interface cc.redberry.rings.poly.IPolynomial

Method Detail

parse

create

monomial

zero

one

constant

setCoefficientRingFrom

modulus

modulus

modulus

modulus

toBigPoly

mignotteBound

evaluateAtRational

getRange

createArray

createArray2d

createArray2d

sameCoefficientRingWith

createFromArray

createMonomial

isOverField

isOverFiniteField

isOverZ

coefficientRingCardinality

coefficientRingCharacteristic

isOverPerfectPower

coefficientRingPerfectPowerBase

coefficientRingPerfectPowerExponent

content

monic

monic

divideOrNull

divideByLC

multiplyByBigInteger

multiply

square

derivative

clone

parsePoly

coefficientRingToString

composition

asMultivariate

degree

get

set

setLC

firstNonZeroCoefficientPosition

lc

lcAsPoly

ccAsPoly

getAsPoly

cc

ensureInternalCapacity

createMonomial

createLinear

createConstant

createZero

createOne

isZeroAt

setZero

setFrom

isZero

isOne

isMonic

isUnitCC

isConstant

isMonomial

signumOfLC

norm1

norm2

normMax

maxAbsCoefficient

toZero