Package cc.redberry.rings.poly.univar
Class UnivariatePolynomialZ64
- 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 useUnivariatePolynomial
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
Modifier and Type Method Description lPoly
add(long val)
Add constant to this.lPoly
add(lPoly oth)
Addsoth
tothis
.lPoly
addMonomial(long coefficient, int exponent)
Addscoefficient*x^exponent
tothis
lPoly
addMul(lPoly oth, long factor)
Addsoth * factor
tothis
AMultivariatePolynomial
asMultivariate(Comparator<DegreeVector> ordering)
Convert to multivariate polynomiallong
cc()
Returns the constant coefficient of this polylPoly
ccAsPoly()
Returns the constant coefficient as a constant polyUnivariatePolynomialZ64
clone()
Deep copy of thisBigInteger
coefficientRingCardinality()
Returns cardinality of the coefficient ring of this polyBigInteger
coefficientRingCharacteristic()
Returns characteristic of the coefficient ring of this polyBigInteger
coefficientRingPerfectPowerBase()
Returnsbase
so thatcoefficientRingCardinality() == base^exponent
or null if cardinality is not finiteBigInteger
coefficientRingPerfectPowerExponent()
Returnsexponent
so thatcoefficientRingCardinality() == base^exponent
or null if cardinality is not finiteString
coefficientRingToString(IStringifier<UnivariatePolynomialZ64> stringifier)
String representation of the coefficient ring of thisint
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 valuelong
content()
Returns the content of this poly (gcd of its coefficients)lPoly
contentAsPoly()
Returns the content of this (gcd of coefficients) as a constant polystatic UnivariatePolynomialZ64
create(long... data)
Creates Z[x] polynomial from the specified coefficientsUnivariatePolynomialZ64[]
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 formcc + x * lc
(with the same coefficient ring)lPoly
createMonomial(int degree)
Creates new monomialx^degree
(with the same coefficient ring)UnivariatePolynomialZ64
createMonomial(long coefficient, int degree)
Creates monomialcoefficient * 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 thisint
degree()
Returns the degree of this polynomialUnivariatePolynomialZ64
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 ofother
or returnsnull
(causing loss of internal data) if some of the elements can't be exactly divided by theother.lc()
.UnivariatePolynomialZ64
divideOrNull(long factor)
Divides this polynomial by afactor
or returnsnull
(causing loss of internal data) if some of the elements can't be exactly divided by thefactor
.void
ensureInternalCapacity(int desiredCapacity)
ensures that internal storage has enough size to storedesiredCapacity
elementsboolean
equals(Object obj)
long
evaluate(long point)
Evaluates this poly at a givenpoint
(via Horner method).long
evaluateAtRational(long num, long den)
Evaluates this poly at a given rational pointnum/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 polynomiallong[]
getDataReferenceUnsafe()
internal API >>> direct unsafe access to internal storageUnivariatePolynomialZ64
getRange(int from, int to)
Creates polynomial formed from the coefficients of this starting fromfrom
(inclusive) toto
(exclusive)int
hashCode()
lPoly
increment()
Adds 1 to thisboolean
isConstant()
Returnstrue
if this polynomial has only constant termboolean
isMonic()
Returnstrue
if this polynomial is monicboolean
isMonomial()
Returnstrue
if this polynomial has only one monomial termboolean
isOne()
Returnstrue
if this is oneboolean
isOverField()
Returns whether the coefficient ring of this polynomial is a fieldboolean
isOverFiniteField()
Returns whether the coefficient ring of this polynomial is a finite fieldboolean
isOverPerfectPower()
Returns whether thecoefficientRingCardinality()
is a perfect powerboolean
isOverZ()
Returns whether the coefficient ring of this polynomial is Zboolean
isUnitCC()
Returns true if constant term is equal to oneboolean
isZero()
Returnstrue
if this is zeroboolean
isZeroAt(int i)
Returns whether i-th coefficient of this is zerolong
lc()
Returns the leading coefficient of this polylPoly
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 polydouble
mignotteBound()
Returns Mignotte's bound (sqrt(n+1) * 2^n max |this|)UnivariatePolynomialZp64
modulus(long modulus)
Reduces (copied) polynomial modulomodulus
and returns the result.UnivariatePolynomialZp64
modulus(long modulus, boolean copy)
Reduces this polynomial modulomodulus
and returns the result.UnivariatePolynomialZp64
modulus(IntegersZp64 ring)
Reduces (copied) polynomial modulomodulus
and returns the result.UnivariatePolynomialZp64
modulus(IntegersZp64 ring, boolean copy)
Reduces this polynomial modulomodulus
and returns the result.UnivariatePolynomialZ64
monic()
Setsthis
to its monic part (that isthis
divided by its leading coefficient), or returnsnull
(causing loss of internal data) if some of the elements can't be exactly divided by thelc()
.UnivariatePolynomialZ64
monic(long factor)
Setsthis
to its monic part multiplied by thefactor
;lPoly
monicWithLC(lPoly other)
Setsthis
to its monic part multiplied by the leading coefficient ofother
;static UnivariatePolynomialZ64
monomial(long coefficient, int exponent)
Creates monomialcoefficient * x^exponent
lPoly
multiply(long factor)
Multiplies this byfactor
UnivariatePolynomialZ64
multiply(UnivariatePolynomialZ64 oth)
Multiplies this byoth
UnivariatePolynomialZ64
multiplyByBigInteger(BigInteger factor)
Multiplies this byfactor
lPoly
multiplyByLC(lPoly other)
Multiply this by the leading coefficient ofother
lPoly
negate()
Negates this and returnsdouble
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 polystatic UnivariatePolynomialZ64
one()
Creates unit polynomialstatic UnivariatePolynomialZ64
parse(String string)
Parse string into polynomialUnivariatePolynomialZ64
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 polylPoly
reverse()
Reverses the coefficients of thisboolean
sameCoefficientRingWith(UnivariatePolynomialZ64 oth)
Returns whetheroth
andthis
have the same coefficient ringlPoly
set(int i, long el)
Sets i-th element of this poly with the specified valuelPoly
set(lPoly oth)
Sets the content of this tooth
lPoly
setAndDestroy(lPoly oth)
Sets the content of this withoth
and destroys othUnivariatePolynomialZ64
setCoefficientRingFrom(UnivariatePolynomialZ64 univariatePolynomialZ64)
Set the coefficient ring from specified polylPoly
setFrom(int indexInThis, lPoly poly, int indexInPoly)
Sets i-th element of this by j-th element of other polylPoly
setLC(long lc)
Sets hte leading coefficient of this poly with specified valuelPoly
setZero(int i)
Fills i-th element with zerolPoly
shift(long value)
Shifts variable x -> x + value and returns the result (new instance)lPoly
shiftLeft(int offset)
Returns the quotientthis / x^offset
, it is polynomial with coefficient list formed by shifting coefficients ofthis
to the left byoffset
.lPoly
shiftRight(int offset)
Multipliesthis
by thex^offset
.int
signumOfLC()
Gives signum of the leading coefficientUnivariatePolynomialZ64
square()
Squaresthis
LongStream
stream()
Returns a sequentialStream
with coefficients of this as its source.Stream<lPoly>
streamAsPolys()
Stream polynomial coefficients as constant polynomialslPoly
subtract(long val)
Subtract constant from this.lPoly
subtract(lPoly oth)
Subtractsoth
fromthis
.lPoly
subtract(lPoly oth, long factor, int exponent)
Subtractsfactor * x^exponent * oth
fromthis
UnivariatePolynomial<BigInteger>
toBigPoly()
Converts this to a polynomial over BigIntegersString
toString()
String
toString(IStringifier<lPoly> stringifier)
convert this to string with the use of stringifierString
toStringForCopy()
lPoly
toZero()
Sets this to zerolPoly
truncate(int newDegree)
Returns the remainderthis rem x^(newDegree + 1)
, it is polynomial formed by coefficients of this from zero tonewDegree
(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.IPolynomial
add, assertSameCoefficientRingWith, canonical, coefficientRingToString, copy, createArray, createArray, createArray, monicExact, multiply, multiply, setCoefficientRingFromOptional, subtract, toPositiveLC, toString
-
Methods inherited from interface cc.redberry.rings.poly.univar.IUnivariatePolynomial
asMultivariate, composition, exponents, isLinearExactly, isLinearOrConstant, isZeroCC, mapCoefficientsAsPolys, nNonZeroTerms, size
-
-
-
-
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 monomialcoefficient * x^exponent
- Parameters:
coefficient
- monomial coefficientexponent
- 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 modulomodulus
and returns the result.- Parameters:
modulus
- the moduluscopy
- 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 modulomodulus
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 modulomodulus
and returns the result.- Parameters:
ring
- the moduluscopy
- 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 modulomodulus
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 isRings.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 pointnum/den
- Parameters:
num
- point numeratorden
- 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 fromfrom
(inclusive) toto
(exclusive)- Parameters:
from
- the initial index of the range to be copied, inclusiveto
- 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 whetheroth
andthis
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 monomialcoefficient * x^degree
(with the same coefficient ring)- Parameters:
coefficient
- monomial coefficientdegree
- 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 thecoefficientRingCardinality()
is a perfect power- Returns:
- whether the
coefficientRingCardinality()
is a perfect power
-
coefficientRingPerfectPowerBase
public BigInteger coefficientRingPerfectPowerBase()
Description copied from interface:IPolynomial
Returnsbase
so thatcoefficientRingCardinality() == base^exponent
or null if cardinality is not finite- Returns:
base
so thatcoefficientRingCardinality() == base^exponent
or null if cardinality is not finite
-
coefficientRingPerfectPowerExponent
public BigInteger coefficientRingPerfectPowerExponent()
Description copied from interface:IPolynomial
Returnsexponent
so thatcoefficientRingCardinality() == base^exponent
or null if cardinality is not finite- Returns:
exponent
so thatcoefficientRingCardinality() == 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
Setsthis
to its monic part (that isthis
divided by its leading coefficient), or returnsnull
(causing loss of internal data) if some of the elements can't be exactly divided by thelc()
. NOTE: ifnull
is returned, the content ofthis
is destroyed.- Returns:
- monic
this
ornull
-
monic
public UnivariatePolynomialZ64 monic(long factor)
Setsthis
to its monic part multiplied by thefactor
;- Parameters:
factor
- the factor- Returns:
this
-
divideOrNull
public UnivariatePolynomialZ64 divideOrNull(long factor)
Divides this polynomial by afactor
or returnsnull
(causing loss of internal data) if some of the elements can't be exactly divided by thefactor
. NOTE: isnull
is returned, the content ofthis
is destroyed.- Parameters:
factor
- the factor- Returns:
this
divided by thefactor
ornull
-
divideByLC
public UnivariatePolynomialZ64 divideByLC(UnivariatePolynomialZ64 other)
Description copied from interface:IPolynomial
Divides this polynomial by the leading coefficient ofother
or returnsnull
(causing loss of internal data) if some of the elements can't be exactly divided by theother.lc()
. NOTE: ifnull
is returned, the content ofthis
is destroyed.- Parameters:
other
- the polynomial- Returns:
this
divided by theother.lc()
ornull
if exact division is not possible
-
multiplyByBigInteger
public UnivariatePolynomialZ64 multiplyByBigInteger(BigInteger factor)
Description copied from interface:IPolynomial
Multiplies this byfactor
- Parameters:
factor
- the factor- Returns:
this * factor
-
multiply
public UnivariatePolynomialZ64 multiply(UnivariatePolynomialZ64 oth)
Description copied from interface:IPolynomial
Multiplies this byoth
- Parameters:
oth
- the polynomial- Returns:
this * oth
-
square
public UnivariatePolynomialZ64 square()
Description copied from interface:IPolynomial
Squaresthis
- 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 interfaceIPolynomial<UnivariatePolynomialZ64>
- Specified by:
clone
in interfaceIUnivariatePolynomial<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 interfaceIPolynomial<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 interfaceIUnivariatePolynomial<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 interfaceIPolynomial<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 interfaceIPolynomial<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 interfaceIUnivariatePolynomial<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 storedesiredCapacity
elements- Specified by:
ensureInternalCapacity
in interfaceIUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
-
createMonomial
public final lPoly createMonomial(int degree)
Description copied from interface:IUnivariatePolynomial
Creates new monomialx^degree
(with the same coefficient ring)- Specified by:
createMonomial
in interfaceIUnivariatePolynomial<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 formcc + x * lc
(with the same coefficient ring)- Parameters:
cc
- the constant coefficientlc
- 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 interfaceIPolynomial<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 interfaceIPolynomial<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 interfaceIPolynomial<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 interfaceIUnivariatePolynomial<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 interfaceIUnivariatePolynomial<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 interfaceIUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
- Parameters:
indexInThis
- index in selfpoly
- other polynomialindexInPoly
- index in other polynomial- Returns:
- self
-
isZero
public final boolean isZero()
Description copied from interface:IPolynomial
Returnstrue
if this is zero- Specified by:
isZero
in interfaceIPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
- Returns:
- whether
this
is zero
-
isOne
public final boolean isOne()
Description copied from interface:IPolynomial
Returnstrue
if this is one- Specified by:
isOne
in interfaceIPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
- Returns:
- whether
this
is one
-
isMonic
public final boolean isMonic()
Description copied from interface:IPolynomial
Returnstrue
if this polynomial is monic- Specified by:
isMonic
in interfaceIPolynomial<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 interfaceIPolynomial<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
Returnstrue
if this polynomial has only constant term- Specified by:
isConstant
in interfaceIPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
- Returns:
- whether
this
is constant
-
isMonomial
public final boolean isMonomial()
Description copied from interface:IPolynomial
Returnstrue
if this polynomial has only one monomial term- Specified by:
isMonomial
in interfaceIPolynomial<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 interfaceIPolynomial<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 interfaceIPolynomial<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 tooth
- Specified by:
set
in interfaceIPolynomial<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 withoth
and destroys oth- Specified by:
setAndDestroy
in interfaceIUnivariatePolynomial<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 quotientthis / x^offset
, it is polynomial with coefficient list formed by shifting coefficients ofthis
to the left byoffset
.- Specified by:
shiftLeft
in interfaceIUnivariatePolynomial<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
Multipliesthis
by thex^offset
.- Specified by:
shiftRight
in interfaceIUnivariatePolynomial<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 remainderthis rem x^(newDegree + 1)
, it is polynomial formed by coefficients of this from zero tonewDegree
(both inclusive)- Specified by:
truncate
in interfaceIUnivariatePolynomial<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 interfaceIUnivariatePolynomial<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 interfaceIPolynomial<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 interfaceIPolynomial<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 interfaceIPolynomial<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 givenpoint
(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 interfaceIUnivariatePolynomial<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
Setsthis
to its monic part multiplied by the leading coefficient ofother
;- Specified by:
monicWithLC
in interfaceIPolynomial<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 interfaceIPolynomial<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 interfaceIPolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
- Returns:
this + 1
-
add
public final lPoly add(lPoly oth)
Description copied from interface:IPolynomial
Addsoth
tothis
.- Specified by:
add
in interfaceIPolynomial<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)
Addscoefficient*x^exponent
tothis
- Parameters:
coefficient
- monomial coefficientexponent
- monomial exponent- Returns:
this + coefficient*x^exponent
-
addMul
public final lPoly addMul(lPoly oth, long factor)
Addsoth * factor
tothis
- Parameters:
oth
- the polynomialfactor
- the factor- Returns:
this + oth * factor
modulomodulus
-
subtract
public final lPoly subtract(lPoly oth)
Description copied from interface:IPolynomial
Subtractsoth
fromthis
.- Specified by:
subtract
in interfaceIPolynomial<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)
Subtractsfactor * x^exponent * oth
fromthis
- Parameters:
oth
- the polynomialfactor
- the factorexponent
- 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 interfaceIPolynomial<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 ofother
- Specified by:
multiplyByLC
in interfaceIPolynomial<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 byfactor
- Specified by:
multiply
in interfaceIPolynomial<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 interfaceComparable<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
-
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 interfaceStringifiable<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 interfaceIUnivariatePolynomial<lPoly extends cc.redberry.rings.poly.univar.AUnivariatePolynomial64<lPoly>>
-
stream
public final LongStream stream()
Returns a sequentialStream
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 ofstream().mapToObj(mapper).collect(new PolynomialCollector<>(ring))
.- Type Parameters:
T
- result elements type- Parameters:
ring
- ring of the new polynomialmapper
- function that maps coefficients of this to coefficients of the result- Returns:
- a new polynomial with the coefficients obtained from this by applying
mapper
-
-