root
API
Generated with
root/scas/scas.polynomial/scas.polynomial.tree/MultivariatePolynomial

MultivariatePolynomial

scas.polynomial.tree.MultivariatePolynomial
See theMultivariatePolynomial companion object
trait MultivariatePolynomial[C] extends TreePolynomial[C, Array[Int]], MultivariatePolynomial[Element, C, Array[Int]], Conv[Element[C, Array[Int]]]

Attributes

Companion
object
Graph
Supertypes
trait Conv[Element[C, Array[Int]]]
trait Conv[Element[C, Array[Int]]]
trait Conv[Element[C, Array[Int]]]
trait Conv[Element[C, Array[Int]]]
trait Conv[Element[C, Array[Int]]]
trait Conv[Element[C, Array[Int]]]
trait Conv[Element[C, Array[Int]]]
trait MultivariatePolynomial[Element, C, Array[Int]]
trait PolynomialOverUFD[Element[C, Array[Int]], C, Array[Int]]
trait UniqueFactorizationDomain[Element[C, Array[Int]]]
trait NotQuiteField[Element[C, Array[Int]]]
trait TreePolynomial[C, Array[Int]]
trait Polynomial[Element[C, Array[Int]], C, Array[Int]]
trait AlgebraOverRing[Element[C, Array[Int]], C]
trait Module[Element[C, Array[Int]], C]
trait Ring[Element[C, Array[Int]]]
trait Monoid[Element[C, Array[Int]]]
trait SemiGroup[Element[C, Array[Int]]]
trait AbelianGroup[Element[C, Array[Int]]]
trait Structure[Element[C, Array[Int]]]
trait Show[Element[C, Array[Int]]]
trait Equiv[Element[C, Array[Int]]]
trait Equiv[Element[C, Array[Int]]]
trait Serializable
class Object
trait Matchable
class Any
Show all
Known subtypes

Members list

Value members

Abstract methods

def variables: Seq[Variable]

Inherited methods

def abs[U : Conversion[Element[C, Array[Int]]]](x: U): Element[C, Array[Int]]

Attributes

Inherited from:
AbelianGroup
def abs(x: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
AbelianGroup
def apply(s: (Array[Int], C)*): Element[C, Array[Int]]

Attributes

Inherited from:
TreePolynomial
def apply(m: Array[Int], c: C): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def apply(value: Array[Int]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def apply(value: C): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def characteristic: BigInteger

Attributes

Inherited from:
Polynomial
def content(x: Element[C, Array[Int]]): C

Attributes

Inherited from:
PolynomialOverUFD
def contentAndPrimitivePart(x: Element[C, Array[Int]]): (C, Element[C, Array[Int]])

Attributes

Inherited from:
PolynomialOverUFD
def equiv(x: Element[C, Array[Int]], y: Element[C, Array[Int]]): Boolean

Attributes

Inherited from:
Polynomial
def equiv(x: (Array[Int], C), y: (Array[Int], C)): Boolean

Attributes

Inherited from:
Polynomial
def fenced(s: String): String

Attributes

Inherited from:
Structure
def fromInt[U : Conversion[BigInteger]](x: U): Element[C, Array[Int]]

Attributes

Inherited from:
Ring
def fromInt(n: BigInteger): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def gcd[U : Conversion[Element[C, Array[Int]]], V : Conversion[Element[C, Array[Int]]]](x: U, y: V): Element[C, Array[Int]]

Attributes

Inherited from:
UniqueFactorizationDomain
def gcd(x: Element[C, Array[Int]], y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial
def generator(n: Int): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def generators: List[Element[C, Array[Int]]]

Attributes

Inherited from:
Polynomial
def lcm[U : Conversion[Element[C, Array[Int]]], V : Conversion[Element[C, Array[Int]]]](x: U, y: V): Element[C, Array[Int]]

Attributes

Inherited from:
UniqueFactorizationDomain
def lcm(x: Element[C, Array[Int]], y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
UniqueFactorizationDomain
def modifiable(x: Element[C, Array[Int]]): TreeMap[Array[Int], C]

Attributes

Inherited from:
TreePolynomial
override def normalize(x: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Definition Classes
Inherited from:
PolynomialOverUFD
def primitivePart(x: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
PolynomialOverUFD
def random(numbits: Int)(using rnd: Random): Element[C, Array[Int]]

Attributes

Inherited from:
Structure
def s_polynomial(x: Element[C, Array[Int]], y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def same(s: Element[C, Array[Int]]*): Unit

Attributes

Inherited from:
Polynomial
def toMathML: String

Attributes

Inherited from:
Polynomial
def toMathML(fenced: Boolean): String

Attributes

Inherited from:
Polynomial
override def toString: String

Returns a string representation of the object.

Returns a string representation of the object.

The default representation is platform dependent.

Attributes

Returns

a string representation of the object.

Definition Classes
Polynomial -> Any
Inherited from:
Polynomial
def unmodifiable(x: Element[C, Array[Int]]): SortedMap[Array[Int], C]

Attributes

Inherited from:
TreePolynomial

Inherited and Abstract methods

def gcd1(x: Element[C, Array[Int]], y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial
def newInstance: [C] => (x$1: UniqueFactorizationDomain[C], x$2: PowerProduct[Array[Int]]) => MultivariatePolynomial[Element, C, Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial

Inherited fields

val drop: PowerProduct[Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial
override val one: Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
val take: PowerProduct[Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial
override val zero: Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial

Givens

Givens

override given pp: PowerProduct[Array[Int]]

Inherited givens

given bigInt2ring[U : Conversion[BigInteger]]: U => Element[C, Array[Int]]

Attributes

Inherited from:
Ring
given coef2poly[D : Conversion[C]]: D => Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial

Inherited and Abstract givens

given ring: UniqueFactorizationDomain[C]

Attributes

Inherited from:
PolynomialOverUFD

Extensions

Inherited extensions

extension (a: Element[C, Array[Int]])
def \[U : Conversion[BigInteger]](b: U): Element[C, Array[Int]]

Attributes

Inherited from:
Monoid
def \:[U : Conversion[BigInteger]](b: U): Element[C, Array[Int]]

Attributes

Inherited from:
Monoid
def pow(b: BigInteger): Element[C, Array[Int]]

Attributes

Inherited from:
Monoid
extension [U : Conversion[Element[C, Array[Int]]]](a: U)
def \[V : Conversion[BigInteger]](b: V): Element[C, Array[Int]]

Attributes

Inherited from:
Conv
extension [U : Conversion[Element[C, Array[Int]]], V : Conversion[BigInteger]](a: U)
def \:(b: V): Element[C, Array[Int]]

Attributes

Inherited from:
Conv
extension (c: C)
def multiplyLeft(x: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
extension (ring: UniqueFactorizationDomain[C])
def apply(s: Element[C, Array[Int]]*): PolynomialOverUFD[Element[C, Array[Int]], C, Array[Int]]

Attributes

Inherited from:
PolynomialOverUFD
extension (ring: Ring[C])
def apply(s: Element[C, Array[Int]]*): Polynomial[Element[C, Array[Int]], C, Array[Int]]

Attributes

Inherited from:
Polynomial
extension (ring: Ring[C])
def pow(n: Int): Module[Element[C, Array[Int]], C]

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
inline def <>[U : Conversion[Element[C, Array[Int]]]](y: U): Boolean

Attributes

Inherited from:
Equiv
inline def ><[U : Conversion[Element[C, Array[Int]]]](y: U): Boolean

Attributes

Inherited from:
Equiv
extension (x: Element[C, Array[Int]])
inline def /[U : Conversion[Element[C, Array[Int]]]](y: U): Element[C, Array[Int]]

Attributes

Inherited from:
NotQuiteField
extension (x: Element[C, Array[Int]])
inline def *[U : Conversion[Element[C, Array[Int]]]](y: U): Element[C, Array[Int]]

Attributes

Inherited from:
SemiGroup
extension (x: Element[C, Array[Int]])
inline def +[U : Conversion[Element[C, Array[Int]]]](y: U): Element[C, Array[Int]]

Attributes

Inherited from:
AbelianGroup
inline def -[U : Conversion[Element[C, Array[Int]]]](y: U): Element[C, Array[Int]]

Attributes

Inherited from:
AbelianGroup
def unary_-: Element[C, Array[Int]]

Attributes

Inherited from:
AbelianGroup
extension (x: Element[C, Array[Int]])
def show: String

Attributes

Inherited from:
Structure
extension [U : Conversion[C]](x: U)
def *%(y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
Module
extension [U : Conversion[Element[C, Array[Int]]]](x: U)
inline def <>[V : Conversion[Element[C, Array[Int]]]](y: V): Boolean

Attributes

Inherited from:
Conv
inline def ><[V : Conversion[Element[C, Array[Int]]]](y: V): Boolean

Attributes

Inherited from:
Conv
extension [U : Conversion[Element[C, Array[Int]]]](x: U)
inline def /[V : Conversion[Element[C, Array[Int]]]](y: V): Element[C, Array[Int]]

Attributes

Inherited from:
Conv
extension [U : Conversion[Element[C, Array[Int]]]](x: U)
inline def *[V : Conversion[Element[C, Array[Int]]]](y: V): Element[C, Array[Int]]

Attributes

Inherited from:
Conv
extension (x: Element[C, Array[Int]])
inline def %[U : Conversion[Element[C, Array[Int]]]](y: U): Element[C, Array[Int]]

Attributes

Inherited from:
UniqueFactorizationDomain
inline def /%[U : Conversion[Element[C, Array[Int]]]](y: U): (Element[C, Array[Int]], Element[C, Array[Int]])

Attributes

Inherited from:
UniqueFactorizationDomain
def divide(y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
UniqueFactorizationDomain
def factorOf(y: Element[C, Array[Int]]): Boolean

Attributes

Inherited from:
UniqueFactorizationDomain
def remainder(y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
UniqueFactorizationDomain
inline def |[U : Conversion[Element[C, Array[Int]]]](y: U): Boolean

Attributes

Inherited from:
UniqueFactorizationDomain
extension (x: Element[C, Array[Int]])
def %/(c: C): Element[C, Array[Int]]

Attributes

Inherited from:
PolynomialOverUFD
def divideAndRemainder(y: Element[C, Array[Int]]): (Element[C, Array[Int]], Element[C, Array[Int]])

Attributes

Inherited from:
PolynomialOverUFD
def divideRight(c: C): Element[C, Array[Int]]

Attributes

Inherited from:
PolynomialOverUFD
override def factorOf(s: Array[Int], a: C, strict: Boolean): Boolean

Attributes

Definition Classes
Inherited from:
PolynomialOverUFD
override def reduce(m: Array[Int], a: C, y: Element[C, Array[Int]], b: C, strict: Boolean): Element[C, Array[Int]]

Attributes

Definition Classes
Inherited from:
PolynomialOverUFD
override def reduce(strict: Boolean, tail: Boolean, ys: Element[C, Array[Int]]*): Element[C, Array[Int]]

Attributes

Definition Classes
Inherited from:
PolynomialOverUFD
def remainder(ys: Element[C, Array[Int]]*): Element[C, Array[Int]]

Attributes

Inherited from:
PolynomialOverUFD
extension (x: Element[C, Array[Int]])
def add(y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
TreePolynomial
extension (x: Element[C, Array[Int]])
def isOne: Boolean

Attributes

Inherited from:
Monoid
extension [U : Conversion[Element[C, Array[Int]]]](x: U)
inline def +[V : Conversion[Element[C, Array[Int]]]](y: V): Element[C, Array[Int]]

Attributes

Inherited from:
Conv
inline def -[V : Conversion[Element[C, Array[Int]]]](y: V): Element[C, Array[Int]]

Attributes

Inherited from:
Conv
extension (x: Element[C, Array[Int]])
override def coefficient(m: Array[Int]): C

Attributes

Definition Classes
Inherited from:
TreePolynomial
def getOrElse(m: Array[Int], c: C): C

Attributes

Inherited from:
TreePolynomial
def head: (Array[Int], C)

Attributes

Inherited from:
TreePolynomial
override def isZero: Boolean

Attributes

Definition Classes
Inherited from:
TreePolynomial
override def iterator(m: Array[Int]): Iterator[(Array[Int], C)]

Attributes

Definition Classes
Inherited from:
TreePolynomial
def iterator: Iterator[(Array[Int], C)]

Attributes

Inherited from:
TreePolynomial
def last: (Array[Int], C)

Attributes

Inherited from:
TreePolynomial
def map(f: (Array[Int], C) => (Array[Int], C)): Element[C, Array[Int]]

Attributes

Inherited from:
TreePolynomial
def size: Int

Attributes

Inherited from:
TreePolynomial
override def sort: Element[C, Array[Int]]

Attributes

Definition Classes
Inherited from:
TreePolynomial
override def toSeq: Seq[(Array[Int], C)]

Attributes

Definition Classes
Inherited from:
TreePolynomial
extension (x: Element[C, Array[Int]])
def signum: Int

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
def convert(from: PowerProduct[Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial
extension (x: Element[C, Array[Int]])
def subtract(y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
def convertTo(using p: MultivariatePolynomial[Element, C, Array[Int]], s: MultivariatePolynomial[Element, Element[C, Array[Int]], Array[Int]]): Element[Element[C, Array[Int]], Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial
extension [U : Conversion[Element[C, Array[Int]]]](x: U)
inline def %[V : Conversion[Element[C, Array[Int]]]](y: V): Element[C, Array[Int]]

Attributes

Inherited from:
Conv
inline def /%[V : Conversion[Element[C, Array[Int]]]](y: V): (Element[C, Array[Int]], Element[C, Array[Int]])

Attributes

Inherited from:
Conv
inline def |[V : Conversion[Element[C, Array[Int]]]](y: V): Boolean

Attributes

Inherited from:
Conv
extension (x: Element[Element[C, Array[Int]], Array[Int]])
def convertFrom(s: MultivariatePolynomial[Element, Element[C, Array[Int]], Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
MultivariatePolynomial
extension (x: Element[C, Array[Int]])
def isUnit: Boolean

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
override def %*[U : Conversion[C]](y: U): Element[C, Array[Int]]

Attributes

Definition Classes
Inherited from:
Polynomial
def %*(m: Array[Int]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def multiply(y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
def toCode(level: Level): String

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
def toCode(level: Level, plus: String, times: String): String

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
def toMathML: String

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
def toMathML(plus: String, times: String): String

Attributes

Inherited from:
Polynomial
extension (x: Element[C, Array[Int]])
def coefOne: Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def coefficient(y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def degree: BigInteger

Attributes

Inherited from:
Polynomial
def headCoefficient: C

Attributes

Inherited from:
Polynomial
def headPowerProduct: Array[Int]

Attributes

Inherited from:
Polynomial
def lastCoefficient: C

Attributes

Inherited from:
Polynomial
def multiply(m: Array[Int], c: C): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def multiplyRight(c: C): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
final def reduce(strict: Boolean, m: Array[Int], ys: Element[C, Array[Int]]*): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
final def reduce(strict: Boolean, ys: Element[C, Array[Int]]*): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def reduce(ys: Element[C, Array[Int]]*): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial
def reverseIterator: Iterator[(Array[Int], C)]

Attributes

Inherited from:
Polynomial
def subtract(m: Array[Int], c: C, y: Element[C, Array[Int]]): Element[C, Array[Int]]

Attributes

Inherited from:
Polynomial

Exports

Inherited defined exports

final val Level: Level
Exported from prettyprint

Attributes

Inherited from:
Structure
final type Level = Level
Exported from prettyprint

Attributes

Inherited from:
Structure
Generated with