The companion object for OrderedEuclideanRing. Import as
import com.alecdorrington.scalgebra.ordered.OrderedEuclideanRing.{*, given}
to receive all necessary syntax for working with ordered Euclidean rings.
Attributes
- Companion
- trait
- Experimental
- true
- Graph
-
- Supertypes
-
trait OrderedEuclideanRingOpstrait OrderedRingOpstrait OrderedSemiringOpstrait OrderedAdditiveGroupOpstrait OrderedAdditiveMonoidOpstrait OrderingOpstrait EuclideanRingOpstrait EuclideanMonoidOpstrait RingOpstrait DifferenceSemiringOpstrait SemiringOpstrait MultiplicativeMonoidOpstrait AdditiveGroupOpstrait AdditiveInverseOpstrait DifferenceMonoidOpstrait AdditiveMonoidOpstrait AdditiveIdentityOpstrait AdditiveSemigroupOpstrait OrderedFieldBuildertrait TupleIsOrderedFieldtrait FractionalIsOrderedFieldtrait SingletonIsOrderedFieldtrait UnitIsOrderedFieldtrait NothingIsOrderedFieldtrait NoneIsOrderedFieldtrait FloatIsOrderedFieldtrait EmptyTupleIsOrderedFieldclass Objecttrait Matchableclass AnyShow all
- Self type
-
OrderedEuclideanRing.type
Members list
Type members
Inherited classlikes
Attributes
- Inherited from:
- BigIntIsOrderedEuclideanRing
- Supertypes
-
trait OrderedEuclideanRing[BigInt]trait OrderedEuclideanMonoid[BigInt]trait OrderedRing[BigInt]trait OrderedDifferenceSemiring[BigInt]trait OrderedSemiring[BigInt]trait OrderedMultiplicativeMonoid[BigInt]trait OrderedMultiplicativeIdentity[BigInt]trait OrderedMultiplicativeSemigroup[BigInt]trait OrderedAdditiveGroup[BigInt]trait OrderedAdditiveInverse[BigInt]trait OrderedDifferenceMonoid[BigInt]trait OrderedAdditiveMonoid[BigInt]trait OrderedAdditiveIdentity[BigInt]trait OrderedAdditiveSemigroup[BigInt]trait Ordering[BigInt]trait PartialOrdering[BigInt]trait Equiv[BigInt]trait Serializabletrait Comparator[BigInt]trait EuclideanRing[BigInt]trait EuclideanMonoid[BigInt]trait Ring[BigInt]trait DifferenceSemiring[BigInt]trait Semiring[BigInt]trait MultiplicativeMonoid[BigInt]trait MultiplicativeIdentity[BigInt]trait MultiplicativeSemigroup[BigInt]trait AdditiveGroup[BigInt]trait AdditiveInverse[BigInt]trait DifferenceMonoid[BigInt]trait AdditiveMonoid[BigInt]trait AdditiveIdentity[BigInt]trait AdditiveSemigroup[BigInt]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- ByteIsOrderedEuclideanRing
- Supertypes
-
trait OrderedEuclideanRing[Byte]trait OrderedEuclideanMonoid[Byte]trait OrderedRing[Byte]trait OrderedDifferenceSemiring[Byte]trait OrderedSemiring[Byte]trait OrderedMultiplicativeMonoid[Byte]trait OrderedMultiplicativeIdentity[Byte]trait OrderedMultiplicativeSemigroup[Byte]trait OrderedAdditiveGroup[Byte]trait OrderedAdditiveInverse[Byte]trait OrderedDifferenceMonoid[Byte]trait OrderedAdditiveMonoid[Byte]trait OrderedAdditiveIdentity[Byte]trait OrderedAdditiveSemigroup[Byte]trait Ordering[Byte]trait PartialOrdering[Byte]trait Equiv[Byte]trait Serializabletrait Comparator[Byte]trait EuclideanRing[Byte]trait EuclideanMonoid[Byte]trait Ring[Byte]trait DifferenceSemiring[Byte]trait Semiring[Byte]trait MultiplicativeMonoid[Byte]trait MultiplicativeIdentity[Byte]trait MultiplicativeSemigroup[Byte]trait AdditiveGroup[Byte]trait AdditiveInverse[Byte]trait DifferenceMonoid[Byte]trait AdditiveMonoid[Byte]trait AdditiveIdentity[Byte]trait AdditiveSemigroup[Byte]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- IntIsOrderedEuclideanRing
- Supertypes
-
trait OrderedEuclideanRing[Int]trait OrderedEuclideanMonoid[Int]trait OrderedRing[Int]trait OrderedDifferenceSemiring[Int]trait OrderedSemiring[Int]trait OrderedMultiplicativeMonoid[Int]trait OrderedMultiplicativeIdentity[Int]trait OrderedMultiplicativeSemigroup[Int]trait OrderedAdditiveGroup[Int]trait OrderedAdditiveInverse[Int]trait OrderedDifferenceMonoid[Int]trait OrderedAdditiveMonoid[Int]trait OrderedAdditiveIdentity[Int]trait OrderedAdditiveSemigroup[Int]trait Ordering[Int]trait PartialOrdering[Int]trait Equiv[Int]trait Serializabletrait Comparator[Int]trait EuclideanRing[Int]trait EuclideanMonoid[Int]trait Ring[Int]trait DifferenceSemiring[Int]trait Semiring[Int]trait MultiplicativeMonoid[Int]trait MultiplicativeIdentity[Int]trait MultiplicativeSemigroup[Int]trait AdditiveGroup[Int]trait AdditiveInverse[Int]trait DifferenceMonoid[Int]trait AdditiveMonoid[Int]trait AdditiveIdentity[Int]trait AdditiveSemigroup[Int]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- LongIsOrderedEuclideanRing
- Supertypes
-
trait OrderedEuclideanRing[Long]trait OrderedEuclideanMonoid[Long]trait OrderedRing[Long]trait OrderedDifferenceSemiring[Long]trait OrderedSemiring[Long]trait OrderedMultiplicativeMonoid[Long]trait OrderedMultiplicativeIdentity[Long]trait OrderedMultiplicativeSemigroup[Long]trait OrderedAdditiveGroup[Long]trait OrderedAdditiveInverse[Long]trait OrderedDifferenceMonoid[Long]trait OrderedAdditiveMonoid[Long]trait OrderedAdditiveIdentity[Long]trait OrderedAdditiveSemigroup[Long]trait Ordering[Long]trait PartialOrdering[Long]trait Equiv[Long]trait Serializabletrait Comparator[Long]trait EuclideanRing[Long]trait EuclideanMonoid[Long]trait Ring[Long]trait DifferenceSemiring[Long]trait Semiring[Long]trait MultiplicativeMonoid[Long]trait MultiplicativeIdentity[Long]trait MultiplicativeSemigroup[Long]trait AdditiveGroup[Long]trait AdditiveInverse[Long]trait DifferenceMonoid[Long]trait AdditiveMonoid[Long]trait AdditiveIdentity[Long]trait AdditiveSemigroup[Long]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- ShortIsOrderedEuclideanRing
- Supertypes
-
trait OrderedEuclideanRing[Short]trait OrderedEuclideanMonoid[Short]trait OrderedRing[Short]trait OrderedDifferenceSemiring[Short]trait OrderedSemiring[Short]trait OrderedMultiplicativeMonoid[Short]trait OrderedMultiplicativeIdentity[Short]trait OrderedMultiplicativeSemigroup[Short]trait OrderedAdditiveGroup[Short]trait OrderedAdditiveInverse[Short]trait OrderedDifferenceMonoid[Short]trait OrderedAdditiveMonoid[Short]trait OrderedAdditiveIdentity[Short]trait OrderedAdditiveSemigroup[Short]trait Ordering[Short]trait PartialOrdering[Short]trait Equiv[Short]trait Serializabletrait Comparator[Short]trait EuclideanRing[Short]trait EuclideanMonoid[Short]trait Ring[Short]trait DifferenceSemiring[Short]trait Semiring[Short]trait MultiplicativeMonoid[Short]trait MultiplicativeIdentity[Short]trait MultiplicativeSemigroup[Short]trait AdditiveGroup[Short]trait AdditiveInverse[Short]trait DifferenceMonoid[Short]trait AdditiveMonoid[Short]trait AdditiveIdentity[Short]trait AdditiveSemigroup[Short]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- DoubleIsOrderedEuclideanRing
- Supertypes
-
trait OrderedField[Double]trait OrderedDifferenceSemifield[Double]trait OrderedSemifield[Double]trait OrderedMultiplicativeGroup[Double]trait OrderedMultiplicativeInverse[Double]trait OrderedEuclideanRing[Double]trait OrderedEuclideanMonoid[Double]trait OrderedRing[Double]trait OrderedDifferenceSemiring[Double]trait OrderedSemiring[Double]trait OrderedMultiplicativeMonoid[Double]trait OrderedMultiplicativeIdentity[Double]trait OrderedMultiplicativeSemigroup[Double]trait OrderedAdditiveGroup[Double]trait OrderedAdditiveInverse[Double]trait OrderedDifferenceMonoid[Double]trait OrderedAdditiveMonoid[Double]trait OrderedAdditiveIdentity[Double]trait OrderedAdditiveSemigroup[Double]trait Ordering[Double]trait PartialOrdering[Double]trait Equiv[Double]trait Serializabletrait Comparator[Double]trait Field[Double]trait DifferenceSemifield[Double]trait Semifield[Double]trait MultiplicativeGroup[Double]trait MultiplicativeInverse[Double]trait EuclideanRing[Double]trait EuclideanMonoid[Double]trait Ring[Double]trait DifferenceSemiring[Double]trait Semiring[Double]trait MultiplicativeMonoid[Double]trait MultiplicativeIdentity[Double]trait MultiplicativeSemigroup[Double]trait AdditiveGroup[Double]trait AdditiveInverse[Double]trait DifferenceMonoid[Double]trait AdditiveMonoid[Double]trait AdditiveIdentity[Double]trait AdditiveSemigroup[Double]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- EmptyTupleIsOrderedField
- Supertypes
-
trait OrderedField[EmptyTuple]trait OrderedDifferenceSemifield[EmptyTuple]trait OrderedSemifield[EmptyTuple]trait OrderedMultiplicativeGroup[EmptyTuple]trait OrderedMultiplicativeInverse[EmptyTuple]trait OrderedEuclideanRing[EmptyTuple]trait OrderedEuclideanMonoid[EmptyTuple]trait OrderedRing[EmptyTuple]trait OrderedDifferenceSemiring[EmptyTuple]trait OrderedSemiring[EmptyTuple]trait OrderedMultiplicativeMonoid[EmptyTuple]trait OrderedMultiplicativeIdentity[EmptyTuple]trait OrderedMultiplicativeSemigroup[EmptyTuple]trait OrderedAdditiveGroup[EmptyTuple]trait OrderedAdditiveInverse[EmptyTuple]trait OrderedDifferenceMonoid[EmptyTuple]trait OrderedAdditiveMonoid[EmptyTuple]trait OrderedAdditiveIdentity[EmptyTuple]trait OrderedAdditiveSemigroup[EmptyTuple]trait Ordering[EmptyTuple]trait PartialOrdering[EmptyTuple]trait Equiv[EmptyTuple]trait Serializabletrait Comparator[EmptyTuple]trait Field[EmptyTuple]trait DifferenceSemifield[EmptyTuple]trait Semifield[EmptyTuple]trait MultiplicativeGroup[EmptyTuple]trait MultiplicativeInverse[EmptyTuple]trait EuclideanRing[EmptyTuple]trait EuclideanMonoid[EmptyTuple]trait Ring[EmptyTuple]trait DifferenceSemiring[EmptyTuple]trait Semiring[EmptyTuple]trait MultiplicativeMonoid[EmptyTuple]trait MultiplicativeIdentity[EmptyTuple]trait MultiplicativeSemigroup[EmptyTuple]trait AdditiveGroup[EmptyTuple]trait AdditiveInverse[EmptyTuple]trait DifferenceMonoid[EmptyTuple]trait AdditiveMonoid[EmptyTuple]trait AdditiveIdentity[EmptyTuple]trait AdditiveSemigroup[EmptyTuple]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- FloatIsOrderedField
- Supertypes
-
trait OrderedField[Float]trait OrderedDifferenceSemifield[Float]trait OrderedSemifield[Float]trait OrderedMultiplicativeGroup[Float]trait OrderedMultiplicativeInverse[Float]trait OrderedEuclideanRing[Float]trait OrderedEuclideanMonoid[Float]trait OrderedRing[Float]trait OrderedDifferenceSemiring[Float]trait OrderedSemiring[Float]trait OrderedMultiplicativeMonoid[Float]trait OrderedMultiplicativeIdentity[Float]trait OrderedMultiplicativeSemigroup[Float]trait OrderedAdditiveGroup[Float]trait OrderedAdditiveInverse[Float]trait OrderedDifferenceMonoid[Float]trait OrderedAdditiveMonoid[Float]trait OrderedAdditiveIdentity[Float]trait OrderedAdditiveSemigroup[Float]trait Ordering[Float]trait PartialOrdering[Float]trait Equiv[Float]trait Serializabletrait Comparator[Float]trait Field[Float]trait DifferenceSemifield[Float]trait Semifield[Float]trait MultiplicativeGroup[Float]trait MultiplicativeInverse[Float]trait EuclideanRing[Float]trait EuclideanMonoid[Float]trait Ring[Float]trait DifferenceSemiring[Float]trait Semiring[Float]trait MultiplicativeMonoid[Float]trait MultiplicativeIdentity[Float]trait MultiplicativeSemigroup[Float]trait AdditiveGroup[Float]trait AdditiveInverse[Float]trait DifferenceMonoid[Float]trait AdditiveMonoid[Float]trait AdditiveIdentity[Float]trait AdditiveSemigroup[Float]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- NoneIsOrderedField
- Supertypes
-
trait Ordering[None.type]trait PartialOrdering[None.type]trait Equiv[None.type]trait Serializabletrait Comparator[None.type]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- NothingIsOrderedField
- Supertypes
-
trait OrderedField[Nothing]trait OrderedDifferenceSemifield[Nothing]trait OrderedSemifield[Nothing]trait OrderedMultiplicativeGroup[Nothing]trait OrderedMultiplicativeInverse[Nothing]trait OrderedEuclideanRing[Nothing]trait OrderedEuclideanMonoid[Nothing]trait OrderedRing[Nothing]trait OrderedDifferenceSemiring[Nothing]trait OrderedSemiring[Nothing]trait OrderedMultiplicativeMonoid[Nothing]trait OrderedMultiplicativeIdentity[Nothing]trait OrderedMultiplicativeSemigroup[Nothing]trait OrderedAdditiveGroup[Nothing]trait OrderedAdditiveInverse[Nothing]trait OrderedDifferenceMonoid[Nothing]trait OrderedAdditiveMonoid[Nothing]trait OrderedAdditiveIdentity[Nothing]trait OrderedAdditiveSemigroup[Nothing]trait Ordering[Nothing]trait PartialOrdering[Nothing]trait Equiv[Nothing]trait Serializabletrait Comparator[Nothing]trait Field[Nothing]trait DifferenceSemifield[Nothing]trait Semifield[Nothing]trait MultiplicativeGroup[Nothing]trait MultiplicativeInverse[Nothing]trait EuclideanRing[Nothing]trait EuclideanMonoid[Nothing]trait Ring[Nothing]trait DifferenceSemiring[Nothing]trait Semiring[Nothing]trait MultiplicativeMonoid[Nothing]trait MultiplicativeIdentity[Nothing]trait MultiplicativeSemigroup[Nothing]trait AdditiveGroup[Nothing]trait AdditiveInverse[Nothing]trait DifferenceMonoid[Nothing]trait AdditiveMonoid[Nothing]trait AdditiveIdentity[Nothing]trait AdditiveSemigroup[Nothing]class Objecttrait Matchableclass AnyShow all
Attributes
- Inherited from:
- UnitIsOrderedField
- Supertypes
-
trait OrderedField[Unit]trait OrderedDifferenceSemifield[Unit]trait OrderedSemifield[Unit]trait OrderedMultiplicativeGroup[Unit]trait OrderedMultiplicativeInverse[Unit]trait OrderedEuclideanRing[Unit]trait OrderedEuclideanMonoid[Unit]trait OrderedRing[Unit]trait OrderedDifferenceSemiring[Unit]trait OrderedSemiring[Unit]trait OrderedMultiplicativeMonoid[Unit]trait OrderedMultiplicativeIdentity[Unit]trait OrderedMultiplicativeSemigroup[Unit]trait OrderedAdditiveGroup[Unit]trait OrderedAdditiveInverse[Unit]trait OrderedDifferenceMonoid[Unit]trait OrderedAdditiveMonoid[Unit]trait OrderedAdditiveIdentity[Unit]trait OrderedAdditiveSemigroup[Unit]trait Ordering[Unit]trait PartialOrdering[Unit]trait Equiv[Unit]trait Serializabletrait Comparator[Unit]trait Field[Unit]trait DifferenceSemifield[Unit]trait Semifield[Unit]trait MultiplicativeGroup[Unit]trait MultiplicativeInverse[Unit]trait EuclideanRing[Unit]trait EuclideanMonoid[Unit]trait Ring[Unit]trait DifferenceSemiring[Unit]trait Semiring[Unit]trait MultiplicativeMonoid[Unit]trait MultiplicativeIdentity[Unit]trait MultiplicativeSemigroup[Unit]trait AdditiveGroup[Unit]trait AdditiveInverse[Unit]trait DifferenceMonoid[Unit]trait AdditiveMonoid[Unit]trait AdditiveIdentity[Unit]trait AdditiveSemigroup[Unit]class Objecttrait Matchableclass AnyShow all
Value members
Concrete methods
The OrderedEuclideanRing instance describing the current algebra system.
Inherited methods
The unique representation of -1 in this algebra system.
The unique representation of the multiplicative identity (1) in this algebra system. Typically corresponds to values such as 1 or 1.0F.
The unique representation of the multiplicative identity (1) in this algebra system. Typically corresponds to values such as 1 or 1.0F.
Attributes
- Inherited from:
- MultiplicativeIdentityOps
The unique representation of 2 in this algebra system.
The unique representation of the additive identity (0) in this algebra system. Typically corresponds to values such as 0, 0.0F, or Seq.empty.
The unique representation of the additive identity (0) in this algebra system. Typically corresponds to values such as 0, 0.0F, or Seq.empty.
Attributes
- Inherited from:
- AdditiveIdentityOps
Givens
Inherited givens
Attributes
- Inherited from:
- TupleIsOrderedEuclideanRing
Attributes
- Inherited from:
- IntegralIsOrderedEuclideanRing
Attributes
- Inherited from:
- BigIntIsOrderedEuclideanRing
Attributes
- Inherited from:
- ByteIsOrderedEuclideanRing
Attributes
- Inherited from:
- IntIsOrderedEuclideanRing
Attributes
- Inherited from:
- LongIsOrderedEuclideanRing
Attributes
- Inherited from:
- ShortIsOrderedEuclideanRing
Attributes
- Inherited from:
- TupleIsOrderedEuclideanRing
Attributes
- Inherited from:
- TupleIsOrderedEuclideanRing
Attributes
- Inherited from:
- TupleIsOrderedEuclideanRing
Attributes
- Inherited from:
- TupleIsOrderedEuclideanRing
Attributes
- Inherited from:
- TupleIsOrderedEuclideanRing
Attributes
- Inherited from:
- TupleIsOrderedField
Attributes
- Inherited from:
- FractionalIsOrderedField
Attributes
- Inherited from:
- DoubleIsOrderedEuclideanRing
Attributes
- Inherited from:
- EmptyTupleIsOrderedField
Attributes
- Inherited from:
- FloatIsOrderedField
Attributes
- Inherited from:
- NoneIsOrderedField
Attributes
- Inherited from:
- NothingIsOrderedField
Attributes
- Inherited from:
- UnitIsOrderedField
Attributes
- Inherited from:
- SingletonIsOrderedField
Extensions
Inherited extensions
Attributes
- Returns
-
trueif the left operand is smaller than the right. - Inherited from:
- OrderingOps
Attributes
- Returns
-
trueif the left operand is not larger than the right. - Inherited from:
- OrderingOps
Attributes
- Returns
-
trueif the right operand is larger than the left. - Inherited from:
- OrderingOps
Attributes
- Returns
-
trueif the right operand is not larger than the left. - Inherited from:
- OrderingOps
Clamps this value to the inclusive range [lb, ub].
Clamps this value to the inclusive range [lb, ub].
Attributes
- Returns
-
lb if this value is less than lb, ub if greater than ub, or this value otherwise.
- Inherited from:
- OrderingOps
Determines the relative order of both operands
Determines the relative order of both operands
Attributes
- Returns
-
-1if in-order (this < x),1if out-of-order (this > x), and0if equal (this == x). - Inherited from:
- OrderingOps
Attributes
- Returns
-
the larger of both operands.
- Inherited from:
- OrderingOps
Attributes
- Returns
-
the smaller of both operands.
- Inherited from:
- OrderingOps
Computes the additive inverse (negative) of this value.
Computes the additive inverse (negative) of this value.
Attributes
- Inherited from:
- AdditiveInverseOps
Attributes
- Returns
-
trueif this value equals zero. - Inherited from:
- AdditiveIdentityOps
Multiplies this value on the left by a strictly positive integer.
Multiplies this value on the left by a strictly positive integer.
Attributes
- Throws
-
IllegalArgumentException
if
n ≤ 0. - Inherited from:
- AdditiveSemigroupOps
Computes the sum of both operands.
Multiplies this value on the right by a strictly positive integer.
Multiplies this value on the right by a strictly positive integer.
Attributes
- Throws
-
IllegalArgumentException
if
n ≤ 0. - Inherited from:
- AdditiveSemigroupOps
Attributes
- Returns
-
trueif this value equals one. - Inherited from:
- MultiplicativeIdentityOps
Computes the signed remainder between both operands.
Computes the difference between both operands.
Computes the product of both operands.
Computes this value raised to the power n, for any strictly positive n.
Computes this value raised to the power n, for any strictly positive n.
Attributes
- Inherited from:
- MultiplicativeSemigroupOps
Computes the quotient between both operands.
Multiplies this value on the left by any integer.
Multiplies this value on the right by any integer.
Multiplies this value on the left by a non-negative integer.
Multiplies this value on the left by a non-negative integer.
Attributes
- Throws
-
IllegalArgumentException
if
n < 0. - Inherited from:
- AdditiveMonoidOps
Multiplies this value on the right by a non-negative integer.
Multiplies this value on the right by a non-negative integer.
Attributes
- Throws
-
IllegalArgumentException
if
n < 0. - Inherited from:
- AdditiveMonoidOps
Computes this value raised to the power n, for any non-negative n.
Computes this value raised to the power n, for any non-negative n.
Attributes
- Inherited from:
- MultiplicativeMonoidOps
Computes the absolute value of this value.