Scalgebra
API
Generated with
Scalgebra/com.alecdorrington.scalgebra

com.alecdorrington.scalgebra

package com.alecdorrington.scalgebra

Members list

Packages

package com.alecdorrington.scalgebra.builder
package com.alecdorrington.scalgebra.connector
package com.alecdorrington.scalgebra.evidence
package com.alecdorrington.scalgebra.ops
package com.alecdorrington.scalgebra.ordered

Type members

Experimental classlikes

trait AdditiveGroup[X] extends DifferenceMonoid[X], AdditiveInverse[X]

For algebraic structures with addition and negation.

For algebraic structures with addition and negation.

Attributes

Companion
object
Experimental
true
Supertypes
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedRing[X]
trait OrderedField[X]
trait Ring[X]
trait EuclideanRing[X]
trait Field[X]
Show all
object AdditiveGroup extends AdditiveGroupBuilder, AdditiveGroupOps

The companion object for AdditiveGroup. Import as

The companion object for AdditiveGroup. Import as

import com.alecdorrington.scalgebra.AdditiveGroup.{*, given}

to receive all necessary syntax for working with additive groups.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait AdditiveIdentity[+X]

For algebraic structures with an additive identity (zero).

For algebraic structures with an additive identity (zero).

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait OrderedRing[X]
trait OrderedField[X]
trait OrderedSemiring[X]
trait OrderedSemifield[X]
trait AdditiveMonoid[X]
trait DifferenceMonoid[X]
trait AdditiveGroup[X]
trait Ring[X]
trait EuclideanRing[X]
trait Field[X]
trait Semiring[X]
trait Semifield[X]
Show all
object AdditiveIdentity extends AdditiveIdentityBuilder, AdditiveIdentityOps

The companion object for AdditiveIdentity. Import as

The companion object for AdditiveIdentity. Import as

import com.alecdorrington.scalgebra.Zero.{*, given}

to receive all necessary syntax for working with zero.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait AdditiveInverse[X]

For algebraic structures with an additive inverse.

For algebraic structures with an additive inverse.

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait OrderedRing[X]
trait OrderedField[X]
trait AdditiveGroup[X]
trait Ring[X]
trait EuclideanRing[X]
trait Field[X]
Show all
object AdditiveInverse extends AdditiveInverseBuilder, AdditiveInverseOps

The companion object for AdditiveInverse. Import as

The companion object for AdditiveInverse. Import as

import com.alecdorrington.scalgebra.AdditiveInverse.{*, given}

to receive all necessary syntax for working with additive inverses.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
object AdditiveMonoid extends AdditiveMonoidBuilder, AdditiveMonoidOps

The companion object for AdditiveMonoid. Import as

The companion object for AdditiveMonoid. Import as

import com.alecdorrington.scalgebra.AdditiveMonoid.{*, given}

to receive all necessary syntax for working with additive monoids.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait AdditiveMonoid[X] extends AdditiveSemigroup[X], AdditiveIdentity[X]

For algebraic structures with addition and an identity.

For algebraic structures with addition and an identity.

Attributes

Companion
object
Experimental
true
Supertypes
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Known subtypes
trait OrderedRing[X]
trait OrderedField[X]
trait OrderedSemiring[X]
trait OrderedSemifield[X]
trait DifferenceMonoid[X]
trait AdditiveGroup[X]
trait Ring[X]
trait EuclideanRing[X]
trait Field[X]
trait Semiring[X]
trait Semifield[X]
Show all
object AdditiveSemigroup extends AdditiveSemigroupBuilder, AdditiveSemigroupOps

The companion object for AdditiveSemigroup. Import as

The companion object for AdditiveSemigroup. Import as

import com.alecdorrington.scalgebra.AdditiveSemigroup.{*, given}

to receive all necessary syntax for working with additive semigroups.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait AdditiveSemigroup[X]

For algebraic structures with an associative addition operator.

For algebraic structures with an associative addition operator.

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait OrderedRing[X]
trait OrderedField[X]
trait OrderedSemiring[X]
trait OrderedSemifield[X]
trait AdditiveMonoid[X]
trait DifferenceMonoid[X]
trait AdditiveGroup[X]
trait Ring[X]
trait EuclideanRing[X]
trait Field[X]
trait Semiring[X]
trait Semifield[X]
Show all
object DifferenceMonoid extends DifferenceMonoidBuilder, DifferenceMonoidOps

The companion object for DifferenceMonoid. Import as

The companion object for DifferenceMonoid. Import as

import com.alecdorrington.scalgebra.DifferenceMonoid.{*, given}

to receive all necessary syntax for working with difference monoids.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait DifferenceMonoid[X] extends AdditiveMonoid[X]

For algebraic structures with addition and subtraction.

For algebraic structures with addition and subtraction.

Attributes

Companion
object
Experimental
true
Supertypes
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedRing[X]
trait OrderedField[X]
trait AdditiveGroup[X]
trait Ring[X]
trait EuclideanRing[X]
trait Field[X]
Show all
object DifferenceSemifield extends DifferenceSemifieldBuilder, DifferenceSemifieldOps

The companion object for DifferenceSemifield. Import as

The companion object for DifferenceSemifield. Import as

import com.alecdorrington.scalgebra.DifferenceSemifield.{*, given}

to receive all necessary syntax for working with difference semifields.

Attributes

Companion
trait
Experimental
true
Supertypes
trait SemifieldOps
trait SemiringOps
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait DifferenceSemifield[X] extends DifferenceSemiring[X], Semifield[X]

For algebraic structures with addition, subtraction, multiplication, and reciprocation.

For algebraic structures with addition, subtraction, multiplication, and reciprocation.

Attributes

Companion
object
Experimental
true
Supertypes
trait Semifield[X]
trait EuclideanMonoid[X]
trait DifferenceMonoid[X]
trait Semiring[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedField[X]
trait Field[X]
Show all
object DifferenceSemiring extends DifferenceSemiringBuilder, DifferenceSemiringOps

The companion object for DifferenceSemiring. Import as

The companion object for DifferenceSemiring. Import as

import com.alecdorrington.scalgebra.DifferenceSemiring.{*, given}

to receive all necessary syntax for working with difference semirings.

Attributes

Companion
trait
Experimental
true
Supertypes
trait SemiringOps
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait DifferenceSemiring[X] extends Semiring[X], DifferenceMonoid[X]

For algebraic structures with addition, subtraction, and multiplication.

For algebraic structures with addition, subtraction, and multiplication.

Attributes

Companion
object
Experimental
true
Supertypes
trait DifferenceMonoid[X]
trait Semiring[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedField[X]
trait OrderedRing[X]
trait Field[X]
trait Ring[X]
trait EuclideanRing[X]
Show all
trait EuclideanMonoid[X] extends MultiplicativeMonoid[X]

For algebraic structures with multiplication and division.

For algebraic structures with multiplication and division.

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedField[X]
trait OrderedSemifield[X]
trait EuclideanRing[X]
trait Field[X]
trait Semifield[X]
Show all
object EuclideanMonoid extends EuclideanMonoidBuilder, EuclideanMonoidOps

The companion object for EuclideanMonoid. Import as

The companion object for EuclideanMonoid. Import as

import com.alecdorrington.scalgebra.EuclideanMonoid.{*, given}

to receive all necessary syntax for working with Euclidean monoids.

Attributes

Companion
trait
Experimental
true
Supertypes
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
object EuclideanRing extends EuclideanRingBuilder, EuclideanRingOps

The companion object for EuclideanRing. Import as

The companion object for EuclideanRing. Import as

import com.alecdorrington.scalgebra.EuclideanRing.{*, given}

to receive all necessary syntax for working with Euclidean rings.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingOps
trait SemiringOps
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait EuclideanRing[X] extends Ring[X], EuclideanMonoid[X]

For algebraic structures with addition, multiplication, and division.

For algebraic structures with addition, multiplication, and division.

Attributes

Companion
object
Experimental
true
Supertypes
trait EuclideanMonoid[X]
trait Ring[X]
trait Semiring[X]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedField[X]
trait Field[X]
Show all
object Field extends FieldBuilder, FieldOps

The companion object for Field. Import as

The companion object for Field. Import as

import com.alecdorrington.scalgebra.Field.{*, given}

to receive all necessary syntax for working with fields.

Attributes

Companion
trait
Experimental
true
Supertypes
trait FieldOps
trait SemifieldOps
trait RingOps
trait SemiringOps
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
Field.type
trait Field[X] extends EuclideanRing[X], DifferenceSemifield[X]

For algebraic structures with addition, multiplication, and inverses.

For algebraic structures with addition, multiplication, and inverses.

Attributes

Companion
object
Experimental
true
Supertypes
trait Semifield[X]
trait EuclideanRing[X]
trait EuclideanMonoid[X]
trait Ring[X]
trait Semiring[X]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedField[X]
Show all
trait MultiplicativeGroup[X] extends EuclideanMonoid[X], MultiplicativeInverse[X]

For algebraic structures with multiplication and reciprocation.

For algebraic structures with multiplication and reciprocation.

Attributes

Companion
object
Experimental
true
Supertypes
trait EuclideanMonoid[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedSemifield[X]
trait OrderedField[X]
trait Semifield[X]
trait Field[X]
Show all
object MultiplicativeGroup extends MultiplicativeGroupBuilder, MultiplicativeGroupOps

The companion object for MultiplicativeGroup. Import as

The companion object for MultiplicativeGroup. Import as

import com.alecdorrington.scalgebra.MultiplicativeGroup.{*, given}

to receive all necessary syntax for working with multiplicative groups.

Attributes

Companion
trait
Experimental
true
Supertypes
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
object MultiplicativeIdentity extends MultiplicativeIdentityBuilder, MultiplicativeIdentityOps

The companion object for MultiplicativeIdentity. Import as

The companion object for MultiplicativeIdentity. Import as

import com.alecdorrington.scalgebra.One.{*, given}

to receive all necessary syntax for working with one.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait MultiplicativeIdentity[+X]

For algebraic structures with a multiplicative identity (one).

For algebraic structures with a multiplicative identity (one).

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait OrderedField[X]
trait OrderedSemifield[X]
trait OrderedSemiring[X]
trait OrderedRing[X]
trait EuclideanMonoid[X]
trait EuclideanRing[X]
trait Field[X]
trait Semifield[X]
trait Semiring[X]
trait Ring[X]
Show all
object MultiplicativeInverse extends MultiplicativeInverseBuilder, MultiplicativeInverseOps

The companion object for MultiplicativeInverse. Import as

The companion object for MultiplicativeInverse. Import as

import com.alecdorrington.scalgebra.MultiplicativeInverse.{*, given}

to receive all necessary syntax for working with multiplicative inverses.

Attributes

Companion
trait
Experimental
true
Supertypes
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait MultiplicativeInverse[X]

For algebraic structures with a multiplicative inverse.

For algebraic structures with a multiplicative inverse.

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait OrderedSemifield[X]
trait OrderedField[X]
trait Semifield[X]
trait Field[X]
Show all
trait MultiplicativeMonoid[X] extends MultiplicativeSemigroup[X], MultiplicativeIdentity[X]

For algebraic structures with multiplication and an identity.

For algebraic structures with multiplication and an identity.

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait OrderedField[X]
trait OrderedSemifield[X]
trait OrderedSemiring[X]
trait OrderedRing[X]
trait EuclideanMonoid[X]
trait EuclideanRing[X]
trait Field[X]
trait Semifield[X]
trait Semiring[X]
trait Ring[X]
Show all
object MultiplicativeMonoid extends MultiplicativeMonoidBuilder, MultiplicativeMonoidOps

The companion object for MultiplicativeMonoid. Import as

The companion object for MultiplicativeMonoid. Import as

import com.alecdorrington.scalgebra.MultiplicativeMonoid.{*, given}

to receive all necessary syntax for working with multiplicative monoids.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
object MultiplicativeSemigroup extends MultiplicativeSemigroupBuilder, MultiplicativeSemigroupOps

The companion object for MultiplicativeSemigroup. Import as

The companion object for MultiplicativeSemigroup. Import as

import com.alecdorrington.scalgebra.MultiplicativeSemigroup.{*, given}

to receive all necessary syntax for working with multiplicative semigroups.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
trait MultiplicativeSemigroup[X]

For algebraic structures with an associative multiplication operator.

For algebraic structures with an associative multiplication operator.

Attributes

Companion
object
Experimental
true
Supertypes
class Object
trait Matchable
class Any
Known subtypes
trait OrderedField[X]
trait OrderedSemifield[X]
trait OrderedSemiring[X]
trait OrderedRing[X]
trait EuclideanMonoid[X]
trait EuclideanRing[X]
trait Field[X]
trait Semifield[X]
trait Semiring[X]
trait Ring[X]
Show all
trait Ring[X] extends AdditiveGroup[X], DifferenceSemiring[X]

For algebraic structures with addition, negation, and multiplication.

For algebraic structures with addition, negation, and multiplication.

Attributes

Companion
object
Experimental
true
Supertypes
trait Semiring[X]
trait AdditiveGroup[X]
trait AdditiveInverse[X]
trait DifferenceMonoid[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedRing[X]
trait OrderedField[X]
trait EuclideanRing[X]
trait Field[X]
Show all
object Ring extends RingBuilder, RingOps

The companion object for Ring. Import as

The companion object for Ring. Import as

import com.alecdorrington.scalgebra.Ring.{*, given}

to receive all necessary syntax for working with rings.

Attributes

Companion
trait
Experimental
true
Supertypes
trait RingOps
trait SemiringOps
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
Ring.type
trait Semifield[X] extends Semiring[X], MultiplicativeGroup[X]

For algebraic structures with addition, multiplication, and reciprocation.

For algebraic structures with addition, multiplication, and reciprocation.

Attributes

Companion
object
Experimental
true
Supertypes
trait EuclideanMonoid[X]
trait Semiring[X]
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedSemifield[X]
trait OrderedField[X]
trait Field[X]
Show all
object Semifield extends SemifieldBuilder, SemifieldOps

The companion object for Semifield. Import as

The companion object for Semifield. Import as

import com.alecdorrington.scalgebra.Semifield.{*, given}

to receive all necessary syntax for working with semifields.

Attributes

Companion
trait
Experimental
true
Supertypes
trait SemifieldOps
trait SemiringOps
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
Semifield.type
trait Semiring[X] extends AdditiveMonoid[X], MultiplicativeMonoid[X]

For algebraic structures with both addition and multiplication.

For algebraic structures with both addition and multiplication.

Attributes

Companion
object
Experimental
true
Supertypes
trait AdditiveMonoid[X]
trait AdditiveIdentity[X]
class Object
trait Matchable
class Any
Show all
Known subtypes
trait OrderedSemiring[X]
trait OrderedField[X]
trait OrderedRing[X]
trait OrderedSemifield[X]
trait Field[X]
trait Ring[X]
trait EuclideanRing[X]
trait Semifield[X]
Show all
object Semiring extends SemiringBuilder, SemiringOps

The companion object for Semiring. Import as

The companion object for Semiring. Import as

import com.alecdorrington.scalgebra.Semiring.{*, given}

to receive all necessary syntax for working with semirings.

Attributes

Companion
trait
Experimental
true
Supertypes
trait SemiringOps
trait RingBuilder
trait FutureIsRing
trait TupleIsRing
trait FieldBuilder
trait TupleIsField
class Object
trait Matchable
class Any
Show all
Self type
Semiring.type
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