Module org.meeuw.math.abstractalgebra.test

Package org.meeuw.theories.abstractalgebra

Interface VectorSpaceTheory<V extends Vector<V,S>,S extends ScalarFieldElement<S>>

All Superinterfaces:

AbelianRingTheory<V>, AdditiveAbelianGroupTheory<V>, AdditiveAbelianSemiGroupTheory<V>, AdditiveGroupTheory<V>, AdditiveMonoidTheory<V>, AdditiveSemiGroupTheory<V>, AlgebraicStructureTheory<V>, BasicObjectTheory<V>, ElementTheory<V>, MagmaTheory<V>, MultiplicativeMonoidTheory<V>, MultiplicativeSemiGroupTheory<V>, RingTheory<V>, RngTheory<V>

public interface VectorSpaceTheory<V extends Vector<V,S>,S extends ScalarFieldElement<S>>
extends AbelianRingTheory<V>

Since:

0.4

Author:

Michiel Meeuwissen

Field Summary

Fields inherited from interface org.meeuw.theories.abstractalgebra.AlgebraicStructureTheory

COUNTS, ERROR_COUNTS, ERROR_UCOUNTS, STRUCTURE, UCOUNTS

Fields inherited from interface org.meeuw.theories.BasicObjectTheory

DATAPOINTS, DATAPOINTS_OR_NULL, EQUAL_DATAPOINTS, RANDOMS

Fields inherited from interface org.meeuw.theories.abstractalgebra.ElementTheory

ELEMENTS

Method Summary

Modifier and Type	Method	Description
default void	associativity(V v1, V v2, V v3)
default void	commutativity(V v1, V v2)
default void	compatibility(V v, S a, S b)
default void	dimension(V v1)
default void	dotCommutative(V a, V b)
default void	dotDistributive(V a, V b, V c)
default void	negation(V v1)
default void	scalarDistributivity(V v, S e1, S e2)
default void	scalarIdentity(V v)
net.jqwik.api.Arbitrary<? extends S>	scalars()
default void	space(V v1, V v2)
default void	vectorDistributivity(V v1, V v2, S e)
default void	vectorToString(V v1)

Methods inherited from interface org.meeuw.theories.abstractalgebra.AbelianRingTheory

ringCommutative

Methods inherited from interface org.meeuw.theories.abstractalgebra.AdditiveAbelianGroupTheory

minusIsAnticommutative

Methods inherited from interface org.meeuw.theories.abstractalgebra.AdditiveAbelianSemiGroupTheory

additiveCommutativity, additiveCommutativityProperty

Methods inherited from interface org.meeuw.theories.abstractalgebra.AdditiveGroupTheory

additiveGroupOperators, minus, repeatedPlusNegativeTimes, repeatedPlusOneTimes, repeatedPlusPositiveTimes, repeatedPlusZeroTimes

Methods inherited from interface org.meeuw.theories.abstractalgebra.AdditiveMonoidTheory

zero

Methods inherited from interface org.meeuw.theories.abstractalgebra.AdditiveSemiGroupTheory

additionCommutativity, additiveAssociativity, additiveSemiGroupOperators

Methods inherited from interface org.meeuw.theories.abstractalgebra.AlgebraicStructureTheory

algebraicBinaryOperators, algebraicIntOperations, algebraicUnaryOperators, cardinalityAndStreaming, cast, castDirectly, cayleyTables, elementClass, eqMethod, examples, functions, getComparisonOperators, nextRandom, singleton, staticOperators, staticUnaryOperators, structure, structureSameInstance, toStringForStructure, uncertain

Methods inherited from interface org.meeuw.theories.BasicObjectTheory

datapointsOrNull, equalDatapoints, equals, equalsIsConsistent, equalsIsReflexive, equalsIsSymmetric, equalsIsTransitive, equalsReturnFalseOnNull, equalsReturnFalseOnOtherObject, hashCodeIsConsistentWithEquals, hashCodeIsSelfConsistent, log, randoms, toString

Methods inherited from interface org.meeuw.theories.abstractalgebra.ElementTheory

datapoints, elements, getLogger, setupForAll

Methods inherited from interface org.meeuw.theories.abstractalgebra.MagmaTheory

magmaOperators, operatorAndCommutativity

Methods inherited from interface org.meeuw.theories.abstractalgebra.MultiplicativeMonoidTheory

isOne, one, pow0

Methods inherited from interface org.meeuw.theories.abstractalgebra.MultiplicativeSemiGroupTheory

multiplicationCommutativity, multiplicativeAssociativity, multiplicativeSemiGroupOperators, pow1, pow2, pow3, powNegative1, powNegative2, powNegative3, sqr

Methods inherited from interface org.meeuw.theories.abstractalgebra.RingTheory

distributivity

Methods inherited from interface org.meeuw.theories.abstractalgebra.RngTheory

rngOperators

Method Details

dimension

@Property
default void dimension(@ForAll("elements")
 V v1)

vectorToString

@Property
default void vectorToString(@ForAll("elements")
 V v1)

space

@Property
default void space(@ForAll("elements")
 V v1,
 @ForAll("elements")
 V v2)

associativity

@Property
default void associativity(@ForAll("elements")
 V v1,
 @ForAll("elements")
 V v2,
 @ForAll("elements")
 V v3)

commutativity

@Property
default void commutativity(@ForAll("elements")
 V v1,
 @ForAll("elements")
 V v2)

negation

@Property
default void negation(@ForAll("elements")
 V v1)

compatibility

@Property
default void compatibility(@ForAll("elements")
 V v,
 @ForAll("scalars")
 S a,
 @ForAll("scalars")
 S b)

scalarIdentity

@Property
default void scalarIdentity(@ForAll("elements")
 V v)

vectorDistributivity

@Property
default void vectorDistributivity(@ForAll("elements")
 V v1,
 @ForAll("elements")
 V v2,
 @ForAll("scalars")
 S e)

scalarDistributivity

@Property
default void scalarDistributivity(@ForAll("elements")
 V v,
 @ForAll("scalars")
 S e1,
 @ForAll("scalars")
 S e2)

dotCommutative

@Property
default void dotCommutative(@ForAll("elements")
 V a,
 @ForAll("elements")
 V b)

dotDistributive

@Property
default void dotDistributive(@ForAll("elements")
 V a,
 @ForAll("elements")
 V b,
 @ForAll("elements")
 V c)

scalars

@Provide
net.jqwik.api.Arbitrary<? extends S> scalars()