PHP Class MathPHP\SetTheory\SetAxiomsTest

If all the set logic is implemented properly, these tests should all work out according to the axioms. Axioms tested: - Subsets - Ø ⊆ A - A ⊆ A - A = B iff A ⊆ B and B ⊆ A - Union - A ∪ B = B ∪ A - A ∪ (B ∪ C) = (A ∪ B) ∪ C - A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) - A ∪ (A ∩ B) = A - A ⊆ (A ∪ B) - A ∪ A = A - A ∪ Ø = A - |A ∪ B| = |A| + |B| - |A ∩ B| - Intersection - A ∩ B = B ∩ A - A ∩ (B ∩ C) = (A ∩ B) ∩ C - A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) - A ∩ (A ∪ B) = A - (A ∩ B) ⊆ A - A ∩ A = A - A ∩ Ø = Ø - Complement (difference) - A ∖ B ≠ B ∖ A for A ≠ B - A ∖ A = Ø - Symmetric difference - A Δ B = (A ∖ B) ∪ (B ∖ A) - Cartesian product - A × Ø = Ø - A × (B ∪ C) = (A × B) ∪ (A × C) - (A ∪ B) × C = (A × C) ∪ (B × C) - |A × B| = |A| * |B| - Power set - |S| = n, then |P(S)| = 2ⁿ

Inheritance: extends PHPUnit_Framework_TestCase

Exibir arquivo Open project: markrogoyski/math-php

Public Methods

Method	Description
dataProviderForSingleSet ( )
dataProviderForThreeSets ( )
dataProviderForTwoSets ( )
dataProviderForTwoSetsDifferent ( )
testACartesianProductWithEmptySetIsEmptySet ( Set $A )	Axiom: A × Ø = Ø A cartesian product with empty set is the empty set
testACrossUnsionBCEqualsACrossBUnionACrossC ( Set $A, Set $B, Set $C )	Axiom: A × (B ∪ C) = (A × B) ∪ (A × C) A cross union of B and C is the union of A cross B and A cross C
testADiffBDifferentFromBDiffAWhenNotEqual ( Set $A, Set $B )	Axiom: A ∖ B ≠ B ∖ A for A ≠ B A diff B does not equal B diff A if A and B are different sets
testADiffItselfIsEmptySet ( Set $A )	Axiom: A ∖ A = Ø A diff itself is the empty set
testAIntersectionAEqualsA ( Set $A )	Axiom: A ∩ A = A A intersection A equals A
testAIntersectionBIsSubsetOfA ( Set $A, Set $B )	Axiom: (A ∩ B) ⊆ A A intersect B is a subset of A
testAIntersectionEmptySetIsEmptySet ( Set $A )	Axiom: A ∩ Ø = Ø A union empty set is A
testAIsSubsetOfAUnionB ( Set $A, Set $B )	Axiom: A ⊆ (A ∪ B) A is a subset of A union B
testASymmetricDifferentBEqualsUnionADiffBAndBDiffA ( Set $A, Set $B )	Axiom: A Δ B = (A ∖ B) ∪ (B ∖ A) A symmetric different B equals union of A diff B and B diff A
testAUnionAEqualsA ( Set $A )	Axiom: A ∪ A = A A union A equals A
testAUnionEmptySetEqualsA ( Set $A )	Axiom: A ∪ Ø = A A union empty set is A
testAUnsionBCrossCEqualsUnsionOfACRossCAndBCrossC ( Set $A, Set $B, Set $C )	Axiom: (A ∪ B) × C = (A × C) ∪ (B × C) A union B cross C is the union of A cross C and B cross C
testCardinalityOfCartesianProduct ( Set $A, Set $B )	Axiom: \|A × B\| - \|A\| * \|B\| The cardinality (count) of the cartesian product is the product of the cardinality of A and B
testCardinalityOfPowerSet ( Set $A )	Axiom: \|S\| = n, then \|P(S)\| = 2ⁿ The cardinality (count) of a power set of S is 2ⁿ if the cardinality of S is n.
testCardinalityOfUnion ( Set $A, Set $B )	Axiom: \|A ∪ B\| = \|A\| + \|B\| - \|A ∩ B\| The cardinality (count) of unsion of A and B is equal to the cardinality of A + B minus the cardinality of A intersection B
testEmptySetSubsetOfEverySet ( Set $A )	Axiom: Ø ⊆ A The empty set is a subset of every set
testEqualSetsAreSubsetsInBothDirections ( Set $A )	Axiom: A = B iff A ⊆ B and B ⊆ A Sets are equal if and only if they are both subsets of each other.
testIntersectionAbsorbtion ( Set $A, Set $B )	Axiom: A ∩ (A ∪ B) = A Intersection absorbtion law
testIntersectionAssociative ( Set $A, Set $B, Set $C )	Axiom: A ∩ (B ∩ C) = (A ∩ B) ∩ C Intersection is associative
testIntersectionCommutative ( Set $A, Set $B )	Axiom: A ∩ B = B ∩ A Intersection is commutative
testIntersectionDistributive ( Set $A, Set $B, Set $C )	Axiom: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) Intersection is distributive
testSetIsSubsetOfItself ( Set $A )	Axiom: A ⊆ A Every set is a subset of itself
testUnionAbsorbtion ( Set $A, Set $B )	Axiom: A ∪ (A ∩ B) = A Union absorbtion law
testUnionCommutative ( Set $A, Set $B )	Axiom: A ∪ B = B ∪ A Union is commutative
testUnionDistributive ( Set $A, Set $B, Set $C )	Axiom: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) Union is distributive
testUnsionAssociative ( Set $A, Set $B, Set $C )	Axiom: A ∪ (B ∪ C) = (A ∪ B) ∪ C Unsion is associative

Method Details

dataProviderForSingleSet() public method

public dataProviderForSingleSet ( )

dataProviderForThreeSets() public method

public dataProviderForThreeSets ( )

dataProviderForTwoSets() public method

public dataProviderForTwoSets ( )

dataProviderForTwoSetsDifferent() public method

public dataProviderForTwoSetsDifferent ( )

testACartesianProductWithEmptySetIsEmptySet() public method

Axiom: A × Ø = Ø A cartesian product with empty set is the empty set

public testACartesianProductWithEmptySetIsEmptySet ( Set $A )
$A	Set

testACrossUnsionBCEqualsACrossBUnionACrossC() public method

Axiom: A × (B ∪ C) = (A × B) ∪ (A × C) A cross union of B and C is the union of A cross B and A cross C

public testACrossUnsionBCEqualsACrossBUnionACrossC ( Set $A, Set $B, Set $C )
$A	Set
$B	Set
$C	Set

testADiffBDifferentFromBDiffAWhenNotEqual() public method

Axiom: A ∖ B ≠ B ∖ A for A ≠ B A diff B does not equal B diff A if A and B are different sets

public testADiffBDifferentFromBDiffAWhenNotEqual ( Set $A, Set $B )
$A	Set
$B	Set

testADiffItselfIsEmptySet() public method

Axiom: A ∖ A = Ø A diff itself is the empty set

public testADiffItselfIsEmptySet ( Set $A )
$A	Set

testAIntersectionAEqualsA() public method

Axiom: A ∩ A = A A intersection A equals A

public testAIntersectionAEqualsA ( Set $A )
$A	Set

testAIntersectionBIsSubsetOfA() public method

Axiom: (A ∩ B) ⊆ A A intersect B is a subset of A

public testAIntersectionBIsSubsetOfA ( Set $A, Set $B )
$A	Set
$B	Set

testAIntersectionEmptySetIsEmptySet() public method

Axiom: A ∩ Ø = Ø A union empty set is A

public testAIntersectionEmptySetIsEmptySet ( Set $A )
$A	Set

testAIsSubsetOfAUnionB() public method

Axiom: A ⊆ (A ∪ B) A is a subset of A union B

public testAIsSubsetOfAUnionB ( Set $A, Set $B )
$A	Set
$B	Set

testASymmetricDifferentBEqualsUnionADiffBAndBDiffA() public method

Axiom: A Δ B = (A ∖ B) ∪ (B ∖ A) A symmetric different B equals union of A diff B and B diff A

public testASymmetricDifferentBEqualsUnionADiffBAndBDiffA ( Set $A, Set $B )
$A	Set
$B	Set

testAUnionAEqualsA() public method

Axiom: A ∪ A = A A union A equals A

public testAUnionAEqualsA ( Set $A )
$A	Set

testAUnionEmptySetEqualsA() public method

Axiom: A ∪ Ø = A A union empty set is A

public testAUnionEmptySetEqualsA ( Set $A )
$A	Set

testAUnsionBCrossCEqualsUnsionOfACRossCAndBCrossC() public method

Axiom: (A ∪ B) × C = (A × C) ∪ (B × C) A union B cross C is the union of A cross C and B cross C

public testAUnsionBCrossCEqualsUnsionOfACRossCAndBCrossC ( Set $A, Set $B, Set $C )
$A	Set
$B	Set
$C	Set

testCardinalityOfCartesianProduct() public method

Axiom: |A × B| - |A| * |B| The cardinality (count) of the cartesian product is the product of the cardinality of A and B

public testCardinalityOfCartesianProduct ( Set $A, Set $B )
$A	Set
$B	Set

testCardinalityOfPowerSet() public method

Axiom: |S| = n, then |P(S)| = 2ⁿ The cardinality (count) of a power set of S is 2ⁿ if the cardinality of S is n.

public testCardinalityOfPowerSet ( Set $A )
$A	Set

testCardinalityOfUnion() public method

Axiom: |A ∪ B| = |A| + |B| - |A ∩ B| The cardinality (count) of unsion of A and B is equal to the cardinality of A + B minus the cardinality of A intersection B

public testCardinalityOfUnion ( Set $A, Set $B )
$A	Set
$B	Set

testEmptySetSubsetOfEverySet() public method

Axiom: Ø ⊆ A The empty set is a subset of every set

public testEmptySetSubsetOfEverySet ( Set $A )
$A	Set

testEqualSetsAreSubsetsInBothDirections() public method

Axiom: A = B iff A ⊆ B and B ⊆ A Sets are equal if and only if they are both subsets of each other.

public testEqualSetsAreSubsetsInBothDirections ( Set $A )
$A	Set

testIntersectionAbsorbtion() public method

Axiom: A ∩ (A ∪ B) = A Intersection absorbtion law

public testIntersectionAbsorbtion ( Set $A, Set $B )
$A	Set
$B	Set

testIntersectionAssociative() public method

Axiom: A ∩ (B ∩ C) = (A ∩ B) ∩ C Intersection is associative

public testIntersectionAssociative ( Set $A, Set $B, Set $C )
$A	Set
$B	Set
$C	Set

testIntersectionCommutative() public method

Axiom: A ∩ B = B ∩ A Intersection is commutative

public testIntersectionCommutative ( Set $A, Set $B )
$A	Set
$B	Set

testIntersectionDistributive() public method

Axiom: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) Intersection is distributive

public testIntersectionDistributive ( Set $A, Set $B, Set $C )
$A	Set
$B	Set
$C	Set

testSetIsSubsetOfItself() public method

Axiom: A ⊆ A Every set is a subset of itself

public testSetIsSubsetOfItself ( Set $A )
$A	Set

testUnionAbsorbtion() public method

Axiom: A ∪ (A ∩ B) = A Union absorbtion law

public testUnionAbsorbtion ( Set $A, Set $B )
$A	Set
$B	Set

testUnionCommutative() public method

Axiom: A ∪ B = B ∪ A Union is commutative

public testUnionCommutative ( Set $A, Set $B )
$A	Set
$B	Set

testUnionDistributive() public method

Axiom: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) Union is distributive

public testUnionDistributive ( Set $A, Set $B, Set $C )
$A	Set
$B	Set
$C	Set

testUnsionAssociative() public method

Axiom: A ∪ (B ∪ C) = (A ∪ B) ∪ C Unsion is associative

public testUnsionAssociative ( Set $A, Set $B, Set $C )
$A	Set
$B	Set
$C	Set