Set — Math.js Reference

setCartesian

Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.

Syntax

setCartesian(set1 | set2)

Type Signatures

Array | Matrix, Array | Matrix

Parameters

Name	Type	Description
a1	Array \| Matrix	A (multi)set
a2	Array \| Matrix	A (multi)set

Returns

Array | Matrix — The cartesian product of two (multi)sets

Examples

setCartesian([1
2

See Also

setUnion setIntersect setDifference setPowerset

setDifference

Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.

Syntax

setDifference(set1 | set2)

Type Signatures

Array | Matrix, Array | Matrix

Parameters

Name	Type	Description
a1	Array \| Matrix	A (multi)set
a2	Array \| Matrix	A (multi)set

Returns

Array | Matrix — The difference of two (multi)sets

Examples

setDifference([1
2
3
4

See Also

setUnion setIntersect setSymDifference

setDistinct

Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.

Syntax

setDistinct(set)

Type Signatures

Array | Matrix

Parameters

Name	Type	Description
a	Array \| Matrix	A multiset

Returns

Array | Matrix — A set containing the distinct elements of the multiset

Examples

setDistinct([1
1
1
2
2

See Also

setMultiplicity

setIntersect

Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.

Syntax

setIntersect(set1 | set2)

Type Signatures

Array | Matrix, Array | Matrix

Parameters

Name	Type	Description
a1	Array \| Matrix	A (multi)set
a2	Array \| Matrix	A (multi)set

Returns

Array | Matrix — The intersection of two (multi)sets

Examples

setIntersect([1
2
3
4

See Also

setUnion setDifference

setIsSubset

Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.

Syntax

setIsSubset(set1 | set2)

Type Signatures

Array | Matrix, Array | Matrix

Parameters

Name	Type	Description
a1	Array \| Matrix	A (multi)set
a2	Array \| Matrix	A (multi)set

Returns

boolean — Returns true when a1 is a subset of a2, returns false otherwise

Examples

setIsSubset([1
2

See Also

setUnion setIntersect setDifference

setMultiplicity

Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.

Syntax

setMultiplicity(element | set)

Type Signatures

number | BigNumber | Fraction | Complex, Array | Matrix

Parameters

Name	Type	Description
e	number \| BigNumber \| Fraction \| Complex	An element in the multiset
a	Array \| Matrix	A multiset

Returns

number — The number of how many times the multiset contains the element

Examples

setMultiplicity(1
[1
2
2
4

See Also

setDistinct setSize

setPowerset

Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.

Syntax

setPowerset(set)

Type Signatures

Array | Matrix

Parameters

Name	Type	Description
a	Array \| Matrix	A (multi)set

Returns

Array — The powerset of the (multi)set

Examples

setPowerset([1
2
3

See Also

setCartesian

setSize

Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.

Syntax

setSize(set) | setSize(set | unique)

Type Signatures

Array | Matrix, Array | Matrix, boolean

Parameters

Name	Type	Description
a	Array \| Matrix	A multiset
unique	boolean	If true, only the unique values are counted. False by default

Returns

number — The number of elements of the (multi)set

Examples

setSize([1
2
2
4

See Also

setUnion setIntersect setDifference

setSymDifference

Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.

Syntax

setSymDifference(set1 | set2)

Type Signatures

Array | Matrix, Array | Matrix

Parameters

Name	Type	Description
a1	Array \| Matrix	A (multi)set
a2	Array \| Matrix	A (multi)set

Returns

Array | Matrix — The symmetric difference of two (multi)sets

Examples

setSymDifference([1
2
3
4

See Also

setUnion setIntersect setDifference

setUnion

Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.

Syntax

setUnion(set1 | set2)

Type Signatures

Array | Matrix, Array | Matrix

Parameters

Name	Type	Description
a1	Array \| Matrix	A (multi)set
a2	Array \| Matrix	A (multi)set

Returns

Array | Matrix — The union of two (multi)sets

Examples

setUnion([1
2
3
4

See Also

setIntersect setDifference