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Complement[eall,e1,e2,…]

gives the elements in eall that are not in any of the ei.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Generalizations & Extensions  
Options  
SameTest  
Applications  
Properties & Relations  
See Also
Tech Notes
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Complement

Complement[eall,e1,e2,…]

gives the elements in eall that are not in any of the ei.

Details and Options

  • The list returned by Complement is sorted into standard order.
  • Complement[eall,e1,…,SameTest->test] applies test to each pair of elements in eall and the ei to determine whether they should be considered the same.

Examples

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Basic Examples  (1)

Find which elements in the first list are not in any of the subsequent lists:

Wolfram Language code: Complement[{a, b, c, d, e}, {a, c}, {d}]

Generalizations & Extensions  (1)

Complement works with any head, not just List:

Wolfram Language code: Complement[f[a, b, c, d], f[c, a], f[b, b, a]]

Options  (3)

SameTest  (3)

Use equivalence classes based on absolute value:

Wolfram Language code: Complement[{2, -2, 1, 3}, {2, 1, -2, -1}, SameTest -> (Abs[#1] == Abs[#2]&)]

Use equivalence classes based on Floor:

Wolfram Language code: Complement[{1.1, 3.4, .5, 7.6, 7.1, 1.9}, {1.2, 3.3, 1.3}, SameTest -> (Floor[#1] == Floor[#2]&)]

Use Total of list elements:

Wolfram Language code: Complement[{{1, 2}, {3}, {4, 5, 6}, {9, 5}}, {{2, 1}, {8, 4, 3}}, SameTest -> (Total[#1] == Total[#2]&)]

Applications  (4)

Find divisors of 20 that are not also divisors of 12:

Wolfram Language code: Complement[Divisors[20], Divisors[12]]

Find which triples of digits do not occur in the binary decomposition of 12345:

Wolfram Language code: Complement[Tuples[{0, 1}, 3], Partition[IntegerDigits[12345, 2], 3, 1]]

Find which options to Plot are not also options to Graphics:

Wolfram Language code: Complement[First /@ Options[Plot], First /@ Options[Graphics]]

Find which length-5 sequences never occur after 2 steps in any elementary cellular automaton:

Wolfram Language code: Complement[Tuples[{0, 1}, 5], Table[Last[CellularAutomaton[i, {{1}, 0}, {2, All}]], {i, 0, 255}]]

Properties & Relations  (1)

The result of Complement[list1,list2] is sorted and does not contain repeated elements:

Wolfram Language code: Complement[{b, e, d, a, b, c, d}, {b, c}]

This returns the same elements, but preserving the original order and multiplicity in list1:

Wolfram Language code: DeleteCases[{b, e, d, a, b, c, d}, Alternatives@@{b, c}]

Use DeleteDuplicates to preserve order but remove multiplicity:

Wolfram Language code: DeleteDuplicates[%]
Wolfram Research (1988), Complement, Wolfram Language function, https://reference.wolfram.com/language/ref/Complement.html (updated 1996).

Text

Wolfram Research (1988), Complement, Wolfram Language function, https://reference.wolfram.com/language/ref/Complement.html (updated 1996).

CMS

Wolfram Language. 1988. "Complement." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Complement.html.

APA

Wolfram Language. (1988). Complement. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Complement.html

BibTeX

@misc{reference.wolfram_2026_complement, author="Wolfram Research", title="{Complement}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Complement.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_complement, organization={Wolfram Research}, title={Complement}, year={1996}, url={https://reference.wolfram.com/language/ref/Complement.html}, note=[Accessed: 12-June-2026]}