WOLFRAM

Wolfram Language & System Documentation Center

SameTest

is an option whose setting gives a pairwise comparison function to determine whether expressions should be considered the same.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
See Also
Related Guides
History
Cite this Page

SameTest

SameTest

is an option whose setting gives a pairwise comparison function to determine whether expressions should be considered the same.

Details

  • SameTest->f specifies that f[e1,e2] should be evaluated whenever it is necessary to determine whether pairs of expressions e1, e2 should be considered the same.

Examples

open all close all

Basic Examples  (2)

Union of a set of integers:

Wolfram Language code: Union[{0, 3, 2, 4, 2, 0, 2, -5, 2, 0}]

Union considering comparison modulo 3:

Wolfram Language code: Union[{0, 3, 2, 4, 2, 0, 2, -5, 2, 0}, SameTest -> (Mod[#1, 3] == Mod[#2, 3]&)]

Find a fixed point to a tolerance:

Wolfram Language code: FixedPointList[# / 2 + 1 / #&, 1., SameTest -> (Abs[#1 - #2] < 10 ^ -4&)]

Scope  (5)

Union of a set of machine-precision numbers:

Wolfram Language code: Union[{0., 10.^-13, 2., 2. - 10^-13, 2. + 3 10^-15, 10.^-14}]

Union treating roundoff errors of order 10-12 as zeros:

Wolfram Language code: Union[{0., 10.^-13, 2., 2. - 10^-13, 2. + 3 10^-15, 10.^-14}, SameTest -> (Abs[#1 - #2] ≤ 10^-12&)]

Alternately, use Chop:

Wolfram Language code: Union[{0., 10.^-13, 2., 2. - 10^-13, 2. + 3 10^-15, 10.^-14}, SameTest -> (Chop[#1 - #2, 10^-12] == 0&)]

Intersection of two sets of integers:

Wolfram Language code: Intersection[{0, 3, 5, 2}, {0, 2, 5}]

Intersection considering comparison modulo 3:

Wolfram Language code: Intersection[{0, 3, 5, 2}, {0, 2, 5}, SameTest -> (Mod[#1 - #2, 3] == 0&)]

This matrix is antihermitian for a positive real , but AntihermitianMatrixQ gives False:

Wolfram Language code: m = {{I, Exp[Log[I x]]}, {I x, 2I}};
Wolfram Language code: AntihermitianMatrixQ[m]

Use the option SameTest:

Wolfram Language code: AntihermitianMatrixQ[m, SameTest -> (Simplify[#1 - #2, x > 0] == 0&)]

This matrix is symmetric for a positive real , but SymmetricMatrixQ gives False:

Wolfram Language code: m = {{1, Log[x ^ 2]}, {2 Log[x], 2}};
Wolfram Language code: SymmetricMatrixQ[m]

Use the option SameTest:

Wolfram Language code: SymmetricMatrixQ[m, SameTest -> (Simplify[#1 - #2, x > 0] == 0&)]

This matrix is unitary for a positive real , but UnitaryMatrixQ gives False:

Wolfram Language code: m = {{1, Exp[x I]}, {Cos[x] - I Sin[x], -1}} / Sqrt[2];
Wolfram Language code: UnitaryMatrixQ[m]

Use the option SameTest:

Wolfram Language code: UnitaryMatrixQ[m, SameTest -> (Simplify[#1 - #2, x > 0] == 0&)]
Wolfram Research (1991), SameTest, Wolfram Language function, https://reference.wolfram.com/language/ref/SameTest.html.

Text

Wolfram Research (1991), SameTest, Wolfram Language function, https://reference.wolfram.com/language/ref/SameTest.html.

CMS

Wolfram Language. 1991. "SameTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SameTest.html.

APA

Wolfram Language. (1991). SameTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SameTest.html

BibTeX

@misc{reference.wolfram_2026_sametest, author="Wolfram Research", title="{SameTest}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/SameTest.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_sametest, organization={Wolfram Research}, title={SameTest}, year={1991}, url={https://reference.wolfram.com/language/ref/SameTest.html}, note=[Accessed: 12-June-2026]}