is an attribute that can be assigned to a symbol f to indicate that f[arg1,arg2,] should be considered a numeric quantity whenever all the argi are numeric quantities.



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Basic Examples  (1)

Log has the NumericFunction attribute:

When Log has an argument that is a number, constant, or numeric, the result is numeric:

In most cases when NumericQ[expr] gives True, then N[expr] yields an explicit number:

Scope  (1)

Define f to be a numeric function:

If you have not assigned f to yield numerical values, then NumericQ gives misleading results:

Assign f to evaluate for arguments that are approximate numbers:

Applications  (2)

Consider the following two function definitions, where one has the NumericFunction attribute:

Define a function that evaluates faster for numeric input than for arbitrary input:

The evaluation of is faster when it is able to recognize that its argument can be treated as numeric:

Define a function that can represent an exact value:

Assign N[f[a]] to give the derivative with respect to a of the solution of an ODE at :

Assign f for approximate numbers:

f[1] does not evaluate but represents a number:

It will work with any precision (within reasonable limits!):

A plot of the function:

Properties & Relations  (2)

Sin has the attribute NumericFunction:

The NumericFunction attribute informs NumericQ that Sin[1] can be converted into a number when using N:

NumericQ can return True without having to evaluate N[Sin[1]]:

Note that NumberQ returns False:

Some of the system symbols that are numeric functions:

Wolfram Research (1996), NumericFunction, Wolfram Language function,


Wolfram Research (1996), NumericFunction, Wolfram Language function,


Wolfram Language. 1996. "NumericFunction." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (1996). NumericFunction. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_numericfunction, author="Wolfram Research", title="{NumericFunction}", year="1996", howpublished="\url{}", note=[Accessed: 24-June-2024 ]}


@online{reference.wolfram_2024_numericfunction, organization={Wolfram Research}, title={NumericFunction}, year={1996}, url={}, note=[Accessed: 24-June-2024 ]}