NumericFunction

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`NumericFunction`

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NumericFunction

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 arg_i are numeric quantities.

Details

Most standard built‐in mathematical functions have the attribute NumericFunction.
NumericQ checks the NumericFunction attribute of every function it encounters.
If you assign the attribute NumericFunction to a function that does not yield numerical values, then NumericQ will give misleading results. »

Examples

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Basic Examples (1)Summary of the most common use cases

Log has the NumericFunction attribute:

In[1]:=1

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https://wolfram.com/xid/0i1roredu-ednz20

Out[1]=1

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

In[2]:=2

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https://wolfram.com/xid/0i1roredu-bd97xu

Out[2]=2

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

In[3]:=3

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https://wolfram.com/xid/0i1roredu-j21w3g

Out[3]=3

Scope (1)Survey of the scope of standard use cases

Define f to be a numeric function:

In[1]:=1

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https://wolfram.com/xid/0i1roredu-c5q58q

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

In[2]:=2

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https://wolfram.com/xid/0i1roredu-kdhzai

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0i1roredu-i31uv6

Out[3]=3

Assign f to evaluate for arguments that are approximate numbers:

In[4]:=4

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https://wolfram.com/xid/0i1roredu-f1h4mc

In[5]:=5

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https://wolfram.com/xid/0i1roredu-giye0w

Out[5]=5

Applications (2)Sample problems that can be solved with this function

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

In[1]:=1

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https://wolfram.com/xid/0i1roredu-p67kyy

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

In[4]:=4

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https://wolfram.com/xid/0i1roredu-vec6av

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

In[6]:=6

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https://wolfram.com/xid/0i1roredu-pzlq29

Out[6]=6

In[7]:=7

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https://wolfram.com/xid/0i1roredu-mnae8i

Out[7]=7

Define a function that can represent an exact value:

In[1]:=1

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https://wolfram.com/xid/0i1roredu-i4ej2

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

In[2]:=2

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https://wolfram.com/xid/0i1roredu-ld2vt2

Assign f for approximate numbers:

In[3]:=3

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https://wolfram.com/xid/0i1roredu-fukj22

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

In[4]:=4

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https://wolfram.com/xid/0i1roredu-oxzeo

Out[4]=4

In[5]:=5

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https://wolfram.com/xid/0i1roredu-jdlof0

Out[5]=5

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

In[6]:=6

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https://wolfram.com/xid/0i1roredu-818aj

Out[6]=6

A plot of the function:

In[7]:=7

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https://wolfram.com/xid/0i1roredu-bxhtp6

Out[7]=7

Properties & Relations (2)Properties of the function, and connections to other functions

Sin has the attribute NumericFunction:

In[1]:=1

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https://wolfram.com/xid/0i1roredu-jmfe8

Out[1]=1

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

In[2]:=2

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https://wolfram.com/xid/0i1roredu-drgdkq

Out[2]=2

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

In[3]:=3

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https://wolfram.com/xid/0i1roredu-objskq

Out[3]=3

Note that NumberQ returns False:

In[4]:=4

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https://wolfram.com/xid/0i1roredu-qs11yl

Out[4]=4

Some of the system symbols that are numeric functions:

In[1]:=1

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https://wolfram.com/xid/0i1roredu-w3uc59

Out[1]=1

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