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Operate
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Operate

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Operate[p,f[x,y,…]]

gives p[f][x,y,…].

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Operate[p,expr,n]

applies p at level n in the head of expr.

Details

  • Operate[p,f[x]] effectively applies the functional operator p to the function f.
  • Operate is essentially a generalization of Apply, which allows you to apply an operator to the head of an expression, rather than simply to replace the head. »

Examples

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Basic Examples  (2)Summary of the most common use cases

Operate on the head of the expression with p:

In[1]:=1
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https://wolfram.com/xid/0mriq8-lf2
Out[1]=1

Use a pure function:

In[1]:=1
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https://wolfram.com/xid/0mriq8-q7h
Out[1]=1

Scope  (2)Survey of the scope of standard use cases

Level Specifications  (2)

Operate at level 1, the head of the expression (default):

In[1]:=1
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https://wolfram.com/xid/0mriq8-410lzb
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mriq8-0ar8wp
Out[2]=2

Operate at level 2 (the head of the head of the expression):

In[1]:=1
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https://wolfram.com/xid/0mriq8-m8j8he
Out[1]=1

Properties & Relations  (4)Properties of the function, and connections to other functions

Operate can be iterated:

In[1]:=1
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https://wolfram.com/xid/0mriq8-sh9
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mriq8-j7d
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0mriq8-9g12q1
Out[3]=3

Operate[f,expr] is equivalent to MapAt[f,expr,0]:

In[1]:=1
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https://wolfram.com/xid/0mriq8-e9yu0p
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mriq8-rdn8it
Out[2]=2

Apply is a special case of Operate that replaces the head of the expression:

In[1]:=1
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https://wolfram.com/xid/0mriq8-1zt9x8
Out[1]=1

Operate followed by Through is a form of composition:

In[1]:=1
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https://wolfram.com/xid/0mriq8-mgrnca
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mriq8-ny7o61
Out[2]=2
Wolfram Research (1988), Operate, Wolfram Language function, https://reference.wolfram.com/language/ref/Operate.html.
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Wolfram Research (1988), Operate, Wolfram Language function, https://reference.wolfram.com/language/ref/Operate.html.

Text

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

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

CMS

Wolfram Language. 1988. "Operate." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Operate.html.

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Wolfram Language. 1988. "Operate." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Operate.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_operate, author="Wolfram Research", title="{Operate}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Operate.html}", note=[Accessed: 04-June-2025 ]}

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@misc{reference.wolfram_2025_operate, author="Wolfram Research", title="{Operate}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Operate.html}", note=[Accessed: 04-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_operate, organization={Wolfram Research}, title={Operate}, year={1988}, url={https://reference.wolfram.com/language/ref/Operate.html}, note=[Accessed: 04-June-2025 ]}

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@online{reference.wolfram_2025_operate, organization={Wolfram Research}, title={Operate}, year={1988}, url={https://reference.wolfram.com/language/ref/Operate.html}, note=[Accessed: 04-June-2025 ]}