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NHoldRest
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NHoldRest

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is an attribute which specifies that all but the first argument to a function should not be affected by N.

Examples

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

Prevent N from affecting all but the first argument of a function:

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In[1]:=1
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https://wolfram.com/xid/0bdpzoqlu-cpm2h
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In[2]:=2
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https://wolfram.com/xid/0bdpzoqlu-k3vhc6
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Out[2]=2
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In[3]:=3
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https://wolfram.com/xid/0bdpzoqlu-fti8wk
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Out[3]=3

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

System symbols with the NHoldRest attribute:

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In[1]:=1
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https://wolfram.com/xid/0bdpzoqlu-l9p1c
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Out[1]=1

Use Part symbolically:

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In[1]:=1
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https://wolfram.com/xid/0bdpzoqlu-jk3nhc
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Out[1]=1

Using N does not affect the specified parts:

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In[2]:=2
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https://wolfram.com/xid/0bdpzoqlu-f4t6a8
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Out[2]=2

The expression works when x is substituted with a list:

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In[3]:=3
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https://wolfram.com/xid/0bdpzoqlu-ripgf
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Out[3]=3

Applications  (1)Sample problems that can be solved with this function

Define a function that represents the real-valued root for positive and positive integer :

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In[1]:=1
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https://wolfram.com/xid/0bdpzoqlu-cmbj0r
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Prevent its second argument from being converted to real using NHoldRest:

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In[2]:=2
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https://wolfram.com/xid/0bdpzoqlu-ns27p
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An exact representation of the cube root of 2:

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In[3]:=3
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https://wolfram.com/xid/0bdpzoqlu-kcmpvp
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Out[3]=3

Machine-number approximation:

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In[4]:=4
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https://wolfram.com/xid/0bdpzoqlu-eocy2
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Out[4]=4

47-digit approximation:

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In[5]:=5
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https://wolfram.com/xid/0bdpzoqlu-fiwng
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Out[5]=5

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

Subscript by default has the NHoldRest attribute:

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In[1]:=1
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https://wolfram.com/xid/0bdpzoqlu-f1ruiu
Direct link to example
Out[1]=1

This means that subscripts generally do not change under N:

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In[2]:=2
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https://wolfram.com/xid/0bdpzoqlu-beyfit
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Out[2]=2
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In[3]:=3
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https://wolfram.com/xid/0bdpzoqlu-qndf3p
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Out[3]=3

HoldRest prevents evaluation while NHoldRest only prevents numerical evaluation:

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In[1]:=1
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https://wolfram.com/xid/0bdpzoqlu-2rlzr
Direct link to example
Copy to clipboard.
In[2]:=2
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https://wolfram.com/xid/0bdpzoqlu-dqg7
Direct link to example
Out[2]=2
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In[3]:=3
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https://wolfram.com/xid/0bdpzoqlu-cbp2j8
Direct link to example
Out[3]=3
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In[4]:=4
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https://wolfram.com/xid/0bdpzoqlu-m8utr
Direct link to example
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In[5]:=5
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https://wolfram.com/xid/0bdpzoqlu-cj9ifj
Direct link to example
Out[5]=5
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In[6]:=6
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https://wolfram.com/xid/0bdpzoqlu-dipegk
Direct link to example
Out[6]=6

You can prevent both by setting both attributes:

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In[7]:=7
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https://wolfram.com/xid/0bdpzoqlu-dvxl89
Direct link to example
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In[8]:=8
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https://wolfram.com/xid/0bdpzoqlu-csslcd
Direct link to example
Out[8]=8
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In[9]:=9
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https://wolfram.com/xid/0bdpzoqlu-y401c
Direct link to example
Out[9]=9
Wolfram Research (1996), NHoldRest, Wolfram Language function, https://reference.wolfram.com/language/ref/NHoldRest.html.
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Wolfram Research (1996), NHoldRest, Wolfram Language function, https://reference.wolfram.com/language/ref/NHoldRest.html.

Text

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

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

CMS

Wolfram Language. 1996. "NHoldRest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NHoldRest.html.

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Wolfram Language. 1996. "NHoldRest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NHoldRest.html.

APA

Wolfram Language. (1996). NHoldRest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NHoldRest.html

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Wolfram Language. (1996). NHoldRest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NHoldRest.html

BibTeX

@misc{reference.wolfram_2025_nholdrest, author="Wolfram Research", title="{NHoldRest}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/NHoldRest.html}", note=[Accessed: 26-March-2025 ]}

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@misc{reference.wolfram_2025_nholdrest, author="Wolfram Research", title="{NHoldRest}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/NHoldRest.html}", note=[Accessed: 26-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_nholdrest, organization={Wolfram Research}, title={NHoldRest}, year={1996}, url={https://reference.wolfram.com/language/ref/NHoldRest.html}, note=[Accessed: 26-March-2025 ]}

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@online{reference.wolfram_2025_nholdrest, organization={Wolfram Research}, title={NHoldRest}, year={1996}, url={https://reference.wolfram.com/language/ref/NHoldRest.html}, note=[Accessed: 26-March-2025 ]}