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Normal
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Normal

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Normal[expr]

converts expr to a normal expression from a variety of special forms.

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Normal[expr,h]

converts objects with head h in expr to normal expressions.

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Normal[expr,{h1,h2,…}]

converts objects with head hi to normal expressions.

Details

Examples

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Basic Examples  (3)Summary of the most common use cases

Create a normal dense list from a sparse array:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-eid
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bn61gm-dj8
Out[2]=2

Create a normal expression from a series expansion:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-bvt
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bn61gm-nsf
Out[2]=2

Convert an association to a list of rules:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-lmhnl
Out[1]=1

Normal acts on the first level only:

In[2]:=2
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https://wolfram.com/xid/0bn61gm-kju2fu
Out[2]=2

Scope  (5)Survey of the scope of standard use cases

Convert RootSum objects to Root objects:

In[3]:=3
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https://wolfram.com/xid/0bn61gm-ekanw
Out[3]=3
In[2]:=2
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https://wolfram.com/xid/0bn61gm-1f719
Out[2]=2

Typically the RootSum objects will give more accurate numerical values:

In[5]:=5
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https://wolfram.com/xid/0bn61gm-b7dry2
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0bn61gm-6rn1z
Out[6]=6

Convert from a GraphicsComplex object to graphics primitives:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-f8afdl
In[2]:=2
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https://wolfram.com/xid/0bn61gm-e94beo
Out[2]=2

Both forms produce the same image:

In[3]:=3
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https://wolfram.com/xid/0bn61gm-bt4b95
Out[3]=3

Normal will affect expressions nested inside other expressions:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-hhusub
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bn61gm-fvzhz7
Out[2]=2

Normal converts different types of expressions by default:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-x5fjpj
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bn61gm-fm5qbs
Out[2]=2

Convert only the sparse array:

In[3]:=3
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https://wolfram.com/xid/0bn61gm-5182go
Out[3]=3

Normalize the series and the association but not the sparse array:

In[4]:=4
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https://wolfram.com/xid/0bn61gm-0r0w6j
Out[4]=4

Convert CylindricalDecompositionFunction to equations and inequalities:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-bg9zj6
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bn61gm-o4ceg
Out[2]=2

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

Compare the actual error to the theoretical asymptotic error for a difference quotient:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-b57oax

Power series about :

In[2]:=2
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https://wolfram.com/xid/0bn61gm-kz2txv
Out[2]=2

Asymptotic truncation error for small :

In[3]:=3
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https://wolfram.com/xid/0bn61gm-qzgs4
Out[3]=3

Compare actual and asymptotic errors as a function of for at :

In[4]:=4
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https://wolfram.com/xid/0bn61gm-b1roco
Out[4]=4

With higher precision, the asymptotic error holds for smaller :

In[5]:=5
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https://wolfram.com/xid/0bn61gm-hurkcx
Out[5]=5

Properties & Relations  (1)Properties of the function, and connections to other functions

For f that work with SparseArray objects s, often Normal[f[s]]===f[Normal[s]]:

In[1]:=1
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https://wolfram.com/xid/0bn61gm-u9jb7
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bn61gm-b0uguy
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bn61gm-lvb6c
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0bn61gm-jyjfi
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0bn61gm-b58769
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0bn61gm-bq1vbd
Out[6]=6
Wolfram Research (1988), Normal, Wolfram Language function, https://reference.wolfram.com/language/ref/Normal.html (updated 2015).
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Wolfram Research (1988), Normal, Wolfram Language function, https://reference.wolfram.com/language/ref/Normal.html (updated 2015).

Text

Wolfram Research (1988), Normal, Wolfram Language function, https://reference.wolfram.com/language/ref/Normal.html (updated 2015).

✖
Wolfram Research (1988), Normal, Wolfram Language function, https://reference.wolfram.com/language/ref/Normal.html (updated 2015).

CMS

Wolfram Language. 1988. "Normal." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/Normal.html.

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Wolfram Language. 1988. "Normal." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/Normal.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_normal, author="Wolfram Research", title="{Normal}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/Normal.html}", note=[Accessed: 31-March-2025 ]}

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@misc{reference.wolfram_2025_normal, author="Wolfram Research", title="{Normal}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/Normal.html}", note=[Accessed: 31-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_normal, organization={Wolfram Research}, title={Normal}, year={2015}, url={https://reference.wolfram.com/language/ref/Normal.html}, note=[Accessed: 31-March-2025 ]}

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@online{reference.wolfram_2025_normal, organization={Wolfram Research}, title={Normal}, year={2015}, url={https://reference.wolfram.com/language/ref/Normal.html}, note=[Accessed: 31-March-2025 ]}