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


converts objects with head h in expr to normal expressions.


converts objects with head hi to normal expressions.



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Basic Examples  (3)

Create a normal dense list from a sparse array:

Create a normal expression from a series expansion:

Convert an association to a list of rules:

Normal acts on the first level only:

Scope  (5)

Convert RootSum objects to Root objects:

Typically the RootSum objects will give more accurate numerical values:

Convert from a GraphicsComplex object to graphics primitives:

Both forms produce the same image:

Normal will affect expressions nested inside other expressions:

Normal converts different types of expressions by default:

Convert only the sparse array:

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

Convert CylindricalDecompositionFunction to equations and inequalities:

Applications  (1)

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

Power series about :

Asymptotic truncation error for small :

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

With higher precision, the asymptotic error holds for smaller :

Properties & Relations  (1)

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

Wolfram Research (1988), Normal, Wolfram Language function, (updated 2015).


Wolfram Research (1988), Normal, Wolfram Language function, (updated 2015).


Wolfram Language. 1988. "Normal." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015.


Wolfram Language. (1988). Normal. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_normal, author="Wolfram Research", title="{Normal}", year="2015", howpublished="\url{}", note=[Accessed: 27-May-2024 ]}


@online{reference.wolfram_2024_normal, organization={Wolfram Research}, title={Normal}, year={2015}, url={}, note=[Accessed: 27-May-2024 ]}