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ComposeList
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ComposeList

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ComposeList[{f1,f2,…},x]

generates a list of the form {x,f1[x],f2[f1[x]],…}.

Examples

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

Construct a list of the successive application of several functions:

In[1]:=1
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https://wolfram.com/xid/0enxkyr3e-i0t
Out[1]=1

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

Specify a sequence of function applications:

In[1]:=1
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https://wolfram.com/xid/0enxkyr3e-yal
Out[1]=1

Apply two operations that generate a group:

In[1]:=1
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https://wolfram.com/xid/0enxkyr3e-hx4
Out[1]=1

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

The action of ComposeList is equivalent to folding Construct with reversed arguments:

In[1]:=1
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https://wolfram.com/xid/0enxkyr3e-c4c58o
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0enxkyr3e-dpjjx8
Out[2]=2

The action of ComposeList is equivalent to folding RightComposition and then applying all functions:

In[1]:=1
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https://wolfram.com/xid/0enxkyr3e-ts5bcq
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0enxkyr3e-hy9k16
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0enxkyr3e-laag5w
Out[3]=3
Wolfram Research (1991), ComposeList, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeList.html.
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Wolfram Research (1991), ComposeList, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeList.html.

Text

Wolfram Research (1991), ComposeList, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeList.html.

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Wolfram Research (1991), ComposeList, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeList.html.

CMS

Wolfram Language. 1991. "ComposeList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComposeList.html.

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Wolfram Language. 1991. "ComposeList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComposeList.html.

APA

Wolfram Language. (1991). ComposeList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComposeList.html

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Wolfram Language. (1991). ComposeList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComposeList.html

BibTeX

@misc{reference.wolfram_2025_composelist, author="Wolfram Research", title="{ComposeList}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/ComposeList.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_composelist, author="Wolfram Research", title="{ComposeList}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/ComposeList.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_composelist, organization={Wolfram Research}, title={ComposeList}, year={1991}, url={https://reference.wolfram.com/language/ref/ComposeList.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_composelist, organization={Wolfram Research}, title={ComposeList}, year={1991}, url={https://reference.wolfram.com/language/ref/ComposeList.html}, note=[Accessed: 29-March-2025 ]}