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GroupActionBase
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GroupActionBase

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is an option to specify a base for a group.

Details

  • A base of a group is a list of points of its domain of action such that the only element in the group fixing them all is the identity.
  • Reordering the points in a base gives a different base.
  • The choice of base affects the ordering of group elements in the functions GroupElements and GroupElementPosition.
  • If the list of points given is not a base, the Wolfram Language will add more points until obtaining a base. In particular, GroupActionBase->{} will make the Wolfram Language choose an appropriate base.

Examples

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

Elements of a group in standard order:

In[1]:=1
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https://wolfram.com/xid/0btn85o6o1js-qjhwsy
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0btn85o6o1js-34g6sd
Out[2]=2

Sort them, specifying different priorities with a base:

In[3]:=3
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https://wolfram.com/xid/0btn85o6o1js-szfkhp
Out[3]=3
Wolfram Research (2010), GroupActionBase, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupActionBase.html.
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Wolfram Research (2010), GroupActionBase, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupActionBase.html.

Text

Wolfram Research (2010), GroupActionBase, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupActionBase.html.

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Wolfram Research (2010), GroupActionBase, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupActionBase.html.

CMS

Wolfram Language. 2010. "GroupActionBase." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GroupActionBase.html.

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Wolfram Language. 2010. "GroupActionBase." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GroupActionBase.html.

APA

Wolfram Language. (2010). GroupActionBase. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GroupActionBase.html

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Wolfram Language. (2010). GroupActionBase. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GroupActionBase.html

BibTeX

@misc{reference.wolfram_2025_groupactionbase, author="Wolfram Research", title="{GroupActionBase}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GroupActionBase.html}", note=[Accessed: 04-April-2025 ]}

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@misc{reference.wolfram_2025_groupactionbase, author="Wolfram Research", title="{GroupActionBase}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GroupActionBase.html}", note=[Accessed: 04-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_groupactionbase, organization={Wolfram Research}, title={GroupActionBase}, year={2010}, url={https://reference.wolfram.com/language/ref/GroupActionBase.html}, note=[Accessed: 04-April-2025 ]}

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@online{reference.wolfram_2025_groupactionbase, organization={Wolfram Research}, title={GroupActionBase}, year={2010}, url={https://reference.wolfram.com/language/ref/GroupActionBase.html}, note=[Accessed: 04-April-2025 ]}