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Sage notebook wiki-output examples (paste below): Trying out html2moin.py processor; this is one step in processing doc pages for a notebook help browser, as well as a step to making a wiki-version of the documentation. This is just a test using a random doc page.

14.3 Abelian group elements

||[http://modular.math.washington.edu/sage/doc/html/ref/module-sage.groups.abelian-gps.abelian-group.html prev]||[http://modular.math.washington.edu/sage/doc/html/ref/node144.html parent]||[http://modular.math.washington.edu/sage/doc/html/ref/module-sage.groups.abelian-gps.abelian-group-morphism.html next]||<style="width:90%; text-align: center;">[http://modular.math.washington.edu/sage/doc/html/ref/contents.html ''SAGE'' Reference Manual]||[http://modular.math.washington.edu/sage/doc/html/ref/modindex.html module index]||[http://modular.math.washington.edu/sage/doc/html/ref/genindex.html general index]||

 '''Previous:''' [http://modular.math.washington.edu/sage/doc/html/ref/module-sage.groups.abelian-gps.abelian-group.html 14.2 Multiplicative Abelian Groups]
 '''Up:''' [http://modular.math.washington.edu/sage/doc/html/ref/node144.html 14. Groups]
 '''Next:''' [http://modular.math.washington.edu/sage/doc/html/ref/module-sage.groups.abelian-gps.abelian-group-morphism.html 14.4 Homomorphisms of abelian]


----

## End of Navigation Panel


= 14.3 Abelian group elements =
[[Anchor(SECTION0016300000000000000000)]]
 '''Module:''' {{{sage.groups.abelian_gps.abelian_group_element}}}

[[Anchor(module-sage.groups.abelian-gps.abelian-group-element)]]

 '''Author Log:''' [[BR]]


 * David Joyner (2006-02); based on free_abelian_monoid_element.py, written
 by David Kohel.[[BR]]

 * David Joyner (2006-05); bug fix in order[[BR]]

 * " (2006-08); bug fix+new method in pow for negatives+fixed corresponding
 examples.[[BR]]

Recall an example from abelian groups.
{{{#!python
sage: F = AbelianGroup(5,[4,5,5,7,8],names = list("abcde"))
sage: (a,b,c,d,e) = F.gens()
sage: x = a*b^2*e*d^20*e^12
sage: x
a*b^2*d^6*e^5
sage: x = a^10*b^12*c^13*d^20*e^12
sage: x
a^2*b^2*c^3*d^6*e^4
sage: y = a^13*b^19*c^23*d^27*e^72
sage: y
a*b^4*c^3*d^6
sage: x*y
a^3*b*c*d^5*e^4
sage: x.list()
[2, 2, 3, 6, 4]
}}}

It is important to note that lists are mutable and the returned list is not
a copy. As a result, reassignment of an element of the list changes the
object.
{{{
sage: x.list()[0] = 3
sage: x.list()
[3, 2, 3, 6, 4]
sage: x
a^3*b^2*c^3*d^6*e^4
}}}
 '''Module-level Functions'''



 ''' `is_AbelianGroupElement` ''' (x )


 '''Class: {{{AbelianGroupElement}}}'''


 '''class `AbelianGroupElement` '''
 ''' `AbelianGroupElement` ''' (self, F, x )
Create the element x of the AbelianGroup F.


{{{
sage: F = AbelianGroup(5, [3,4,5,8,7], 'abcde')
sage: a, b, c, d, e = F.gens()
sage: a^2 * b^3 * a^2 * b^-4
a*b^3
sage: b^-11
b
sage: a^-11
a
sage: a*b in F
True
}}}


 '''Functions:''' `as_permutation` , `list` , `order` , `random` , `word_problem`



 ''' `as_permutation` ''' (self )
Return the element of the permutation group G (isomorphic to the abelian
group A) associated to a in A.

Trying out html2moin.py processor; this is one step in processing doc pages for a notebook help browser, as well as a step to making a wiki-version of the documentation. This is just a test using a random doc page.

14.3 Abelian group elements

[http://modular.math.washington.edu/sage/doc/html/ref/module-sage.groups.abelian-gps.abelian-group.html prev]

[http://modular.math.washington.edu/sage/doc/html/ref/node144.html parent]

[http://modular.math.washington.edu/sage/doc/html/ref/module-sage.groups.abelian-gps.abelian-group-morphism.html next]

[http://modular.math.washington.edu/sage/doc/html/ref/contents.html SAGE Reference Manual]

[http://modular.math.washington.edu/sage/doc/html/ref/modindex.html module index]

[http://modular.math.washington.edu/sage/doc/html/ref/genindex.html general index]


14.3 Abelian group elements

Anchor(SECTION0016300000000000000000)

  • Module: sage.groups.abelian_gps.abelian_group_element

Anchor(module-sage.groups.abelian-gps.abelian-group-element)

  • Author Log: BR

  • David Joyner (2006-02); based on free_abelian_monoid_element.py, written

    by David Kohel.BR

  • David Joyner (2006-05); bug fix in orderBR

  • " (2006-08); bug fix+new method in pow for negatives+fixed corresponding

    examples.BR

Recall an example from abelian groups.

   1 sage: F = AbelianGroup(5,[4,5,5,7,8],names = list("abcde"))
   2 sage: (a,b,c,d,e) = F.gens()
   3 sage: x = a*b^2*e*d^20*e^12
   4 sage: x
   5 a*b^2*d^6*e^5
   6 sage: x = a^10*b^12*c^13*d^20*e^12
   7 sage: x
   8 a^2*b^2*c^3*d^6*e^4
   9 sage: y = a^13*b^19*c^23*d^27*e^72
  10 sage: y
  11 a*b^4*c^3*d^6
  12 sage: x*y
  13 a^3*b*c*d^5*e^4
  14 sage: x.list()
  15 [2, 2, 3, 6, 4]

It is important to note that lists are mutable and the returned list is not a copy. As a result, reassignment of an element of the list changes the object.

sage: x.list()[0] = 3
sage: x.list()
[3, 2, 3, 6, 4]
sage: x
a^3*b^2*c^3*d^6*e^4
  • Module-level Functions

    is_AbelianGroupElement (x )

    Class: AbelianGroupElement

    class AbelianGroupElement AbelianGroupElement (self, F, x )

Create the element x of the AbelianGroup F.

sage: F = AbelianGroup(5, [3,4,5,8,7], 'abcde')
sage: a, b, c, d, e = F.gens()
sage: a^2 * b^3 * a^2 * b^-4
a*b^3
sage: b^-11
b
sage: a^-11
a
sage: a*b in F
True
  • Functions: as_permutation , list , order , random , word_problem

    as_permutation (self )

Return the element of the permutation group G (isomorphic to the abelian group A) associated to a in A.

dmr/example (last edited 2008-11-14 13:41:51 by localhost)