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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
Previous: 14.2 Multiplicative Abelian Groups Up: 14. Groups Next: 14.4 Homomorphisms of abelian
14.3 Abelian group elements
Module: sage.groups.abelian_gps.abelian_group_element
Author Log:
- David Joyner (2006-02); based on free_abelian_monoid_element.py, written
by David Kohel.
David Joyner (2006-05); bug fix in order
- " (2006-08); bug fix+new method in pow for negatives+fixed corresponding
examples.
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.