Differences between revisions 2 and 6 (spanning 4 versions)
> * 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.{{{#!pythonsage: 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^12sage: xa*b^2*d^6*e^5sage: x = a^10*b^12*c^13*d^20*e^12sage: xa^2*b^2*c^3*d^6*e^4sage: y = a^13*b^19*c^23*d^27*e^72sage: ya*b^4*c^3*d^6sage: x*ya^3*b*c*d^5*e^4sage: x.list()[2, 2, 3, 6, 4]}}}It is important to note that lists are mutable and the returned list is nota copy. As a result, reassignment of an element of the list changes theobject.{{{sage: x.list()[0] = 3sage: x.list()[3, 2, 3, 6, 4]sage: xa^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^-4a*b^3sage: b^-11bsage: a^-11asage: a*b in FTrue}}} '''Functions:''' `as_permutation` , `list` , `order` , `random` , `word_problem` ''' `as_permutation` ''' (self )Return the element of the permutation group G (isomorphic to the abeliangroup 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

 prev parent next ''SAGE'' Reference Manual module index general index

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.

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