MHB Describes elements of D_5 using SAGE

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The discussion focuses on the elements of the dihedral group $D_5$, which include rotations and reflections, specifically noted as $R_0$, $R_{72}$, $R_{144}$, $R_{216}$, $R_{288}$, and $F_1$ to $F_5$. Users express interest in creating a Cayley table for $D_5$ using SAGE, with one participant sharing their experience of using SageMath to explore the group and generate a Cayley table. There is a discussion about formatting output in LaTeX, with attempts to get SAGE to produce LaTeX code directly. The conversation highlights the relationship between the elements and their characteristics, emphasizing clarity in representation. Overall, the thread illustrates the process of using SAGE for group theory computations and formatting results.
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Describes the elements of $D_5$
ok I think the elements of $D_5$ are
$$R_0\quad R_{72} \quad R_{144} \quad R_{216} \quad R_{288} \quad F_1 \quad F_2 \quad F_3 \quad F_4 \quad F_5$$

ok from this was going to make a cayley table
but was wondering if anybody know how to do this with SAGE

otherwise I presume we could just create it with latex table
 

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karush said:
Describes the elements of $D_5$
ok I think the elements of $D_5$ are
$$R_0\quad R_{72} \quad R_{144} \quad R_{216} \quad R_{288} \quad F_1 \quad F_2 \quad F_3 \quad F_4 \quad F_5$$

ok from this was going to make a cayley table
but was wondering if anybody know how to do this with SAGE

otherwise I presume we could just create it with latex table

Usually we write the elements such that their relation to the other elements is clear.
And also that we can easily distinguish the ones with different characteristics.

We might write it as:
$$I\quad R \quad R^2 \quad R^3 \quad R^4 \quad F \quad FR \quad FR^2 \quad FR^3 \quad FR^4$$

Just for fun I installed SageMath to see what it does:

sage:[/color] D_5 = DihedralGroup(5)
sage:[/color] D_5
Dihedral group of order 10 as a permutation group

sage:[/color] D_5.list()
[(),
(1,5,4,3,2),
(1,4,2,5,3),
(1,3,5,2,4),
(1,2,3,4,5),
(2,5)(3,4),
(1,5)(2,4),
(1,4)(2,3),
(1,3)(4,5),
(1,2)(3,5)]

sage:[/color] D_5.cayley_table()
* a b c d e f g h i j
+--------------------
a| a b c d e f g h i j
b| b c d e a j f g h i
c| c d e a b i j f g h
d| d e a b c h i j f g
e| e a b c d g h i j f
f| f g h i j a b c d e
g| g h i j f e a b c d
h| h i j f g d e a b c
i| i j f g h c d e a b
j| j f g h i b c d e a
​
 
wow, that is great help

I am going to dive into it a lot more tommorro

I was curious there is a way to get SAGE to output in latex I tried \latex but no
already spent about an hour trying to this but no success
I noticed yours is screenshot

oh this is going to be our new rail access from the campus
 
Last edited:
Klaas van Aarsen said:
Usually we write the elements such that their relation to the other elements is clear.
And also that we can easily distinguish the ones with different characteristics.

We might write it as:
$$I\quad R \quad R^2 \quad R^3 \quad R^4 \quad F \quad FR \quad FR^2 \quad FR^3 \quad FR^4$$

Just for fun I installed SageMath to see what it does:
sage: D_5 = DihedralGroup(5)
sage: D_5
Dihedral group of order 10 as a permutation group

sage: D_5.list()
[(),
(1,5,4,3,2),
(1,4,2,5,3),
(1,3,5,2,4),
(1,2,3,4,5),
(2,5)(3,4),
(1,5)(2,4),
(1,4)(2,3),
(1,3)(4,5),
(1,2)(3,5)]

sage: D_5.cayley_table()
* a b c d e f g h i j
+--------------------
a| a b c d e f g h i j
b| b c d e a j f g h i
c| c d e a b i j f g h
d| d e a b c h i j f g
e| e a b c d g h i j f
f| f g h i j a b c d e
g| g h i j f e a b c d
h| h i j f g d e a b c
i| i j f g h c d e a b
j| j f g h i b c d e a
​


ok done in latex but want to see if SAGE can return this
it may not be an align tho

D_5=DihedralGroup(5)
D_5
D_5.list()
\begin{align*}
&[().\\
&(1,5,4,3,2),\\
&(1,4,2,5,3)\\
&(1,3,5,2,4)\\
&(1,2,3,4,5)\\
&(2,5)(3,4)\\
&(1,5)(2,4)\\
&(1,4)(2,3)\\
&(1,2)(3,5)]\\
\end{align*}
 
I get:

sage:[/color] latex(D_5.list())
$$\left[, (1,5,4,3,2), (1,4,2,5,3), (1,3,5,2,4), (1,2,3,4,5), (2,5)(3,4), (1,5)(2,4), (1,4)(2,3), (1,3)(4,5), (1,2)(3,5)\right]$$​
 
https://www.physicsforums.com/attachments/8594
ok I did this to get the latex output
there might be a deference in SAGE and cocalc which uses SAGE
 
https://dl.orangedox.com/GXEVNm73NxaGC9F7Cy

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