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## How to simplify noncommutative expressions?...

I am trying to simplify noncommutative expressions that use the 'dot' operator: `.`. The following is a minimal example:

, which evaluates to:

This should simplify to 'a1', as I am expecting `.` to work like noncommutative multiplication. If there is any way to define this behavior I would appreciate some help. Alternatively, I would also be happy with reworking 'simplify' to work in this scenario. If it helps, I am working with finitely presented groups. If you see the Maple package 'GroupTheory', you'll see that the 'Group' function has this built in. If we input generators and relators it will simplify expressions of the above type, so I know it can be done!

Lastly, I would prefer displaying '1/a1' as 'a1^-1', but that is just for aesthetics.

Here is a minimal document: minimalexample.mw

## Is it possible to create a mapping ...

from permutation group to permutation group and inverse this mapping?

how to do?

## How to find these products?...

assume not starting from resolvent of quartic,

how to find [[1,2],[3,4]] and [[1,3],[2,4]] and [[1,4],[2,3]] ?

a1*a2 + a3*a4 if [[1,3,2,4],[1,2]]

a1*a3 + a2*a4 if [2,3][[1,3,2,4],[1,2]]

a1*a4 + a2*a3 if [2,4],[[1,3,2,4],[1,2]]

moreover, i use multiplication of permutation group can not multiply below

though i know how to operate multiplication by hand, i follow the syntax to do multiplication, seems not the way

with(group):
mulperms([[2,3]], [[1,3,2,4],[1,2]]);
mulperms([[1,3,2,4],[1,2]], [[2,3]]);

mulperms([2,3], [[1,3,2,4],[1,2]]);
mulperms([[1,3,2,4],[1,2]], [2,3]);

## Error in Subgroup...

i use normaliser's example's code in maple help file

generators is [50] originally, then i calculated again , it become [51], [52], [53] , i do not know whether virus change my library

then i use another computer to calculate, the result is [50]

then i further calculate subgroup got error below

with(GroupTheory):
with(group):
G := AlternatingGroup(5);
IsFinite(G);
GroupOrder(G);
spg := SylowSubgroup(5, G);
IsAbelian(spg);
Elements(spg);
lprint(%);
H := Subgroup(Elements(G), spg);
N := Normaliser(G, spg);
#N := Normaliser(spg, G);
Elements(N);
lprint(%);
Elements(G);
H2 := Subgroup({[[5,2],[3,4]]}, G);
H2 := Subgroup(Elements(G), G);
elements2 := convert(Elements(G), 'list');
generators := map(ListTools:-Search, [Perm([[1,2,3]])], elements2);
H2 := Subgroup(generators, G);

H2 := Subgroup(Perm([generators]), G);
Error, invalid input: GroupTheory:-Subgroup expects its 1st argument, generators, to be of type {list, set, identical(undefined)}, but received module () local cycles, p, d, work; option object; end module
H2 := Subgroup(generators, G);
Error, (in Perm:-normalform) invalid input: map expects 2 or more arguments, but received 1

SubgroupMembership(H2, G);

## How to simplify element in FPG?...

1. Take a group for example. First we can set up a group G by

G:=<<a,b>|<a2=1,b3=1,(a.b)2=1>>. Actually,G=S3. So how to simplify a long production,

such as "a.b.b.a.b.b.a.b"?

2. How to define a finitely presented algebra over some field, such as the enveloping algebra

or quantum group of a Lie algebra? And moreover how to do the similar computation about

simplifying a long production?

## A cycle index related to multigraphs with loops

by:

Dear friends,

some time ago I shared a story here on the use of Maple to compute the cycle index of the induced action on the edges of an ordinary graph of the symmetric group permuting the vertices and the use of the Polya Enumeration Theorem to count non-isomorphic graphs by the number of edges. It can be found at the following Mapleprimes link.

I am writing today to alert you to another simple Maple program that is closely related and demonstrates Maple's capability to implement concepts from group theory and Polya enumeration. This link at Math.Stackexchange.com shows how to use the cycle index of the induced action by the symmetric group permuting vertices on the edges of a multigraph that includes loops to count set partitions of multisets containing two instances of n distinct types of items. The sequence that corresponds to these set partitions is OEIS A020555 where it is pointed out that we can equivalently count multigraphs with n labeled i.e. distinct edges where the vertices of the graph represent the multisets of the multiset partition and are connected by an edge k if the two instances of the value k are included in the sets represented by the two vertices that constitute the edge. The problem then reduces to a simple substitution into the aforementioned cycle index of a polynomial representing the set of labels on an edge including no labels on an edge that is not included.

This computation presents a remarkable simplicity while also implementing a non-trivial application of Polya counting. It is hoped that MaplePrimes users will enjoy reading this program, possibly profit from some of the techniques employed and be motivated to use Maple in their work on combinatorics problems.

Best regards,

Marko Riedel

Maple

## how to represent a function as an algebraic curve ...

f := x^2*(y/x+sqrt(-7*y^2/x^2))/(y^2*(x/y+sqrt(-7*x^2/y^2)));
v := parametrization(f, x, y, t);

it can not parametrize.

i do not know which book teach group theory and algebraic curve

can we call this algebraic curve over finite field ?

how to represent a function as an algebraic curve equation for parametrization?

## which group do four differential electromagnetism ...

http://www.gap-system.org/Manuals/doc/ref/chap50.html

which group do four differential electromagnetism belong to in library available in gap system?

what is the order of the group?

do maple 17 have this group? how to show?

## how to select execution group without having to sc...

Another worksheet dilemma  I am having with Maple.

I have number of "execution groups", like this, I created using CTRL-J

Now I wanted to put these in a section, so it becomes like this: (I had to make new worksheet now)

Since I did not know how put existing groups inside a new section I wanted to create (the section always comes at different level that does not include the groups), I thought I can create the section first, then go copy the groups and paste them to the new section.

The problem is how does one actually select multiple execution groups for the purpose of copying them?  The obvious way is to use the mouse, and select all groups with the mouse.

Well, this a big problem, since my groups are so large, I can spend 5-10 minutes scrolling down, very slowly to select them. my hand gets tired and I get tired doing this. I also one time got an error from Maple, saying selection too large, and something about rtf memory error or something. This is after wasting 10 minutes scrolling down carefully to select over 10,000 lines that is one large list.

In Mathematica, I can simply select a cell, no matter how large (an execution group in Maple talk) by just clicking on the edge of the cell.  I can select multiple cells the same way (hold, click on the edge of all). Very easy. I do not have to scroll down to select the content as I do with Maple

But here, with Maple, I put the mouse of the left edge, and can't select the group. Nothing happens. So I have to actually scroll down. I do not see the point of having a left [ edge to a group if one can't use it to select the group?

So my question is: How to select one or more execution groups without scrolling the mouse over all the content?

## how to classify topological space which a poset is...

1. is module in algebraic geometry for classification of topological space which a poset is a frame

2. which invariant is for doing this classification of topological space in algebraic geometry or group cohomology?

3. if want to do full combination before classification, which kind of polynomials be a full combination

4. is poset just like function fst and snd function for meet and join in functional programming instead of using "and" and "or" logic? how a matrix group related with topological space which a poset is a frame?

5. is there any invariant function for classification of topological space in maple?

## How to group grades for questions in an assignment...

It is possible to add groups of questions to an assignment in Maple T.A. But how do you see the grades divided into these groups? As an example, suppose we have two groups of questions say 5 questions in the group "algebra" and 5 questions in the group "geometry". The class grades show the grades for all 10 questions all together, but I would like to see the grades for two groups individually.

## Frobenius Groups...

Does there exist a Frobenius Group which is not  neither a Dihedralgroup nor  Symm(3) ?

Best regards

Kurt Ewald

## which theory can explain the interaction of compos...

which theory can explain the interaction of composition of group for combination of composition of group

if succeed to search a list of groups, what is the next step research them?