added an example, updated readme, fixed deprecations
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# Magma Jupyter Kernel
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A simple Jupyter kernel for the Magma computer algebra system.
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## Requirements
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- Magma must be installed and runnable using the standard path, i.e., typing the command `magma`
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will run Magma.
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- Jupyter running on Python 3.
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## Installation
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If `pip` and `python` point to their Python 3 versions, you can install the kernel as a user with
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the commands:
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```sh
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pip install git+https://git.phc.dm.unipi.it/phc/magma_kernel
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python -m magma_kernel.install
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```
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On some systems, you may need to use `pip3` and `python3` instead.
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### Using a remote magma installation
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If the magma instance is on a remote machine, you can add an ssh key to the remote machine and add
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the following function in your `.bashrc` or `.zshrc`
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```sh
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function magma() {
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ssh -qt user@remote "magma $*"
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}
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```
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Then, you can use it "locally" with the following command:
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```sh
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$ magma
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```
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## Usage
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To use the kernel, run one of the following commands
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```sh
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# Select "New" -> "Notebook" and then in the new tab select "Magma" as the kernel
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jupyter notebook
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# Or run the console with the Magma kernel (still better than pure magma)
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jupyter console --kernel magma
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```
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## Development
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To install the kernel in development mode, clone the repository and run
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```sh
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# Create a virtual environment
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python -m venv venv
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source venv/bin/activate
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# Locally install the kernel
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pip install -r requirements.txt
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python -m magma_kernel.install
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```
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## Credits
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This code is based on a Magma kernel for IPython written by [@nbruin](https://github.com/nbruin),
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which was in turn based on [@cgranade/magma_kernel](https://github.com/cgranade/magma_kernel) the
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Bash example kernel by Thomas Kluyver. Improvements made in the current version include:
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- Removed some deprecated function usages
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- Added a `requirements.txt` file
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@ -1,32 +0,0 @@
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A simple Jupyter kernel for the Magma computer algebra system
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This kernel requires that Magma is installed and runnable using the
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standard path, i.e., that typing the command ``magma`` will run magma.
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Furthermore, it requires Jupyter running on Py3.
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If ``pip`` and ``python`` point to their Py3 versions, you can install the
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kernel as a user with the commands::
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pip install git+https://github.com/nbruin/magma_kernel --user
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python -m magma_kernel.install
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On some systems you may need to use ``pip3`` and ``python3`` instead::
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pip3 install git+https://github.com/nbruin/magma_kernel --user
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python3 -m magma_kernel.install
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To use it, run one of:
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.. code:: shell
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jupyter notebook
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# In the notebook interface, select Magma from the 'New' menu
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jupyter qtconsole --kernel magma
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jupyter console --kernel magma
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This code is based on a Magma kernel for IPython written by Christopher
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Granade, which was in turn based on the Bash example kernel by Thomas
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Kluyver. Improvements made in the current version include Tab
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completion, processing of help requests by returning an appropriate
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help query URL for Magma online documentation, and the reporting of
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partial output.
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File diff suppressed because it is too large
Load Diff
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/******
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Elementary approach to enumerating groups of order 2^n, n \leq 6
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*******/
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/*
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Compute the Cayley embedding of a finite group G
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*/
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function CayleyEmbedding(G)
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// Get the order of the group
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n := #G;
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// Define the symmetric group on n elements
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S := SymmetricGroup(n);
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// Get the elements of G
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elements := [g : g in G];
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// Create a map from G to S_n
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CayleyMap := hom<G -> S | g :-> S![Index(elements, g * elements[i]) : i in [1..n]]>;
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return Image(CayleyMap), CayleyMap;
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end function;
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/*
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Construct the "double" of a permutation sigma
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*/
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function DoublePermutation(sigma)
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n := Degree(Parent(sigma));
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S2n := Sym(2*n);
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L := [i^sigma : i in [1..n]] cat [i^sigma + n : i in [1..n]];
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return S2n!L;
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end function;
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/*
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Construct the "double" of a group G
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*/
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function DoubleGroup(G)
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H := CayleyEmbedding(G);
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n := #H;
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HDouble := sub< Sym(2*n) | [ DoublePermutation(h) : h in Generators(H) ] >;
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return HDouble;
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end function;
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/*
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Given a group G, construct a list of groups H
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such that G < H with index 2, and up to isomorphism,
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every group H with this property appears in the list.
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The first version is elementary; the second uses the
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correspondence theorem for subgroups; and the third
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one optimises by not repeating subgroups that are
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obviously conjugate to one another and only considering
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a 2-Sylow subgroup of the normaliser.
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*/
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function ConstructDoubleCovers(G)
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GDouble := DoubleGroup(G);
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N := Normaliser( Sym(2*#G), GDouble );
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subs := Subgroups(N : OrderEqual := 2*#G );
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subs := [sub`subgroup : sub in subs];
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subs := [H : H in subs | GDouble subset H ];
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return subs;
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end function;
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function ConstructDoubleCovers2(G)
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GDouble := DoubleGroup(G);
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N := Normaliser( Sym(2*#G), GDouble );
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Quoziente, Proiezione := N/GDouble;
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Sezione := Proiezione^(-1);
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Els2 := [q : q in Quoziente | Order(q) eq 2];
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subs := [ sub< N | GDouble, Sezione(q) > : q in Els2 ];
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return subs;
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end function;
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function ConstructDoubleCovers3(G)
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"Computing double";
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time GDouble := DoubleGroup(G);
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"Computing normaliser";
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time N := Normaliser( Sym(2*#G), GDouble );
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"Computing Sylow subgroup";
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Sylow2 := SylowSubgroup(N, 2);
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"Computing quotient";
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"Order of quotient:", #Sylow2 / #GDouble;
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time Quoziente, Proiezione := Sylow2/GDouble;
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"Computing section";
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time Sezione := Proiezione^(-1);
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"Computing elements of order 2 in the quotient";
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time Els2 := Subgroups(Quoziente : OrderEqual := 2);
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"Computing subgroups";
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time subs := [ sub< N | GDouble, Sezione(q`subgroup) > : q in Els2 ];
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return subs;
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end function;
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/*
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Given a list L of groups, returns a list L' that contains
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every isomorphism class of groups in L precisely once
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*/
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function FilterDuplicates(list)
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CleanList := [];
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for H in list do
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test := true;
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for H2 in CleanList do
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if test then
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test := test and not IsIsomorphic(H, H2);
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end if;
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end for;
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if test then
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CleanList := CleanList cat [H];
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end if;
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end for;
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return CleanList;
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end function;
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function FilterDuplicatesFast(list)
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CleanList := [];
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CleanNames := [];
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for H in list do
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if not GroupName(H) in CleanNames then
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CleanList := CleanList cat [H];
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CleanNames := CleanNames cat [GroupName(H)];
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end if;
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end for;
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return CleanList;
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end function;
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/*
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Given a list L of groups [G_i], returns a list L' = [H_j]
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where each H_j contains some G_i with index 2, every
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group with this property appears in L', and L' contains no
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duplicates up to isomorphism.
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*/
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function DoubleListSlow(L)
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LNew := [];
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for G in L do
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dc := ConstructDoubleCovers(G);
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dc := FilterDuplicates(dc);
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LNew := LNew cat dc;
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end for;
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return FilterDuplicates(LNew);
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end function;
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function DoubleList(L)
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LNew := [];
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for G in L do
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time dc := ConstructDoubleCovers3(G);
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time dc := FilterDuplicatesFast(dc);
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LNew := LNew cat dc;
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end for;
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return FilterDuplicatesFast(LNew);
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end function;
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list2 := [CyclicGroup(2)];
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time list4 := DoubleList(list2);
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time list8 := DoubleList(list4);
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time list16 := DoubleList(list8);
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time list32 := DoubleList(list16);
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time list64 := DoubleList(list32);
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assert #list32 eq NumberOfSmallGroups(32);
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assert #list64 eq NumberOfSmallGroups(64);
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@ -0,0 +1,96 @@
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anyio==4.6.2.post1
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argon2-cffi==23.1.0
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argon2-cffi-bindings==21.2.0
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arrow==1.3.0
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asttokens==2.4.1
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async-lru==2.0.4
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attrs==24.2.0
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babel==2.16.0
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beautifulsoup4==4.12.3
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bleach==6.2.0
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certifi==2024.8.30
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cffi==1.17.1
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charset-normalizer==3.4.0
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comm==0.2.2
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debugpy==1.8.9
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decorator==5.1.1
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defusedxml==0.7.1
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executing==2.1.0
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fastjsonschema==2.20.0
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fqdn==1.5.1
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h11==0.14.0
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httpcore==1.0.7
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httpx==0.27.2
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idna==3.10
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ipykernel==6.29.5
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ipython==8.29.0
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ipywidgets==8.1.5
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isoduration==20.11.0
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jedi==0.19.2
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Jinja2==3.1.4
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json5==0.9.28
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jsonpointer==3.0.0
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jsonschema==4.23.0
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jsonschema-specifications==2024.10.1
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jupyter==1.1.1
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jupyter-console==6.6.3
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jupyter-events==0.10.0
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jupyter-lsp==2.2.5
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jupyter_client==8.6.3
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jupyter_core==5.7.2
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jupyter_server==2.14.2
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jupyter_server_terminals==0.5.3
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jupyterlab==4.2.6
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jupyterlab_pygments==0.3.0
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jupyterlab_server==2.27.3
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jupyterlab_widgets==3.0.13
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-e git+https://github.com/nbruin/magma_kernel@4418bd79d1756c7558374086b6ef47b4e18207c2#egg=magma_kernel
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MarkupSafe==3.0.2
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matplotlib-inline==0.1.7
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mistune==3.0.2
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nbclient==0.10.0
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nbconvert==7.16.4
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nbformat==5.10.4
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nest-asyncio==1.6.0
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notebook==7.2.2
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notebook_shim==0.2.4
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overrides==7.7.0
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packaging==24.2
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pandocfilters==1.5.1
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parso==0.8.4
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pexpect==4.9.0
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platformdirs==4.3.6
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prometheus_client==0.21.0
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prompt_toolkit==3.0.48
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psutil==6.1.0
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ptyprocess==0.7.0
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pure_eval==0.2.3
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pycparser==2.22
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Pygments==2.18.0
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python-dateutil==2.9.0.post0
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python-json-logger==2.0.7
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PyYAML==6.0.2
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pyzmq==26.2.0
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referencing==0.35.1
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requests==2.32.3
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rfc3339-validator==0.1.4
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rfc3986-validator==0.1.1
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rpds-py==0.21.0
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Send2Trash==1.8.3
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setuptools==75.6.0
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six==1.16.0
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sniffio==1.3.1
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soupsieve==2.6
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stack-data==0.6.3
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terminado==0.18.1
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tinycss2==1.4.0
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tornado==6.4.2
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traitlets==5.14.3
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types-python-dateutil==2.9.0.20241003
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uri-template==1.3.0
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urllib3==2.2.3
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wcwidth==0.2.13
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webcolors==24.11.1
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webencodings==0.5.1
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websocket-client==1.8.0
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widgetsnbextension==4.0.13
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