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| == Basic Commands == explanation |
== Calling Groups from GAP == explanation of what we are doing (calling GAP), what gap is and what its limitations are === Group of Order n === Use this interact to call a group of order n from the GAP library. {{{#!sagecell #Last edited 8/5/21 2:45pm pretty_print(html("<h1>Order n </h1>")) pretty_print(html("<h>Choose a group order and a group number.<h>")) @interact def foo(n = input_box(default='10', label="Order:"), m = input_box(default='1', label= "Group Number:")): top = len(gap(n).AllSmallGroups()) print('There are', top, 'groups of order', n ,'in the GAP library.') print('Group', m , 'of', top, 'is', gap(gap(n).SmallGroup(m)).StructureDescription()) }}} === Group of Order n of a Certain Type === Use this interact to specify a type of group to call. {{{#!sagecell #Last edited 8/5/21 2:45pm pretty_print(html("<h1>Pick a Group</h1>")) pretty_print(html("<h>Choose a group order, a group type and a group number.<h>")) @interact def foo(n = input_box(default='10', label="Order:"), Parameter = ["IsGroup","IsAbelian","IsCyclic","IsSolvable","IsNilpotent","IsSimple","IsDihedralGroup", "IsSymmetricGroup","IsAlternatingGroup","IsPerfectGroup","IsPolycyclicGroup"], m = input_box(default='1', label= "Group Number:")): top = len(gap(n).AllSmallGroups(Parameter)) print('There are', top, Parameter, 'groups of order', n ,'in the GAP library.') print('Group', m , 'of', top, 'is', gap(gap(n).SmallGroup(m)).StructureDescription()) }}} === All Groups of Order n === Use this interact to call all groups of order n from the GAP library. {{{#!sagecell #Last edited 8/5/21 2:45pm pretty_print(html("<h1>Order n </h1>")) pretty_print(html("<h>Choose a group order.<h>")) @interact def foo(n = input_box(default='10', label="Order:")): h = gap(n).AllSmallGroups() for x in [1..len(h)]: print(h[x].StructureDescription()) }}} === All Groups of Order n of a Certain Type === Use this interact to specify a type of group to call. {{{#!sagecell #Last edited 8/5/21 2:45pm pretty_print(html("<h1>Order n </h1>")) pretty_print(html("<h>Choose a group order and a group type.<h>")) @interact def foo(n = input_box(default='10', label="Order:"), Parameter = ["IsGroup","IsAbelian","IsCyclic","IsSolvable","IsNilpotent","IsSimple","IsDihedralGroup", "IsSymmetricGroup","IsAlternatingGroup","IsPerfectGroup","IsPolycyclicGroup"]): h = gap(n).AllSmallGroups(Parameter) for x in [1..len(h)]: print(h[x].StructureDescription()) }}} === Small Group Info === Use this interact to learn information about the small groups of order n contained in the GAP library. {{{#!sagecell #Last edited 8/5/21 2:45pm pretty_print(html("<h1>Order n </h1>")) pretty_print(html("<h>Choose a group order.<h>")) @interact def foo(n = input_box(default='32', label="Order:")): print(gap(n).SmallGroupsInformation()) }}} == Calling a List of Groups from GAP == explanation part 2 |
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| You can use this interact to call all the lists from the GAP library that are order less than or equal to your desired value. | Use this interact to call all groups from the GAP library that have order less than or equal to your desired value. |
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| You can use this interact to call all the lists from the GAP library that have order between m and n | Use this interact to call all the groups from the GAP library that have order between m and n |
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| === Groups Meeting Selected Parameters === You can use this interact to |
=== Groups of a Certain Type === Use this interact to call all groups of a certain type from the GAP library that have order between m and n |
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| pretty_print(html("<h>Select a parameter.<h>")) | pretty_print(html("<h>Select a group type, an upper bound and a lower bound.<h>")) |
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| === Direct or Semidirect Groups === |
=== Direct or Semi-direct Product Groups === Use this interact to specify groups that contain direct or semi-direct products. |
Sage Interactions - Groups
This page was first created for Google Summer of Code by Alexis Newton, with mentorship by Mckenzie West.
If you have group-related interactions that you are interested in adding to this page, please do so. You can also contact Alexis Newton at [email protected].
goto interact main page
Calling Groups from GAP
explanation of what we are doing (calling GAP), what gap is and what its limitations are
Group of Order n
Use this interact to call a group of order n from the GAP library.
Group of Order n of a Certain Type
Use this interact to specify a type of group to call.
All Groups of Order n
Use this interact to call all groups of order n from the GAP library.
All Groups of Order n of a Certain Type
Use this interact to specify a type of group to call.
Small Group Info
Use this interact to learn information about the small groups of order n contained in the GAP library.
Calling a List of Groups from GAP
explanation part 2
Groups Order Less Than or Equal to n
Use this interact to call all groups from the GAP library that have order less than or equal to your desired value.
Groups Order Between m and n
Use this interact to call all the groups from the GAP library that have order between m and n
Groups of a Certain Type
Use this interact to call all groups of a certain type from the GAP library that have order between m and n
Direct or Semi-direct Product Groups
Use this interact to specify groups that contain direct or semi-direct products.