Differences between revisions 1 and 9 (spanning 8 versions)

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

Contents

Sage Interactions - Groups
1. Calling Groups from GAP
2. Calling a List of Groups from GAP

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 are 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

You can use this interact to

-  ⇤ ← Revision 1 as of 2021-08-05 15:32:46 → 
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-== Basic Commands ==

explanation

=== All groups of order less than or equal to n ===


You can use this interact to call all the lists from the GAP library that are order less than or equal to your desired n value.


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Groups</h1>"))
pretty_print(html("<h>put in the n and m<h>"))
+== 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.<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>Select the order and type of group.<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.<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

=== Groups Order Less Than or Equal to n ===


Use this interact to call all groups from the GAP library that are order less than or equal to your desired value.


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Upper Bound on Order </h1>"))
pretty_print(html("<h>Choose an upper bound for the order.<h>"))
-Line 51:
+Line 158:
-=== All groups of order between m and n ===


You can use this interact to call all the lists from the GAP library that are between m and n


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Groups</h1>"))
pretty_print(html("<h>put in the n and m<h>"))
+=== 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


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Upper and Lower Bound on Order</h1>"))
pretty_print(html("<h>Choose an upper bound and a lower bound for the order.<h>"))
-Line 84:
+Line 191:
-=== All groups of which meet certain parameters ===


You can use this interact to call all the lists from the GAP library that are order less than or equal to your desired n value.


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Groups</h1>"))
pretty_print(html("<h>put in the n and m<h>"))
+=== Groups of a Certain Type ===


You can use this interact to 


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Group Type</h1>"))
pretty_print(html("<h>Select a parameter.<h>"))
-Line 120:
+Line 227:
-=== All groups of which meet certain parameters ===


You can use this interact to call all the lists from the GAP library that are order less than or equal to your desired n value.


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Groups</h1>"))
pretty_print(html("<h>put in the n and m<h>"))
+=== Direct or Semidirect Product Groups ===


{{{#!sagecell
#Last edited 8/5/21 2:45pm
pretty_print(html("<h1>Direct or Semidirect</h1>"))
pretty_print(html("<h>Check a box to limit the results<h>"))

Diff for "interact/groups"