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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 firstname.lastname@emory.edu.
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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Order n </h1>"))pretty_print(html("<h>Choose a group order and a group number.<h>"))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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Pick a Group</h1>"))pretty_print(html("<h>Choose a group order, a group type and a group number.<h>"))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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Order n </h1>"))pretty_print(html("<h>Choose a group order.<h>"))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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Order n </h1>"))pretty_print(html("<h>Choose a group order and a group type.<h>"))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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Order n </h1>"))pretty_print(html("<h>Choose a group order.<h>"))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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Upper Bound on Order </h1>"))pretty_print(html("<h>Choose an upper bound for the order.<h>"))def order_n(n, *parameter, start=1): below_order_n = gap('EmptyPlist(1)') #documentation on AllSmallGroups command and Structure description #is in the GAP System reference guide for i in range(start,n+1): g=gap(i).AllSmallGroups(*parameter) for x in range(1,len(g)+1): r=gap(g[x]).StructureDescription() gap.Add(below_order_n,r) #convert gap object to python string below_order_n = libgap(below_order_n).sage() return below_order_ndef foo(n = input_box(default='10', label="Upper Bound:")): print(order_n(n))
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
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_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>"))def order_n(n, *parameter, start=1): below_order_n = gap('EmptyPlist(1)') #documentation on AllSmallGroups command and Structure description #is in the GAP System reference guide for i in range(start,n+1): g=gap(i).AllSmallGroups(*parameter) for x in range(1,len(g)+1): r=gap(g[x]).StructureDescription() gap.Add(below_order_n,r) #convert gap object to python string below_order_n = libgap(below_order_n).sage() return below_order_ndef foo(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:")): print(order_n(n,start=m))
Groups of a Certain Type
You can use this interact to
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Group Type</h1>"))pretty_print(html("<h>Select a group type.<h>"))def order_n(n, *parameter, start=1): below_order_n = gap('EmptyPlist(1)') #documentation on AllSmallGroups command and Structure description #is in the GAP System reference guide for i in range(start,n+1): g=gap(i).AllSmallGroups(*parameter) for x in range(1,len(g)+1): r=gap(g[x]).StructureDescription() gap.Add(below_order_n,r) #convert gap object to python string below_order_n = libgap(below_order_n).sage() return below_order_ndef foo(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:"), Parameter = ["IsGroup","IsAbelian","IsCyclic","IsSolvable","IsNilpotent","IsSimple","IsDihedralGroup", "IsSymmetricGroup","IsAlternatingGroup","IsPerfectGroup","IsPolycyclicGroup"]): print(order_n(n,Parameter,start=m))
Direct or Semidirect Product Groups
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Direct or Semidirect</h1>"))pretty_print(html("<h>Check a box to limit the results<h>"))def _directprod(order_n): new_order_n = [] for i in range(0,len(order_n)): word=order_n[i].split(' ') if 'x' in word: new_order_n.append(order_n[i]) return new_order_ndef _semidirectprod(order_n): new_order_n = [] for i in range(0,len(order_n)): word=order_n[i].split(' ') if ':' in word: new_order_n.append(order_n[i]) return new_order_ndef order_n(n, *parameter, start=1,directproduct=False, semidirectproduct=False): below_order_n = gap('EmptyPlist(1)') #documentation on AllSmallGroups command and Structure description #is in the GAP System reference guide for i in range(start,n+1): g=gap(i).AllSmallGroups(*parameter) for x in range(1,len(g)+1): r=gap(g[x]).StructureDescription() gap.Add(below_order_n,r) #convert gap object to python string below_order_n = libgap(below_order_n).sage() #only print out direct or semi direct prod if asked if directproduct == True: below_order_n = _directprod(below_order_n) if semidirectproduct == True: below_order_n = _semidirectprod(below_order_n) return below_order_ndef foo(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:"), Parameter = ["IsGroup","IsAbelian","IsCyclic","IsSolvable","IsNilpotent","IsSimple","IsDihedralGroup", "IsSymmetricGroup","IsAlternatingGroup","IsPerfectGroup","IsPolycyclicGroup"], Direct = checkbox(default = False), Semidirect = checkbox(default = False)): if (Direct == True) and (Semidirect == True): print(order_n(n,Parameter,start=m,directproduct=true, semidirectproduct=true)) if Direct == True and Semidirect == False: print(order_n(n,Parameter,start=m,directproduct=true)) if Direct == False and Semidirect == True: print(order_n(n,Parameter,start=m,semidirectproduct=true))