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We rely heavily on the SmallGroup and AllSmallGroups GAP commands within this page. The documentation for these can be found in the GAP System website. |
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
GAP is a system... explain.. explanation of what we are doing (calling GAP), what gap is and what its limitations are
We rely heavily on the SmallGroup and AllSmallGroups GAP commands within this page. The documentation for these can be found in the GAP System website.
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 have 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
Use this interact to call all groups of a certain type from the GAP library that have order between m and n
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Group Type</h1>"))pretty_print(html("<h>Select a group type, an upper bound and a lower bound.<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 Semi-direct Product Groups
Use this interact to specify groups that contain direct or semi-direct products.
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))