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⇤ ← Revision 1 as of 2021-08-05 15:32:46
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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 n value. | 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. |
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| pretty_print(html("<h1>Groups</h1>")) pretty_print(html("<h>put in the n and m<h>")) |
pretty_print(html("<h1>Version 1/h1>")) pretty_print(html("<h>Choose an upper bound for the order.<h>")) |
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| You can use this interact to call all the lists from the GAP library that are between m and n | You can use this interact to call all the lists from the GAP library that have order between m and n |
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| pretty_print(html("<h1>Groups</h1>")) pretty_print(html("<h>put in the n and m<h>")) |
pretty_print(html("<h1>Version 2</h1>")) pretty_print(html("<h>Choose an upper bound and a lower bound for the order.<h>")) |
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| pretty_print(html("<h1>Groups</h1>")) pretty_print(html("<h>put in the n and m<h>")) |
pretty_print(html("<h1>Version 3</h1>")) pretty_print(html("<h>Choose a parameter.<h>")) |
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| === All groups of which meet certain parameters === | === All groups of which meet certain parameters, and direct/semi dircet === |
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| pretty_print(html("<h1>Groups</h1>")) pretty_print(html("<h>put in the n and m<h>")) |
pretty_print(html("<h1>Version 4</h1>")) pretty_print(html("<h>Direct or Semidirect?<h>")) |
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
Contents
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 value.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Version 1/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))
All groups of order between m and n
You can use this interact to call all the lists from the GAP library that have order between m and n
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Version 2</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))
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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Version 3</h1>"))pretty_print(html("<h>Choose a parameter.<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))
All groups of which meet certain parameters, and direct/semi dircet
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.
xxxxxxxxxx#Last edited 8/5/21 2:45pmpretty_print(html("<h1>Version 4</h1>"))pretty_print(html("<h>Direct or Semidirect?<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))