{"text_format":"3","workbook":"xls","n_sheets":3,"sheets":["Sheet1","Explanation of Functions","Sample Cayley Table"],"not_rendered":{"images":2,"macros":1,"external_links":1,"defined_names":1},"read":"whole","date_system":"1900","formulas":"cached_only"}

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[null,null,"[D4]"]
[null,null,"e"]
[null,null,"(1234)"]
[null,null,"(13)(24)"]
[null,null,"(1432)"]
[null,null,"(14)(23)"]
[null,null,"(12)(34)"]
[null,null,"(13)"]
[null,null,"(24)"]
[]
[]
[]
[]
[null,null,"e"]
[null,null,"(1234)",{"$nulls":13},""]
[null,null,"(13)(24)"]
[null,null,"(1432)"]
[]
[]
[{"$nulls":10},""]

{"sheet":"Explanation of Functions","index":1,"n_rows":43,"n_cols":2,"rows_kept":43,"merged":[[5,2,6,2]],"flags":["formulas_cached_only"]}
[]
[null,"Enter permutation as a string.  If it is obviously not a number, e.g. (13)(24)(57),  then Excel will treat it as a string.  If there is only one cycle, e.g. (12345) then Excel may treat it as a negative unless you prefix it with a single quote.  The quote has no effect on processing, and does not display.  You can enter the identity element as 'e'.  <setlength> can be any number from 1 to 9, and denotes the length of the sequence used, e.g. a setlength of 8 means that the labels 1,2,3..........8 are in use.\nUseful tip: to display a perm in 'standard form' with lowest label first in cycle and cycle containing lowest label first, just compose it with 'e'."]
[]
[]
[null,"FUNCTIONS"]
[null,"Compose(perm1,perm2)"]
[null,"Returns <perm1>o <perm2>"]
[]
[null,"mCompose(perm1,perm2,......)"]
[null,"Returns perm1 o perm2 o perm3 ....i.e. perm (n-1) o perm(n) is performed first"]
[]
[null,"rCompose(<range>)"]
[null,"Returns one perm which is the composition of all elements in the range.  The last  two perms in the range are composed first."]
[]
[null,"Inverse(perm)"]
[null,"Returns inverse of <perm>"]
[]
[null,"Order(perm,setlength)"]
[null,"Returns order of <perm>, i.e. power <perm> must be raised to to get 'e'"]
[]
[null,"RaiseToPower(perm,power)"]
[null,"Returns <perm> to power <power>"]
[]
[null,"Conjugate(perm1,perm2)"]
[null,"Returns the result of composing <perm1> o <perm2> o Inverse(<perm1>)"]
[]
[null,"Disjoint(perm)"]
[null,"Returns <perm> as a disjoint perm if was not already so, otherwise does nothing"]
[]
[null,"CycleSymbol(perm)"]
[null,"Returns a cycle symbol for perm, as used in Polya's Counting Theorem"]
[]
[null,"EquivalenceClasses(range,colours)"]
[null,"Returns the number of equivalence classes for colouring the object described by the group in <range>, using <colours>, <setlength> has its usual meaning, and <grouporder> is the order of the group"]
[]
[null,"hcf(a,b)"]
[null,"Returns Highest Common Factor of a and b"]
[]
[null,"lcm(a,b)"]
[null,"Returns Lowest Commmon Multiple of a and b"]
[]
[null,"CycleSymbol(perm,setlength)"]
[null,"Returns cycle symbol for <perm> in the form used in Polya's Counting Theorem"]

{"sheet":"Sample Cayley Table","index":2,"n_rows":12,"n_cols":10,"rows_kept":12,"flags":["formulas_cached_only"]}
[]
[null,"Group: Direct symmetries  of square prism (isomorphous to D4)"]
[]
[null,null,"e","(2345)","(24)(35)","(16)(24)","(2543)","(16)(23)(45)","(16)(25)(34)","(16)(35)"]
[null,"e","e","(2345)","(24)(35)","(16)(24)","(2543)","(16)(23)(45)","(16)(25)(34)","(16)(35)"]
[null,"(2345)","(2345)","(24)(35)","(2543)","(16)(25)(34)","e","(16)(24)","(16)(35)","(16)(23)(45)"]
[null,"(24)(35)","(24)(35)","(2543)","e","(16)(35)","(2345)","(16)(25)(34)","(16)(23)(45)","(16)(24)"]
[null,"(16)(24)","(16)(24)","(16)(23)(45)","(16)(35)","e","(16)(25)(34)","(2345)","(2543)","(24)(35)"]
[null,"(2543)","(2543)","e","(2345)","(16)(23)(45)","(24)(35)","(16)(35)","(16)(24)","(16)(25)(34)"]
[null,"(16)(23)(45)","(16)(23)(45)","(16)(35)","(16)(25)(34)","(2543)","(16)(24)","e","(24)(35)","(2345)"]
[null,"(16)(25)(34)","(16)(25)(34)","(16)(24)","(16)(23)(45)","(2345)","(16)(35)","(24)(35)","e","(2543)"]
[null,"(16)(35)","(16)(35)","(16)(25)(34)","(16)(24)","(24)(35)","(16)(23)(45)","(2543)","(2345)","e"]