Peter Alspaugh's Website

 This is intended to be somewhat of an informal CV/portfolio for me. In the posts, you will find updates on my work, along with some GAP coding work.

  # the function will try each monoid for arg4 seconds before moving on to the next. The relevant function is TestCoxeterOrigami NumberCombos:=function(m,n,lists,iteration) local i,j,list,list2,lists2; lists2:=[]; if iteration<m+1 then if lists=[] then for i in [0..n] do Add(lists2,[i]); od; else for list in lists do for i in [0..3] do list2:=ShallowCopy(list); Add(list2,Random([0..n])); Add(lists2, list2); od; od; fi; else return lists; fi; j:=iteration+1; return NumberCombos(m,n,lists2,j); end; CreateCoxeterInput := function(numGenerators, n, p) local generators, inputs, a, b, c, d, i, j, k, y, z, blank, range, ranges, pos, rel, numlists, blanker, numbers; # Generate generator names generators := List([1..numGenerators], i -> Concatenation("g", String(i))); # Create relations blank := []; for a in generators do for b in generators do if not a=b then rel:=[a,,b]; Add(blank,rel); fi; ...

Mapper:=function(word,arg) local i, u, v, w, prod, monoid; w:=ExtRepOfObj(word); prod:=[]; if IsMonoid(arg) then monoid:=arg; for i in [1..(Length(w)/2)] do u:=monoid.(w[2*i-1])^(w[2*i]); Add(prod, u); od; elif IsSemigroup(arg) then monoid:=arg; for i in [1..(Length(w)/2)] do u:=monoid.(w[2*i-1])^(w[2*i]); Add(prod, u); od; else for i in [1..(Length(w)/2)] do u:=arg[(w[2*i-1])]^(w[2*i]); Add(prod, u); od; fi; v:=Product(prod); return v; end; OrigamiMonoidIdemp:=function(monoid) local gens, mgens, rels, newrels, mrels, agens, bgens, arels, brels, abgens, bagens, doublegens, doublerels, w, free, left, right, abrels, barels, M, rws, freeaddrules, creatingrules, i, j, n, generatorMap, fgens, pos, gens0, mapped, commrels; # Step 0: Check if M is a finitely presented monoid if not IsFpMonoid(monoid) then Print("Not a monoid. \n"); return fail; fi; gens:=[]; for i in [1..Size(GeneratorsOfMonoid(monoid))] do Add(gens...

  CoxeterMonoid:=function(D) # takes lists of relations of the form ["x",m,"y"] where x,y are generators and n is pos. int. local gens, rels, i, j, k, fm, f, n; gens := []; rels := []; # Collect generators from input D for i in D do Add(gens, i[1]); Add(gens, i[3]); od; gens := Set(gens); # Ensure gens contains unique elements fm := FreeMonoid(gens); # Construct relations based on triples in input D for i in D do j := Position(gens, i[1]); k := Position(gens, i[3]); n:=Int((i[2])/2); # Add matrix relations if n=i[2]/2 then Add(rels, [(fm.(k) * fm.(j))^(n), (fm.(j) * fm.(k))^(n)]); else Add(rels, [(fm.(k) * fm.(j))^(n)*fm.(k), (fm.(j) * fm.(k))^(n)*fm.(j)]); fi; # Add idempotence relations Add(rels, [fm.(j)^2,fm.(j)]); Add(rels, [fm.(k)^2,fm.(k)]); od; rels:=Set(rels); # Define finitely presented monoid with relations f := fm / rels; ...