Merge pull request #47 from kalmarek/enh/kbmag_parsing

Enh/kbmag parsing

Project.toml

@@ -1,10 +1,14 @@
 name = "KnuthBendix"
 uuid = "c2604015-7b3d-4a30-8a26-9074551ec60a"
 authors = ["Marek Kaluba <[email protected]>", "Mikołaj Pabiszczak <[email protected]>"]
-version = "0.1.0"
+version = "0.1.1"
+
+[deps]
+MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 
 [compat]
 julia = "1"
+MacroTools = "0.5"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

kb_data/237

@@ -0,0 +1,11 @@
+#Von Dyck (2,3,7) group - infinite hyperbolic - small tidyint works better
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  tidyint := 20,
+  generatorOrder := [a,A,b,B,c],
+  inverses := [A,a,B,b,c],
+  equations := [
+  [a*a*a*a,A*A*A], [b*b,B], [B*A,c]
+]
+);

kb_data/3a6

@@ -0,0 +1,12 @@
+#3-fold cover of A_6
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,b,A,B],
+  inverses := [A,B,a,b],
+  equations := [[a^3,IdWord],
+                [b^3,IdWord],
+                [(a*b)^4,IdWord],
+                [(a*B)^5,IdWord]
+               ]
+);

kb_data/a4

@@ -0,0 +1,8 @@
+#Group is A_4. Generators named by the enumerated prefix method.
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [g.10,g.20,g.30],
+  inverses := [g.10,g.30,g.20],
+  equations := [ [g.20*g.20,g.30], [g.30*g.10*g.30,g.10*g.20*g.10] ]
+);

kb_data/a4monoid

@@ -0,0 +1,11 @@
+#Presentation of group A_4 regarded as monoid presentation
+# - gives infinite monoid.
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,b,B],
+  inverses := [],
+  equations := [
+    [b*b,B], [B*a*B,a*b*a]
+  ]
+);

kb_data/ab1

@@ -0,0 +1,8 @@
+#infinite cyclic group
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A],
+  inverses := [A,a],
+  equations := []
+);

kb_data/ab2

@@ -0,0 +1,8 @@
+#2-generator free abelian group (with this ordering KB terminates - but no all)
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A,b,B],
+  inverses := [A,a,B,b],
+  equations := [[B*a*b,a]]
+);

kb_data/c2

@@ -0,0 +1,8 @@
+#Cyclic group of order 2.
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a],
+  inverses := [a],
+  equations := [[a^2,IdWord]]
+);

kb_data/cosets

@@ -0,0 +1,13 @@
+#The group is S_4, and the subgroup H of order 4.
+#There are 30 reduced words - 24 for the group elements, and 6 for the
+#6 cosets Hg.
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [H,a,A,b,B],
+  inverses := [,A,a,B,b],
+  equations := [
+    [a^3,IdWord], [b^4,IdWord], [a*b*a*b,IdWord], [H*b,H],
+    [H*H,H], [a*H,H], [b*H,H]
+  ]
+);

kb_data/d22

@@ -0,0 +1,16 @@
+#This group is actually D_22 (although it wasn't meant to be).
+#All generators are unexpectedly involutory. 
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A,b,B,c,C,d,D,e,E,f,F],
+  inverses := [A,a,B,b,C,c,D,d,E,e,F,f],
+  equations := [
+  [a*C*A*d,IdWord],
+  [b*f*B*E,IdWord],
+  [c*e*C*D,IdWord],
+  [d*F*D*a,IdWord],
+  [e*b*E*A,IdWord],
+  [f*C*F*B,IdWord]
+               ]
+);

kb_data/degen1

@@ -0,0 +1,8 @@
+#No generators - no anything!
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [],
+  inverses := [],
+  equations := []
+);

kb_data/degen2

@@ -0,0 +1,8 @@
+#A generator, but trivial.
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A],
+  inverses := [A,a],
+  equations := [[a,IdWord]]
+);

kb_data/degen3

@@ -0,0 +1,8 @@
+#fairly clearly the trivial group
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A,b,B],
+  inverses := [A,a,B,b],
+  equations := [[a*b,IdWord],[a*b*b,IdWord]]
+);

kb_data/degen4a

@@ -0,0 +1,8 @@
+#trivial group - BHN presentation
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A,b,B,c,C],
+  inverses := [A,a,B,b,C,c],
+  equations := [[A*b*a,b^2], [B*c*b,c^2], [C*a*c,a^2] ]
+);

kb_data/degen4b

@@ -0,0 +1,14 @@
+#Second of BHN's series of increasingly complicated presentations of 1.
+#Works quickest with large value of tidyint
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  tidyint := 3000,
+  generatorOrder := [x,X,y,Y,z,Z],
+  inverses := [X,x,Y,y,Z,z],
+  equations := [
+  [y*y*X*Y*x*Y*z*y*Z*Z*X*y*x*Y*Y*z*z*Y*Z*y*z*z*Y*Z*y,IdWord],
+  [z*z*Y*Z*y*Z*x*z*X*X*Y*z*y*Z*Z*x*x*Z*X*z*x*x*Z*X*z,IdWord],
+  [x*x*Z*X*z*X*y*x*Y*Y*Z*x*z*X*X*y*y*X*Y*x*y*y*X*Y*x,IdWord]
+               ]
+);

kb_data/degen4c

@@ -0,0 +1,23 @@
+#Third of BHN's series of increasingly complicated presentations of 1.
+#This is too difficult for KB!!
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  tidyint := 3000,
+  generatorOrder := [r,R,s,S,t,T],
+  inverses := [R,r,S,s,T,t],
+  equations := [
+  [S*t*s*T*T*S*t*s*T*T*s*s*R*S*r*t*t*S*T*s*R*s*r*S*S*t*t*S*T*s*T*r*t*R*R*S*t*s*
+   T*T*r*r*T*R*t*r*r*T*R*t*s*s*R*S*r*S*t*s*T*T*R*s*r*S*S*t*t*S*T*s*t*t*S*T*s*T*
+   r*t*R*R*T*r*t*R*R*t*t*S*T*s*r*r*T*R*t*S*t*s*T*T*T*r*t*R*R*T*r*t*R*R*t*t*S*T*
+   s*r*r*T*R*t*S*t*s*T*T,  IdWord],
+  [T*r*t*R*R*T*r*t*R*R*t*t*S*T*s*r*r*T*R*t*S*t*s*T*T*r*r*T*R*t*R*s*r*S*S*T*r*t*
+   R*R*s*s*R*S*r*s*s*R*S*r*t*t*S*T*s*T*r*t*R*R*S*t*s*T*T*r*r*T*R*t*r*r*T*R*t*R*
+   s*r*S*S*R*s*r*S*S*r*r*T*R*t*s*s*R*S*r*T*r*t*R*R*R*s*r*S*S*R*s*r*S*S*r*r*T*R*
+   t*s*s*R*S*r*T*r*t*R*R,  IdWord],
+  [R*s*r*S*S*R*s*r*S*S*r*r*T*R*t*s*s*R*S*r*T*r*t*R*R*s*s*R*S*r*S*t*s*T*T*R*s*r*
+   S*S*t*t*S*T*s*t*t*S*T*s*r*r*T*R*t*R*s*r*S*S*T*r*t*R*R*s*s*R*S*r*s*s*R*S*r*S*
+   t*s*T*T*S*t*s*T*T*s*s*R*S*r*t*t*S*T*s*R*s*r*S*S*S*t*s*T*T*S*t*s*T*T*s*s*R*S*
+   r*t*t*S*T*s*R*s*r*S*S,  IdWord]
+               ]
+);

kb_data/e8

@@ -0,0 +1,16 @@
+#Weyl group E8 (all gens involutory).
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,b,c,d,e,f,g,h],
+  inverses := [a,b,c,d,e,f,g,h],
+  equations := [
+  [b*a*b,a*b*a],[c*a,a*c],[d*a,a*d],[e*a,a*e],[f*a,a*f],[g*a,a*g],[h*a,a*h],
+  [c*b*c,b*c*b],[d*b,b*d],[e*b,b*e],[f*b,b*f],[g*b,b*g],[h*b,b*h],
+  [d*c*d,c*d*c],[e*c*e,c*e*c],[f*c,c*f],[g*c,c*g],[h*c,c*h],
+  [e*d,d*e],[f*d,d*f],[g*d,d*g],[h*d,d*h],
+  [f*e*f,e*f*e],[g*e,e*g],[h*e,e*h],
+  [g*f*g,f*g*f],[h*f,f*h],
+  [h*g*h,g*h*g]
+ ]
+);

kb_data/f2

@@ -0,0 +1,8 @@
+#Free group on 2 generators
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A,b,B],
+  inverses := [A,a,B,b],
+  equations := []
+);

kb_data/f25

@@ -0,0 +1,9 @@
+#Fibonacci group F(2,5)
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,A,b,B,c,C,d,D,e,E],
+  inverses := [A,a,B,b,C,c,D,d,E,e],
+  equations := [[a*b,c], [b*c,d], [c*d,e], [d*e,a],  [e*a,b]
+               ]
+);

kb_data/f25monoid

@@ -0,0 +1,10 @@
+#Fibonacci group F(2,5) - monoid presentation - has order 12
+# (group elements + empty word)
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,b,c,d,e],
+  inverses := [],
+  equations := [[a*b,c], [b*c,d], [c*d,e], [d*e,a],  [e*a,b]
+               ]
+);

kb_data/f27

@@ -0,0 +1,10 @@
+#Fibonacci group F(2,7) - order 29 - works better with largish tidyint
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  tidyint := 1000,
+  generatorOrder := [a,A,b,B,c,C,d,D,e,E,f,F,g,G],
+  inverses := [A,a,B,b,C,c,D,d,E,e,F,f,G,g],
+  equations := [[a*b,c], [b*c,d], [c*d,e], [d*e,f], [e*f,g], [f*g,a], [g*a,b]
+               ]
+);

kb_data/f27_2gen

@@ -0,0 +1,13 @@
+#Two generator presentation of Fibonacci group F(2,7) - order 29
+#Large value of tidyint works better.
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  tidyint := 3000,
+  generatorOrder := [a,A,b,B],
+  inverses := [A,a,B,b],
+  equations := [
+	[b*a*b*a*b^2*a*b*a*b^2*a*b^2*a*b*a*b^2*a*b,a],
+	[a*b^2*a*b^2*a*b*a*b^2*a*b*a,b]
+  ]
+);

kb_data/f27monoid

@@ -0,0 +1,12 @@
+#monoid presentation of F(2,7) - should produce a monoid of length 30
+#which is the same as the group, together with the empty word.
+#This is a very difficult calculation indeed, however.
+_RWS := rec(
+  isRWS := true,
+  ordering := "recursive",
+  maxstoredlen := [15,15],
+  generatorOrder := [a,b,c,d,e,f,g],
+  inverses := [],
+  equations := [[a*b,c], [b*c,d], [c*d,e], [d*e,f], [e*f,g], [f*g,a], [g*a,b]
+               ]
+);

kb_data/freenilpc3

@@ -0,0 +1,15 @@
+_RWS := rec(
+  isRWS := true,
+  ordering := "recursive",
+  generatorOrder := [e,E,d,D,c,C,b,B,a,A],
+  inverses := [E,e,D,d,C,c,B,b,A,a],
+  equations := [
+    [B*A*b*a,c],
+    [C*A*c*a,d],
+    [C*B*c*b,e],
+    [d*a,a*d],
+    [e*a,a*e],
+    [d*b,b*d],
+    [e*b,b*e]
+  ]
+);

kb_data/funny3

@@ -0,0 +1,18 @@
+_RWS:= rec(
+        isRWS:=true,
+        generatorOrder:=[x,X,y,Y,z,Z],
+        inverses:=[X,x,Y,y,Z,z],
+        ordering:="shortlex",
+        equations:=[
+                [x*x*x,IdWord],
+                [y*y*y,IdWord],
+                [z*z*z,IdWord],
+                [X*Y*x,Y*x*Y],
+                [y*z*Y,z*Y*z],
+                [z*x*Z,x*Z*x],
+                [(x*y*z*X*Y*Z)^3,IdWord],
+                [(Y*z*x*y*Z*X)^3,IdWord],
+                [(z*y*X*Z*Y*x)^3,IdWord]
+                   ]
+);
+

kb_data/heinnilp

@@ -0,0 +1,24 @@
+#This example verifies the nilpotence of the group using the Sims algorithm.
+#The original presentation was <a,b| [b,a,a,a], [b^-1,a,a,a], [a,b,b,b],
+#                          [a^-1,b,b,b], [a,a*b,a*b,a*b], [a^-1,a*b,a*b,a*b] >.
+# (where [] mean left-normed commutators. The presentation here was derived by
+#first applying the NQA to find the maximal nilpotent quotient, and then
+#introducing new generators for the PCP generators.
+_RWS := rec(
+  isRWS := true,
+  ordering := "recursive",
+  generatorOrder := [f,F,e,E,d,D,c,C,b,B,a,A],
+  inverses := [F,f,E,e,D,d,C,c,B,b,A,a],
+  equations := [
+    [B*A*b*a,c],
+    [C*A*c*a,d],
+    [C*B*c*b,e],
+    [D*B*d*b,f],
+    #[d*a,a*d],
+    #[b*a*B*A*b*A*B*a,a*b*a*B*A*b*A*B],
+    [c*B*C*b,b*c*B*C],
+    [b*a*b*A*B*a*B*A,a*b*A*B*a*B*A*b],
+    [c*B*A*C*a*b,a*b*c*B*A*C],
+    [B*a*b*A*B*B*A*b*a*b,a*a*b*A*B*B*A*b]
+  ]
+);

kb_data/l32ext

@@ -0,0 +1,13 @@
+#An extension of 2^6 be L32
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,b,B],
+  inverses := [a,B,b],
+  equations := [
+   [a^2,IdWord],
+   [B^2,b],
+   [B*a*B*a*B*a*B,a*b*a*b*a*b*a],
+   [a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b,B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a ]
+  ]
+);

kb_data/m11

@@ -0,0 +1,13 @@
+#Mathieu group M_11
+_RWS := rec(
+  isRWS := true,
+  ordering := "shortlex",
+  generatorOrder := [a,b,B],
+  inverses := [a,B,b],
+  equations := [ 
+    [B^2,b^2],
+    [B*a*B*a*B*a*B*a*B*a*B,a*b*a*b*a*b*a*b*a*b*a],
+    [b^2*a*b^2*a*b^2*a,a*b^2*a*b^2*a*b^2],
+    [a*B*a*B*a*b*a*b*a*B*a*b*a*B^2*a*B*a*b,IdWord]
+  ]
+);

kb_data/nilp2

@@ -0,0 +1,10 @@
+#Free nilpotent group of rank 2 and class 2
+_RWS := rec(
+           isRWS := true,
+        ordering := "recursive",
+  generatorOrder := [c,C,b,B,a,A],
+        inverses := [C,c,B,b,A,a],
+       equations := [
+         [b*a,a*b*c], [c*a,a*c], [c*b,b*c]
+       ]
+);

kb_data/nonhopf

@@ -0,0 +1,10 @@
+#A nonhopfian group
+_RWS := rec(
+  isRWS := true,
+  maxeqns := 100,
+  maxstates := 200,
+  ordering := "recursive",
+  generatorOrder := [a,A,b,B],
+  inverses := [A,a,B,b],
+  equations := [[B*a^2*b,a^3]]
+);