PERFECT: Reduced the permutation degree for a few groups (gap-system#…

…4573)

The library stores groups through a presentation with words for the subgroup
stabilizer(s). In a few cases the groups created had an unreasonably large
permutation degree. This patch reduces the degrees by changing the
stabilizers. The ptresentations (and thus the groups) are not affected,
reducing the potential for accidental errors.

None of this affects the groups in the ``classical'' perfect groups library

grp/perf13.grp

@@ -3422,64 +3422,12 @@ a*b*a*c^2*b^-1*a^-1*b,
 )^2*a*b*c*a^-1*b^-1*d*b*d*c*b^-1*a^2*d*c^-1*b^-1*d*a*b^-1*d*b*a^-1*b*c^-1, 
   b*d*b*a^2*b^-1*a*b*a*c^2*b^-1*a^-1*c*a*c^2*(b^-1*a)^2*c*a*b^-1*a*b*a*c^2*b^-\
 1*c^-1*b^-1*a^-1*d*b*d*a^2*b*a*c^2*b^-1*a*b^-1*a^-1*b^-1*a*c^-1*b*d*a^-3*b ],
-[ [ d, b^-4, (b^-4)^(a^-1), d^(c^-1*a^-1), d^(c*a^-1), (d*a*d^-1*a^-1)^(a^-1),
-      (d*b*d^-1*b^-1)^(a^-1), d^(b^-1*a), (b^-4)^a, a^-1*c*a*c*d^-1*a^-1, 
-      (c*a^-1*b*a)^a, a^-1*d*a^2*d^-1*a^-1, (d*a^-1*d^-1*a)^a, 
-      a^-1*d*c*a*c*a^-1, (d*c^-1*d^-1*c)^a, d^(a*b^-1), b^2*a*b*c, 
-      b*c*b^-1*a*b^-1*a^-1, (b*c^-1)^2*d^-1*a^-1, (d*a*d^-1*a^-1)^(b^-1), 
-      (d*c*d^-1*c^-1)^(b^-1), b*d*c^-1*b*c^-1*a^-1, b^-1*a^-1*b^-1*c^-1*a^-2, 
-      b^-1*c^-1*b*c^-1*a^2, (d*a*d^-1*a^-1)^b, (d*c*d^-1*c^-1)^b, 
-      (d*c^-1*d^-1*c)^b, c*a*c*d^-1*a^-2, c*a*d*c*a^-2, c*a^-2*d^-1*c*a, 
-      (b^-4)^(c^-1), c^3*d^-1*c, d^(c^-2), c*d*a^-2*c*a, c*d*c^3, 
-      c^-1*a^2*c^-1*d^-1*a^-1, c^-1*a^-1*b^-1*d^-1*c*b, c^-1*b*a*c^2*a, 
-      c^-1*b*c^-1*a^-2*c^-1, (b^-4)^c, d^(c^2), d^(a^-3), 
-      a^2*b^-1*a*d^-1*c^-1*b^-1, (b^-4)^(a^-2), a^2*c^3*a^-1*c^-1, 
-      a^2*d*b^-1*a*c^-1*b^-1, (d*c*d^-1*c^-1)^(a^-2), d^(c^-1*b^-1*a^-1), 
-      d^(c*b^-1*a^-1), (d*a*d^-1*a^-1)^(b^-1*a^-1), a*b^-1*a^2*c*b*c, 
-      (a*b^-1)^2*a*d^-1*b^-1, (b^-1*a*c*a^-1*b^-2)^(a^-1), d^(c^-1*b*a^-1), 
-      (b^-1*c^-1*a*d^-1*b^-2)^(a^-1), (b^-1*d*c^-1*a*b^-2)^(a^-1), 
-      (c*a*b^-1*a^-1*c*b^-1)^(a^-1), (c*a*c*a^-1*d^-1*a^-1)^(a^-1), 
-      (c*b*c*b^-1*a^-2)^(a^-1), (b^-4)^(c^-1*a^-1), a*c*b^-1*c^-3*b^-1, 
-      (c^4*d^-1)^(a^-1), (c^-1*a^2*d^-1*c^-1*a^-1)^(a^-1), a*c^-1*a^-1*c^3*a, 
-      a*c^-1*b*a*b*a^-1*b, a*c^-1*(b*c)^2*c, (b^-4)^(c*a^-1), 
-      (d*c^-1*a^2*c^-1*a^-1)^(a^-1), a^-2*b*a^-1*c^-1*b^-1*c^-1, 
-      (b^-4)^(a^2), a^-2*b^-1*c*a*c^2*a^-1, a^-2*b^-1*c^-1*a*b^-1*c, 
-      a^-2*c^-1*a^3*c*a^-1, a^-2*c^-3*a*c, d^(c*a^2), 
-      a^-1*b*a*b*a^-2*b^-1*a^-1, a^-1*b*a*b^-1*c*b^-2*a^-1, 
-      a^-1*b*a*c^-1*b*a^-3, a^-1*b*a^-2*d^-1*b^-1*c*a^-1, 
-      (a^-1*b)^2*d^-1*a^-1*b, a^-1*b^2*a^-2*c^-1*b*a^-1, 
-      a^-1*b*c*b*a^-1*c^-1*b^-1, (a^-1*b*c^-1)^2*c^-1, a^-1*b^-1*a^2*c^-1*a*b,
-      (b^-1*a*b*a^-1*c)^a, a^-1*b^-1*a*(c^-1*b^-1)^2*a^-1, 
-      a^-1*b^-1*a^-2*b*a*b*a^-1, (b^-1*a^-1*c*b^-1*c)^a, 
-      a^-1*b^-1*a^-1*c^-1*a^-2*b, a^-1*b^-1*c*a^2*d^-1*b, 
-      a^-1*b^-1*c*a^-1*c*b*c*a^-1, a^-1*b^-1*c*b*a*b*a^-2, 
-      a^-1*b^-1*c*d*a^2*b, a^-1*b^-1*c^-1*b*a^-1*c*b, a^-1*b^-1*c^-2*a*c*b, 
-      a^-1*c*b^-1*a^-1*c^-1*b^-1*a^-2, (b^-4)^(c^-1*a), 
-      a^-1*(c*b^-1)^2*a^-1*b^-1, a^-1*c^2*a*(c*a^-1)^2, 
-      a^-1*c^2*a^-1*d^-1*b^-1*c, (a^-1*b*c*a^-1)^(c*a), (b^-4)^(c*a), 
-      (d*b*a*d^-1*a^-1*b^-1)^a, (d*b*c*d^-1*c^-1*b^-1)^a, a^-1*d*b^-1*c*a^2*b,
-      (d*b^-1*c^-1*d^-1*c*b)^a, (b*a^2)^2*c, b*a^2*b^-1*a^-1*b^-1*a^2, 
-      (a^2*c^-1*a^-1*c^-1)^(b^-1), b*a*b^-1*a^2*b*c^-1*a^-1, 
-      (b^-4)^(a^-1*b^-1), (a*c*a^-2*c)^(b^-1), d^(c^-1*a^-1*b^-1), 
-      b*a*c^-1*b*c^-1*a^-1*c, b*a*c^-1*b^-1*a*c*b*a^-1, 
-      b*a^-2*b*c^-1*b^-1*c^-1*a, b*a^-2*b^-1*c^-1*a*b, (a^-2*c*a*c)^(b^-1), 
-      (a^-1*b*c^-1*a*b^-1)^(b^-1), (b^-4)^(a*b^-1), 
-      (a^-1*b^-1*c^-1*b*c^-1*a^-1)^(b^-1), (a^-1*c*a*c*d^-1*a^-1)^(b^-1), 
-      (a^-1*c*d*a*c*a^-1)^(b^-1), (a^-1*c^-1*a^2*c^-1)^(b^-1), 
-      b*a^-1*c^-1*a^-1*b*c*a^2, b*a^-1*(c^-1*b)^2*a^-2, 
-      b^2*a^-2*c^-1*a*b*a^-1, (b*a^-1*b*a*c)^(b^-1), b*(b*c^-1)^2*a^-1*c*a, 
-      b^2*c^-1*b^-1*c^-1*a*b*a^-1, b*c*a*b*c^-1*b^-1*a^-2, 
-      (c*b*a*d^-1*c^-1*b^-1)^(b^-1), b*c*b^3*a*b^-1*a^-1, (b*c)^2*b^-2*a^2, 
-      (c^2*a^-1*c^-1*b*a^-1)^(b^-1), b*c^2*b*a*b*c^-1, (c^2*d*c^2)^(b^-1), 
-      b*c^-1*b^-1*a*b^-1*c^2*a^-1, (d*a^-2*d^-1*a^2)^(b^-1), 
-      (d*a^-1*c*a*c*a^-1)^(b^-1), b^-1*a^2*b*a^2*b^-1*a^-1, 
-      b^-1*a^2*b^-1*a^-1*c*b^-2, (a^2*c^-1*a^-1*c^-1)^b, 
-      b^-1*a*b*c*b^-1*a^-1*b*a^-1, (b^-4)^(a^-1*b), (a*c*a^-2*c)^b, 
-      b^-1*a*c*b*c*a^-1*c^-1, b^-1*a*c^-1*b^-1*c*a^-1*b^-1*a^-1, 
-      (a^-2*c*a*c)^b, b^-1*a^-1*b^3*c^-1*a^-2, (a^-1*c*a*c*d^-1*a^-1)^b ] ]];
+[ [ a, d, d^(b^-1), b^-4, d^(c^-1), d^c, (c^-1*a^-1)^(b^-2), b^(c^-1*b^-1),
+      d^(c*b^-1), b^-1*a*b^-1*d^-1*a*b^-1, d^(c*b), c^-2*a*c*a*c^-1,
+      (b^-4)^(a*b^-1) ] ]];
 end,
-[ 768 ]],
-"PG61440.79",0,2,1,768],
+[ 320 ]],
+"PG61440.79",0,2,1,320],
 # 61440.80
 [[1,"abcde",
 function(a,b,c,d,e)

grp/perf15.grp

@@ -14121,40 +14121,12 @@ e^-1*f, b^-1*c^-1*b*c*f*(f*b)^2*e^-1*b*a^-1*f^-1*a*e^-1*f*c^-1*f*b*e*b^-1*f*e,
 -1, 
   b^-1*f^2*b*a*d*f*d^-1*f*b*f^-1*a*b*e*b^-1*e*c^-1*d*c*a*f^-1*a*(b^-2*e^-1)^2*\
 b^-1*a^-1*f*b^-1*d*b^-1*e*b^-2 ],
-[ [ (e^-2)^(a^-1), a^-1*c^-1*b, (d^-2)^a, (e^-2)^a, (d^-2)^(c^-1), 
-      (e^-2)^(c^-1), (e^-2)^c, d^-1*e^2*d^-1, d^-1*f^2*d^-1, e*b*e^-1*b^-1, 
-      e*b^-1*e^-1*b, e^-1*f^2*e^-1, f*d*f*d^-1, (d^-2)^(b^-1*a^-1), 
-      a*c*a^-1*e^-1*b^-1, (e^-2)^(c^-1*a^-1), (e^-2)^(c*a^-1), 
-      (d^-1*f^2*d^-1)^(a^-1), (e*b*e^-1*b^-1)^(a^-1), (f*d*f*d^-1)^(a^-1), 
-      a^-1*b*a*c*b*a^-1, (d^-2)^(b^-1*a), (f^-2)^(b^-1*a), 
-      a^-1*b^-1*c*b^-1*c^-1, a^-1*c*b*c^-2, b*a*c^-1*e^-1*d*a^-1, 
-      b*a*e*a*c^-1, b*a*e^-1*a*c^-1, b*a^-1*b^-1*c*b*a, b*a^-1*c^-1*e*d^-1, 
-      (d^-2)^(a*b^-1), (e^-2)^(a*b^-1), (d^-2)^(c^-1*b^-1), 
-      (e^-2)^(c^-1*b^-1), b*c^-1*a^-1*f^-1*e^-1*a^-1, (e^-2)^(c*b^-1), 
-      (d*b*a^-1*c^-1)^(b^-1), (e^-2)^(a^-1*b), b^-1*a^-1*d*f^-1*c, 
-      b^-1*a^-1*f*d^-1*c, (e^-2)^(c*b), b^-1*d*b^2*d*b^-1, b^-1*d*f*a*c*a^-1, 
-      b^-1*d^-1*c^-1*a*b^-2, b^-1*f*a*c*d*a^-1, b^-1*f*c*a*f, 
-      b^-1*f^-1*a*c*d^-1*a^-1, b^-1*f^-1*c*a*f^-1, c*a*b^-1*a*e^-1*a^-1, 
-      c*a*c^2*e*b, c*a*c^-1*f*d^-1*a, c*a*e*c^2*b, c*a*f*b^-1*f, 
-      (d^-2)^(b^-1*c^-1), (f^-2)^(b^-1*c^-1), c*b^-1*a^-1*b*f*a^-1, 
-      (c*b^-1)^2*c^-1*b^-1, c^2*b*c^-2*b^-1, c^2*(d*b)^2, c^2*(d^-1*b)^2, 
-      c^2*e*c*a*b, c*d*a*c^-1*f*a, c*d*c^-1*a^-1*d^-1*a, 
-      (e*b^-1*e^-1*b)^(c^-1), c*f*c^-1*a*f^-1*a^-1, (f*d*f*d^-1)^(c^-1), 
-      c*f^-1*c^-1*a*f*a^-1, c^-1*a^-1*d*f^-1*c*a^-1, c^-1*a^-1*d^-1*f*c*a^-1, 
-      (e^-2)^(a*c), c^-1*a^-1*f*d*c*a^-1, c^-1*a^-1*f^-1*d^-1*c*a^-1, 
-      (c^-1*b)^2*c*b, c^-1*b*d*a^-1*b*a^-1, c^-1*b*d^-1*a^-1*b*a^-1, 
-      (f^-2)^(b^-1*c), c^-1*(b^-1*c)^2*b^-1, (f^-2)^(b*c), c^-2*a^-1*c*f^-1*b,
-      c^-2*b*c^2*b^-1, c^-2*b^-1*c^2*b, c^-2*(d*b^-1)^2, 
-      c^-2*d^-1*a^-1*c^-1*b^-1, c^-2*e^-1*b^-1*a^-1*c^-1, (c^-1*f*b*a^-1)^c, 
-      c^-2*f^-1*a^-1*c*b, c^-1*d*b^-1*d^-1*b^-1*c^-1, c^-1*e*a*b*f^-1, 
-      c^-1*e*c*a^-1*c*b^-1, c^-1*f*a*c*d^-1*a, c^-1*f*c*a*f*a^-1, 
-      c^-1*f^-1*c*a*f^-1*a^-1, d*a*c*d*c^-1*a^-1, (d*a)^2*d^-1*a, 
-      (e^-2)^(a^-1*d^-1), d*a^-1*d^-1*a^-1*d*a^-1, d*a^-1*e*c*d*b^-1, 
-      d*a^-1*e^-1*c*d*b^-1, d*b*a^-1*f^-1*e^-1*c^-1, d*b^2*d*b^-2, 
-      d*b*c*a*b^-2 ] ]];
-end,
-[ 1536 ]],
-"PG122880.219",0,4,1,1536],
+[ [ a, d, (f*e^-1)^(b^-1), (f^-1*e^-1)^(b^-1), (f*e)^b, (f^-1*e)^b,
+      (d^-2)^(c^-1), (f^-1*a)^c, (f^-1*a)^(e^-1), f^-1*c*a^-1*c^-1,
+      (e*d)^(a^-1*b^-1), b^2*a^-1*c^2, b^2*c^-1*e^-1*c^-1 ] ]];
+end,
+[ 640 ]],
+"PG122880.219",0,4,1,640],
 # 122880.220
 [[1,"abcde",
 function(a,b,c,d,e)

grp/perf17.grp

@@ -3595,11 +3595,11 @@ f^-1*c*d^-2,
 *c^-1*b^-1*c*e^-1*f^-1*e, 
   a*d^-1*a^-1*e*d^-2*f*b^-2*a*f*d^-1*e^-1*d^-1*a^-1*d*(f*b^-1)^2*e*f*e*f^-1*a\
 ^-1*c*a^-1*d^-1*f^-2*d^-1*f^-1*b^-2*c*d^-2 ],
-[ [ b^-2, (d^-2)^(a^-1), (d^-2)^a, (d^-2)^(b^-1), (b^-2)^(c^-1), (b^-2)^c, 
-      d*a^-1*d^-1*a, d*c*d^-1*c^-1, e*c*e*c^-1, e*c^-1*e^-1*c ] ]];
+[ [ f*d, f^-1*d^-1, (e*d)^(a^-1), (e^-1*d^-1)^(a^-1), (f*d^-1)^(a^-1),
+      (e*d)^a, b^2*d^-1, b*c*f^-1*a, b*c^-1*d^-1*a ] ]];
 end,
-[ 1920 ]],
-"PG245760.48",0,2,1,1920],
+[ 96 ]],
+"PG245760.48",0,2,1,96],
 # 245760.49
 [[1,"abcdef",
 function(a,b,c,d,e,f)
@@ -8311,19 +8311,14 @@ a^-1*b^-1*a^-1*e*f^-1*d^2*a^-1*d^-1,
   b^-1*d^-1*a*f*e*a^-1*e*d^-1*b*e*d^-1*a*f^-1*d*f^-1*c*f^-1*c^-1*e^-1*f^-1*a^\
 -1*f^-1*d*a^-1*b^-1*a^-1*b*a^-1*b^-1*d^-1*(e^-1*a^-1)^2*e^-1*d^-2*a^-1*e*d^-2\
  ],
-[ [ c^-2, d, e, f, a*b*a, a^-1*b*d^-1*a^-1 ], 
-  [ c^-1*a^-1, (e^-1*d^-1)^a, (e*d)^(b^-1), b^-4, (e^-1*d)^b, 
-      e^-1*a*c^-1*d^-1, f*a*f^-1*a^-1, f*c^-2*e^-1, f*d^-1*f*d, f^-1*c^-2*e, 
-      (b^-4)^(a^-1), a*d^-1*c^-1*e^-1*d, (f*c^2*e^-1)^(a^-1), a*f*d*c*d, 
-      a*f^-1*d*a^-1*d^-1, (b^-4)^a, a^-1*c*a*e^-1*f^-1, (c*e^-1*c)^a, 
-      a^-1*c^-1*a^-1*e^-1*f^-1*a^-1, a^-1*d^-1*a*f^-1*d, 
-      (d^-1*c*e^-1*c^-1)^a, a^-1*f*a*e^-1*c*a^-1, a^-1*f*a^-1*e^-1*c^-1, 
-      b*a^-1*c^-1*f*b, b^2*e*c^-1*e^-1*a^-1, b*c*f*a*b, (c^-1*d*f*a)^(b^-1), 
-      b*d*b^-1*f^-1*c*a^-1, (d^-1*a^-1*c^-1*d^-1)^(b^-1), b*d^-1*b*c*f*a^-1 
-     ] ]];
-end,
-[ 40, 1920 ]],
-"PG245760.111",0,4,1,[ 40, 1920 ]],
+[ [ b^-1*a^-1, d^-2, e^-2, f, a*b^-1*d^-1, a*d*c, (c^-2)^a, b*a*e^-1*a,
+      b*c^-1*e^-1, b*e*c^-1, (c*a^-1)^2, (b*c*a*c*b)^a ],
+  [ b^-2, (b^-2)^(a^-1), (d^-2)^(a^-1), (b^-2)^a, (d^-2)^a, (c*a)^2,
+      (b^-2)^c, d^-1*b^2*d^-1, (b^-2)^(e^-1), e*c*e*c^-1, a*b*a^-1*c*b^-1,
+      (b^-2)^(e*a), c*e*b*d^-1*b^-1*a, c^-1*d*e*c^-1*d ] ]];
+end,
+[ 40, 768 ]],
+"PG245760.111",0,4,1,[ 40, 768 ]],
 # 245760.112
 [[1,"abcdef",
 function(a,b,c,d,e,f)

grp/perf19.grp

@@ -427,10 +427,10 @@ return [[ e^2, d^2, b^4, b^-1*d*b*d, b*e*c*e*c^-1*b, b^-1*a^-1*d*a^-1*b^-1*d,
 ^-1)^2*d*b*c^-1, 
   a^-1*c*b*c^-1*b*c*a^-1*b*a^-1*(b^-1*c)^2*b^-1*c^-1*b^-1*a^-1*b^-1*(c*b)^2*c*\
 a*b*c*(b^-1*a^-1)^2*b^-1*c^-1*a^-2*b ],
-[ [ e, e^(a^-1), e^a, b*e*b, a*b*a^2*b^-1, a*c^2*a^-1*c ] ]];
+[ [ d, e, a^-1*d*e^-1*a^-1, a*b*c^2*a, (b*a^-3)^(c^-1) ] ]];
 end,
-[ 2304 ]],
-"PG368640.12",0,4,3,2304],
+[ 1280 ]],
+"PG368640.12",0,4,3,1280],
 # 368640.13
 [[1,"abcde",
 function(a,b,c,d,e)

grp/perf20.grp

@@ -5801,10 +5801,11 @@ return [[ f^2, e^2, a^3, c^2*d^-2, d^-2*b^2, d^4, d^4, (e*f)^2, f*d*f*d^-1,
   e*a^-1*b^-1*e*b*a^-1*e*a^-1*f*d*a^-1*e*b^-1*e*b*a*d*f, 
   (c^-1*f)^2*e*c^-1*b^-1*e*b*e*a*f*a*c*b^-1*e*b*e*a^-1, 
   c*d^-1*f*b*c^-1*d^-1*c*e*b*a*f*a^-1*b^-1*e*b^-1*a^-1*d*c*a^-1*f*d^-1 ],
-[ [ (d*b)^a, e*b*e^-1*d, a*f*a^-1*e^-1*b^-1, d*f*a^-1*b*e^-1*a ] ]];
+[ [ (f*a^-1)^(b^-1*a^-1), a*d*a*f^-1*c^-1, (e*a*f^-1*b^-1)^a,
+      c*b*a*e^-1*a*b^-1 ] ]];
 end,
-[ 3840 ]],
-"PG491520.94",0,2,1,3840],
+[ 1280 ]],
+"PG491520.94",0,2,1,1280],
 # 491520.95
 [[1,"abcdef",
 function(a,b,c,d,e,f)

grp/perf22.grp

@@ -4469,21 +4469,15 @@ a*d*b^-1,
 ^-1*b*a*b^-1*c*f*c^-1*b*a^-1, 
   e*f^-1*d*b*e*b^-1*d^-1*a*e*a^-1*f*b^-1*a*f^-1*a^-1*b^-1*d*e*d^-1*b*f*d^-2*b^\
 2*c*f^-1*c^-1*b*e*f^-1*a*e*a^-1 ],
-[ [ e, f, a^3, f^(a^-1), (c^-2)^a, (c^-2)^(b^-1), e^(b^-1), f^(b^-1), b^-4, 
-      (c*a^-1)^2, c^2*b^-2, e^(c^-1), (c^-1*a^-1)^2, d*a*d^-1*a, 
-      d*a^-1*d^-1*a^-1, d*b*d^-1*b^-1, (b^-1*c^2*b^-1)^(a^-1), 
-      (c^-2)^(d^-1*a^-1), a^-1*b*d*c*b^-1*a^-1 ], 
-  [ b^-2, (b^-2)^(a^-1), (b^-2)^a, c^-4, (b^-2)^(a^-2), a*c*a*c^-1*f, 
-      (c^-4)^(a^-1), a*d^-2*a^2, (c^-4)^a, a^-1*d^2*f^-1*c^-1, 
-      a^-1*e*f^-1*c*e^-1, (b^-2)^(a^-1*b^-1), (b^-2)^(a*b^-1), 
-      b*a^-1*c^-1*b^-1*d^-1, (c^-4)^(b^-1), (d^-1*a^-1*d*a^-1)^(b^-1), 
-      b*d^-1*b*a*d^-1*a, (b^-2)^(a^-1*c^-1), c*a*f^-1*c*a^-2, c*a^-2*f^-1*c*a,
-      c*e*c^-1*a^-1*e^-1*a, (b^-2)^(a^-1*d^-1), d*a*e*d^-1*e^-1*a, 
-      (b^-2)^(a*d^-1), (d*c)^3, d*(c*d^-1)^2*c, (c^-4)^(d^-1), (d*c^-1)^3, 
-      d*(c^-1*d^-1)^2*c^-1, d*e*d*f^-1*c^-2 ] ]];
+[ [ a^-2*d, b*e*c^-1*a^-1, b^-4, b^-1*f^2*b^-1, c^-4, d*a^-1*f^-1*a^-1,
+      (c*b^-1)^(d^-1), (c*b^-1)^d, d^-1*e*f^-1*c, e*c*f*d^-1,
+      b*a^-1*d*b^-1*c^-1*a, b*c*d*f^-1*c*a, (c^-1*a^-1*f*c^-1)^(b^-1) ],
+  [ e, f, e^(a^-1), f^(a^-1), e^a, e^(b^-1), f^(b^-1), b^-4, b^-1*c^2*b^-1,
+      c*a*c^-1*a, c^2*b^-2, d*a^-1*d^-1*a^-1, d*b*d*b^-1, d^-1*c^2*d^-1,
+      a^-1*c*d*c*b^-1*a^-1 ] ]];
 end,
-[ 144, 3840 ]],
-"PG737280.51",0,8,3,[ 144, 3840 ]],
+[ 1024, 144 ]],
+"PG737280.51",0,8,3,[ 1024, 144 ]],
 # 737280.52
 [[1,"abcdef",
 function(a,b,c,d,e,f)