Heisenberg -- Lind

1175 days ago by pub

%gap F := FreeGroup("x", "y", "z"); v := GeneratorsOfGroup(F); x := v[1]; y := v[2]; z := v[3]; G := F / [(y*x)*(x*y*z)^(-1)]; Print(G); phi := IsomorphismFpSemigroup(G); s := Range(phi); rws := KnuthBendixRewritingSystem(s, IsBasicWreathLessThanOrEqual); sgens := GeneratorsOfSemigroup(s); 
        
Group( [ x, y, z ] )
Group( [ x, y, z ] )
%gap xinv := sgens[2]; x := sgens[3]; yinv := sgens[4]; y := sgens[5]; zinv := sgens[6]; z := sgens[7]; Print(y*x=x*y*z) 
        
true
true
x = gap('x'); y = gap('y'); z=gap('z') xinv = gap('xinv'); yinv = gap('yinv'); zinv = gap('zinv') 
       
x*xinv == y*yinv 
        
True
True
xx = FormalSum([(1,x)]) 
       
xx + xx 
        
2*x
2*x
 
       
 
       
%gap f := FreeGroup("gamma", "beta", "alpha"); g := GeneratorsOfGroup(f)[1]; b := GeneratorsOfGroup(f)[2]; a := GeneratorsOfGroup(f)[3]; 
       
 
       
%gap relators := [Comm(a,b)*g^(-1), Comm(a,g), Comm(b,g)]; h := f/relators; 
        
[ alpha^-1*beta^-1*alpha*beta*gamma^-1, alpha^-1*gamma^-1*alpha*gamma, 
  beta^-1*gamma^-1*beta*gamma ]
<fp group on the generators [ gamma, beta, alpha ]>
[ alpha^-1*beta^-1*alpha*beta*gamma^-1, alpha^-1*gamma^-1*alpha*gamma, 
  beta^-1*gamma^-1*beta*gamma ]
<fp group on the generators [ gamma, beta, alpha ]>
%gap v := GeneratorsOfGroup(h); 
        
[ gamma, beta, alpha ]
[ gamma, beta, alpha ]
gamma = gap('v[1]'); beta = gap('v[2]'); alpha = gap('v[3]') 
       
beta^(-1)*gamma^(-1)*beta*gamma 
        
beta^-1*gamma^-1*beta*gamma
beta^-1*gamma^-1*beta*gamma
 
       
 
       
 
       
G= SymmetricGroup(3) 
       
G 
       
R.<x,y,z> = FreeAlgebra(ZZ,3) 
       
S.<X,Y,Z> = R.quotient([y*x - x*y*z]) 
        
Traceback (click to the left of this block for traceback)
...
TypeError: quotient() takes exactly 4 non-keyword arguments (2 given)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/sage/sagenb/sage_notebook/worksheets/wstein/14/code/8.py", line 6, in <module>
    S = R.quotient([y*x - x*y*z],names=(\u0027X\u0027, \u0027Y\u0027, \u0027Z\u0027)); (X, Y, Z,) = S._first_ngens(Integer(3))
  File "/home/sage/sage/local/lib/python2.5/site-packages/SQLAlchemy-0.4.6-py2.5.egg/", line 1, in <module>
    
TypeError: quotient() takes exactly 4 non-keyword arguments (2 given)