Revision history [back]
 | 1 | initial version |
I tried...
sage: G.<w, x> = FreeGroup(2)
sage: A = G.algebra(QQ)
That'a all. Now we can play for instance as follows with the letters:
sage: y, z = w^-1, x^-1
sage: X, Y, Z, W = A(x), A(y), A(z), A(w)
sage: (Y + W)^2
2 + w^-2 + w^2
sage: (X + Z)^2
2 + x^-2 + x^2
sage: (1 + X + Y + Z + W)^2
5 + 2*w^-1 + 2*w + 2*x^-1 + 2*x + w^-2 + w^-1*x^-1 + w^-1*x + w^2 + w*x^-1 + w*x + x^-1*w^-1 + x^-1*w + x^-2 + x*w^-1 + x*w + x^2
