If x is a sequence x = [a, b, c, d] of elements in the base ring of G, this function returns pmatrix(a & b
c & d), provided this is an element of G. If x is an integer the identity matrix is returned. If x is a matrix, it is coerced into G if possible.
Returns a random element of the projective linear group G, with m determining the size of the coefficients.
For g and h elements of PSL2(Z), returns true if g, h have compatible coefficient rings and if g = h, false otherwise. Since the group is projective, returns true if the matrices are equal up to a nonzero scalar multiple.
For g and h elements of PSL2(Z), returns true if g and h are defined of the same field, and if Gg = Gh, i.e. if gh - 1∈G.
For g an elements of PSL2(Z), returns true if g is in the congruence subgroup G, false otherwise.
For a matrix g in a congruence subgroup, and an integer n, returns gn.
Returns the sequence of four numbers which are the entries of the matrix g.
If g and h have the same parent then this returns their product.
For a matrix g and integer n returns gn.
> // examples of defining matrix elements of congruence subgroups: > > G := PSL2(Integers()); > G![2,0,0,2]; [1 0] [0 1] > H := CongruenceSubgroup([2,3,6]); > H![7,6,8,7]; [7 6] [8 7]