Hi,

This is probably more of an algebra/geometry question so I hope I've posted it in the right place. I hope I have the answer to this right but as I'm not 100% sure I thought I'd ask for some feedback. The question is: I have the set of vectors {a=(1,-1), b=(1,2)} as a reduced basis for the plane lattice L. I need to find one of the two glide reflections of L that map the point (1,2) to (-1,1), in the standard form t[d]q[θ] and then in the form q[g,c,θ]. I have selected in standard form t[(-3,0)]q[∏/4] which is reflection in the line ∏/4 followed by translation of (-3,0), and in the other form this is t[(-3/2, -3/2)]q[(3/4,9/4)] ∏/4, which is reflection in ∏/4 through the point (3/4, 9/4) followed by a translation of (-3/2, -3/2), which is in the direction of the reflection line.

Could anyone offer any advice with this question, whether my thinking is correct or am I way off (which wouldn't surprise me!).

Thanks.

Pat