Hi, There are problems doing arithmetic in SL_2(Z): S,T = SL2Z().gens() S*T; # no problem S^2*T^3; # no problem S^-2*T^-3; # no problem but when I multiply two elements with different exponent: S^-2*T^3; S^2*T^-3; T^2*T^-3; I get a <type 'exceptions.TypeError'>: Cannot convert sage.matrix.matrix_integer_2x2.Matrix_integer_2x2 to sage.matrix.matrix_integer_dense.Matrix_integer_dense However, T.parent() and (T^-1).parent() return the same thing (both equal string values "Modular Group SL(2,Z)" and equal when directly compared with == and even with 'is'). When I do sage: S = SL2Z()([0,-1,1,0]) sage: T = SL2Z()([1,1,0,1]) sage: S*T I even get a runtime error: <type 'exceptions.RuntimeError'>: There is a bug in the coercion code in SAGE. In this case in fact the parents are not equal: they are when compared with ==, but not with 'is'. (That's fine, that is more something of the implementation) Finally, if I do sage: G = SL2Z() sage: S = G([0,-1,1,0]) sage: T = G([1,1,0,1]) then I can work correctly with S and T.
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