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I want to define a generalized cross product in sage such the a_i=f^{ijk} b_j c_k, where f^{ijk} are the structure constants of the SU(3) group. Are the structure constants for unitary group predefined is sage. If not what is the best way to define such a generalized cross product? Thanks in advance.

I want to define a generalized cross product in sage such the a_i=f^{ijk} b_j c_k, where f^{ijk} are the structure constants of the SU(3) group. Are the structure constants for unitary group predefined is sage. If not what is the best way to define such a generalized cross product? Thanks in advance.

I want to define a generalized cross product in sage such the a_i=f^{ijk} b_j c_k, where f^{ijk} are the structure constants of the SU(3) group. Are the structure constants for unitary group predefined is sage. If not what is the best way to define such a generalized cross product? Thanks in advance.

Edit: Sorry for not being clear about the question. As Mitesh rightly pointed out I am trying to do a High energy calculation. I have two eight dimensional vectors (say b and c). I want to define a generalized product of these two vectors as described in the original post. Here f are structure constants of SU(3) Lie algebra.

When I try the series of commands suggested by niles

gap> e6 := SimpleLieAlgebra("E",6,Rationals); gap> StructureConstantsTable(Basis(e6));

I get a error in sage but it works if I open gap in a terminal. I think I can manage by copy pasting the results in sage.

Thanks a lot again for the help

I want to define a generalized cross product in sage such the a_i=f^{ijk} b_j c_k, where f^{ijk} are the structure constants of the SU(3) group. Are the structure constants for unitary group predefined is sage. If not what is the best way to define such a generalized cross product? Thanks in advance.

Edit: Sorry for not being clear about the question. As Mitesh rightly pointed out I am trying to do a High energy calculation. I have two eight dimensional vectors (say b and c). I want to define a generalized product of these two vectors as described in the original post. Here f are structure constants of SU(3) Lie algebra.

When I try the series of commands suggested by niles

gap> e6 := SimpleLieAlgebra("E",6,Rationals); gap> StructureConstantsTable(Basis(e6));

I get a error in sage but it works if I open gap in a terminal. I think I can manage by copy pasting the results in sage.

Thanks a lot again for the help