Changes

This follows from the properties of boolean arithmetic, specifically, from the fact that the product ''G''_''ik''''H''_''kj'' is 1 if and only if both ''G''_''ik'' and ''H''_''kj'' are 1, and from the fact that ∑_''k''''F''_''k'' is equal to 1 just in case some ''F''_''k'' is 1.

This follows from the properties of boolean arithmetic, specifically, from the fact that the product ''G''_''ik''''H''_''kj'' is 1 if and only if both ''G''_''ik'' and ''H''_''kj'' are 1, and from the fact that ∑_''k''''F''_''k'' is equal to 1 just in case some ''F''_''k'' is 1.

All that remains in order to obtain a computational formula for the relational composite ''G'' ο ''H'' of the 2-adic relations ''G'' and ''H'' is to collect the coefficients ''G'' ο ''H''_''ij'' over the appropriate basis of elementary relations ''i'':''j'', as ''i'' and ''j'' range through ''X''.

All that remains in order to obtain a computational formula for the relational composite ''G'' ο ''H'' of the 2-adic relations ''G'' and ''H'' is to collect the coefficients (''G'' ο ''H'')_''ij'' over the appropriate basis of elementary relations ''i'':''j'', as ''i'' and ''j'' range through ''X''.

: ''G'' ο ''H'' = ∑_''ij''(''G'' ο ''H'')_''ij''(''i'':''j'') = ∑_''ij''(∑_''k''(''G''_''ik''''H''_''kj''))(''i'':''j'').

: ''G'' ο ''H'' = ∑_''ij''(''G'' ο ''H'')_''ij''(''i'':''j'') = ∑_''ij''(∑_''k''(''G''_''ik''''H''_''kj''))(''i'':''j'').