Description of fast matrix multiplication algorithm: ⟨8×24×27:3090⟩

Algorithm type

24X8Y16Z8+72X4Y16Z4+48X2Y16Z2+120X4Y8Z4+90X4Y4Z4+264X2Y8Z2+12X4Y2Z4+18X2Y6Z2+144XY8Z+396X2Y4Z2+36XY6Z+438X2Y2Z2+288XY4Z+24X2YZ2+36XY3Z+612XY2Z+468XYZ24X8Y16Z872X4Y16Z448X2Y16Z2120X4Y8Z490X4Y4Z4264X2Y8Z212X4Y2Z418X2Y6Z2144XY8Z396X2Y4Z236XY6Z438X2Y2Z2288XY4Z24X2YZ236XY3Z612XY2Z468XYZ24*X^8*Y^16*Z^8+72*X^4*Y^16*Z^4+48*X^2*Y^16*Z^2+120*X^4*Y^8*Z^4+90*X^4*Y^4*Z^4+264*X^2*Y^8*Z^2+12*X^4*Y^2*Z^4+18*X^2*Y^6*Z^2+144*X*Y^8*Z+396*X^2*Y^4*Z^2+36*X*Y^6*Z+438*X^2*Y^2*Z^2+288*X*Y^4*Z+24*X^2*Y*Z^2+36*X*Y^3*Z+612*X*Y^2*Z+468*X*Y*Z

Algorithm definition

The algorithm ⟨8×24×27:3090⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨4×8×9:206⟩.

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.


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