Description of fast matrix multiplication algorithm: ⟨6×12×21:945⟩

Algorithm type

18X4Y6Z4+45X4Y4Z4+6X2Y8Z2+18X4Y2Z4+72X2Y6Z2+12XY8Z+126X2Y4Z2+72XY6Z+36X2Y3Z2+156X2Y2Z2+84XY4Z+36X2YZ2+72XY3Z+132XY2Z+60XYZ18X4Y6Z445X4Y4Z46X2Y8Z218X4Y2Z472X2Y6Z212XY8Z126X2Y4Z272XY6Z36X2Y3Z2156X2Y2Z284XY4Z36X2YZ272XY3Z132XY2Z60XYZ18*X^4*Y^6*Z^4+45*X^4*Y^4*Z^4+6*X^2*Y^8*Z^2+18*X^4*Y^2*Z^4+72*X^2*Y^6*Z^2+12*X*Y^8*Z+126*X^2*Y^4*Z^2+72*X*Y^6*Z+36*X^2*Y^3*Z^2+156*X^2*Y^2*Z^2+84*X*Y^4*Z+36*X^2*Y*Z^2+72*X*Y^3*Z+132*X*Y^2*Z+60*X*Y*Z

Algorithm definition

The algorithm ⟨6×12×21:945⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨3×4×7:63⟩.

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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