Description of fast matrix multiplication algorithm: ⟨15×15×18:2320⟩

Algorithm type

16X4Y9Z3+272X4Y6Z6+16X4Y3Z9+32X8Y3Z3+104X2Y9Z3+408X2Y6Z6+104X2Y3Z9+32X4Y6Z3+32X4Y3Z6+120XY9Z3+120XY3Z9+16X6Y3Z3+64X2Y6Z3+64X2Y3Z6+256X4Y3Z3+24XY6Z3+24XY3Z6+24X3Y3Z3+424X2Y3Z3+168XY3Z316X4Y9Z3272X4Y6Z616X4Y3Z932X8Y3Z3104X2Y9Z3408X2Y6Z6104X2Y3Z932X4Y6Z332X4Y3Z6120XY9Z3120XY3Z916X6Y3Z364X2Y6Z364X2Y3Z6256X4Y3Z324XY6Z324XY3Z624X3Y3Z3424X2Y3Z3168XY3Z316*X^4*Y^9*Z^3+272*X^4*Y^6*Z^6+16*X^4*Y^3*Z^9+32*X^8*Y^3*Z^3+104*X^2*Y^9*Z^3+408*X^2*Y^6*Z^6+104*X^2*Y^3*Z^9+32*X^4*Y^6*Z^3+32*X^4*Y^3*Z^6+120*X*Y^9*Z^3+120*X*Y^3*Z^9+16*X^6*Y^3*Z^3+64*X^2*Y^6*Z^3+64*X^2*Y^3*Z^6+256*X^4*Y^3*Z^3+24*X*Y^6*Z^3+24*X*Y^3*Z^6+24*X^3*Y^3*Z^3+424*X^2*Y^3*Z^3+168*X*Y^3*Z^3

Algorithm definition

The algorithm ⟨15×15×18:2320⟩ is the (Kronecker) tensor product of ⟨3×3×6:40⟩ with ⟨5×5×3:58⟩.

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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