Description of fast matrix multiplication algorithm: ⟨14×15×21:2640⟩

Algorithm type

3X6Y4Z4+30X4Y4Z6+3X2Y10Z2+174X4Y4Z4+9X2Y8Z2+6XY10Z+12X6Y2Z2+3X4Y2Z4+3X2Y6Z2+21X2Y4Z4+24X2Y2Z6+18XY8Z+6X3Y4Z2+60X2Y4Z3+57X4Y2Z2+393X2Y4Z2+75X2Y2Z4+6XY6Z+6X3Y2Z2+60X2Y2Z3+6XY5Z+42XY4Z2+24X3Y2Z+423X2Y2Z2+108XY4Z+48XY2Z3+24X3YZ+114X2Y2Z+6X2YZ2+6XY3Z+192XY2Z2+48XYZ3+114X2YZ+228XY2Z+150XYZ2+138XYZ3X6Y4Z430X4Y4Z63X2Y10Z2174X4Y4Z49X2Y8Z26XY10Z12X6Y2Z23X4Y2Z43X2Y6Z221X2Y4Z424X2Y2Z618XY8Z6X3Y4Z260X2Y4Z357X4Y2Z2393X2Y4Z275X2Y2Z46XY6Z6X3Y2Z260X2Y2Z36XY5Z42XY4Z224X3Y2Z423X2Y2Z2108XY4Z48XY2Z324X3YZ114X2Y2Z6X2YZ26XY3Z192XY2Z248XYZ3114X2YZ228XY2Z150XYZ2138XYZ3*X^6*Y^4*Z^4+30*X^4*Y^4*Z^6+3*X^2*Y^10*Z^2+174*X^4*Y^4*Z^4+9*X^2*Y^8*Z^2+6*X*Y^10*Z+12*X^6*Y^2*Z^2+3*X^4*Y^2*Z^4+3*X^2*Y^6*Z^2+21*X^2*Y^4*Z^4+24*X^2*Y^2*Z^6+18*X*Y^8*Z+6*X^3*Y^4*Z^2+60*X^2*Y^4*Z^3+57*X^4*Y^2*Z^2+393*X^2*Y^4*Z^2+75*X^2*Y^2*Z^4+6*X*Y^6*Z+6*X^3*Y^2*Z^2+60*X^2*Y^2*Z^3+6*X*Y^5*Z+42*X*Y^4*Z^2+24*X^3*Y^2*Z+423*X^2*Y^2*Z^2+108*X*Y^4*Z+48*X*Y^2*Z^3+24*X^3*Y*Z+114*X^2*Y^2*Z+6*X^2*Y*Z^2+6*X*Y^3*Z+192*X*Y^2*Z^2+48*X*Y*Z^3+114*X^2*Y*Z+228*X*Y^2*Z+150*X*Y*Z^2+138*X*Y*Z

Algorithm definition

The algorithm ⟨14×15×21:2640⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨7×5×7:176⟩.

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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