Description of fast matrix multiplication algorithm: ⟨4×6×7:123⟩

Algorithm type

45X2Y2Z2+X3YZ+2X2YZ2+XY3Z+3XY2Z2+10X2YZ+27XY2Z+12XYZ2+22XYZ45X2Y2Z2X3YZ2X2YZ2XY3Z3XY2Z210X2YZ27XY2Z12XYZ222XYZ45*X^2*Y^2*Z^2+X^3*Y*Z+2*X^2*Y*Z^2+X*Y^3*Z+3*X*Y^2*Z^2+10*X^2*Y*Z+27*X*Y^2*Z+12*X*Y*Z^2+22*X*Y*Z

Algorithm definition

The algorithm ⟨4×6×7:123⟩ is taken from:

Manuel Kauers and Issaac Wood. Consequences of the Moosbauer-Poole algorithms. Technical Report 2505.05896, arXiv, May 2025. [ arXiv ]

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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