Description of fast matrix multiplication algorithm: ⟨2×28×29:1233⟩

Algorithm type

4XY19Z+4XY18Z+7XY17Z+8XY16Z+8XY15Z+10XY14Z+6XY13Z+5XY12Z+5XY11Z+XY10Z+2XY9Z+3XY8Z+3XY7Z+3XY6Z+108X2Y3Z2+6XY5Z+283X2Y2Z2+3XY4Z+3XY3Z+137XY2Z+624XYZ4XY19Z4XY18Z7XY17Z8XY16Z8XY15Z10XY14Z6XY13Z5XY12Z5XY11ZXY10Z2XY9Z3XY8Z3XY7Z3XY6Z108X2Y3Z26XY5Z283X2Y2Z23XY4Z3XY3Z137XY2Z624XYZ4*X*Y^19*Z+4*X*Y^18*Z+7*X*Y^17*Z+8*X*Y^16*Z+8*X*Y^15*Z+10*X*Y^14*Z+6*X*Y^13*Z+5*X*Y^12*Z+5*X*Y^11*Z+X*Y^10*Z+2*X*Y^9*Z+3*X*Y^8*Z+3*X*Y^7*Z+3*X*Y^6*Z+108*X^2*Y^3*Z^2+6*X*Y^5*Z+283*X^2*Y^2*Z^2+3*X*Y^4*Z+3*X*Y^3*Z+137*X*Y^2*Z+624*X*Y*Z

Algorithm definition

The algorithm ⟨2×28×29:1233⟩ is taken from:

John Edward Hopcroft and Leslie R. Kerr. On minimizing the number of multiplication necessary for matrix multiplication. SIAM Journal on Applied Mathematics, 20(1), January 1971. [DOI]

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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