Description of fast matrix multiplication algorithm: ⟨2×27×28:1148⟩

Algorithm type

2XY27Z+2XY26Z+2XY25Z+2XY24Z+2XY23Z+2XY22Z+4XY21Z+2XY20Z+2XY19Z+2XY18Z+2XY17Z+2XY16Z+2XY15Z+2XY14Z+6XY13Z+4XY12Z+4XY11Z+4XY10Z+4XY9Z+8XY8Z+4XY7Z+4XY6Z+168X2Y3Z2+4XY5Z+196X2Y2Z2+4XY4Z+4XY3Z+170XY2Z+534XYZ2XY27Z2XY26Z2XY25Z2XY24Z2XY23Z2XY22Z4XY21Z2XY20Z2XY19Z2XY18Z2XY17Z2XY16Z2XY15Z2XY14Z6XY13Z4XY12Z4XY11Z4XY10Z4XY9Z8XY8Z4XY7Z4XY6Z168X2Y3Z24XY5Z196X2Y2Z24XY4Z4XY3Z170XY2Z534XYZ2*X*Y^27*Z+2*X*Y^26*Z+2*X*Y^25*Z+2*X*Y^24*Z+2*X*Y^23*Z+2*X*Y^22*Z+4*X*Y^21*Z+2*X*Y^20*Z+2*X*Y^19*Z+2*X*Y^18*Z+2*X*Y^17*Z+2*X*Y^16*Z+2*X*Y^15*Z+2*X*Y^14*Z+6*X*Y^13*Z+4*X*Y^12*Z+4*X*Y^11*Z+4*X*Y^10*Z+4*X*Y^9*Z+8*X*Y^8*Z+4*X*Y^7*Z+4*X*Y^6*Z+168*X^2*Y^3*Z^2+4*X*Y^5*Z+196*X^2*Y^2*Z^2+4*X*Y^4*Z+4*X*Y^3*Z+170*X*Y^2*Z+534*X*Y*Z

Algorithm definition

The algorithm ⟨2×27×28:1148⟩ 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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