Description of fast matrix multiplication algorithm: ⟨9×10×16:916⟩

Algorithm type

64⁢X4⁢Y6⁢Z6+44⁢X3⁢Y6⁢Z6+48⁢X2⁢Y6⁢Z6+4⁢X⁢Y6⁢Z6+6⁢X4⁢Y4⁢Z4+2⁢X5⁢Y4⁢Z2+32⁢X5⁢Y3⁢Z3+6⁢X3⁢Y4⁢Z4+4⁢X5⁢Y3⁢Z2+6⁢X5⁢Y2⁢Z3+X4⁢Y4⁢Z2+64⁢X4⁢Y3⁢Z3+15⁢X5⁢Y2⁢Z2+3⁢X4⁢Y3⁢Z2+6⁢X4⁢Y2⁢Z3+X3⁢Y4⁢Z2+176⁢X3⁢Y3⁢Z3+27⁢X4⁢Y2⁢Z2+X3⁢Y4⁢Z+2⁢X3⁢Y3⁢Z2+93⁢X2⁢Y3⁢Z3+10⁢X5⁢Y⁢Z+X3⁢Y3⁢Z+26⁢X3⁢Y2⁢Z2+21⁢X3⁢Y⁢Z3+2⁢X2⁢Y4⁢Z+3⁢X2⁢Y3⁢Z2+2⁢X2⁢Y2⁢Z3+37⁢X⁢Y3⁢Z3+16⁢X4⁢Y⁢Z+X3⁢Y2⁢Z+4⁢X3⁢Y⁢Z2+3⁢X2⁢Y3⁢Z+28⁢X2⁢Y2⁢Z2+3⁢X2⁢Y⁢Z3+X⁢Y4⁢Z+2⁢X⁢Y2⁢Z3+41⁢X3⁢Y⁢Z+4⁢X2⁢Y2⁢Z+8⁢X2⁢Y⁢Z2+6⁢X⁢Y2⁢Z2+6⁢X⁢Y⁢Z3+60⁢X2⁢Y⁢Z+X⁢Y2⁢Z+2⁢X⁢Y⁢Z2+23⁢X⁢Y⁢Z64X4Y6Z644X3Y6Z648X2Y6Z64XY6Z66X4Y4Z42X5Y4Z232X5Y3Z36X3Y4Z44X5Y3Z26X5Y2Z3X4Y4Z264X4Y3Z315X5Y2Z23X4Y3Z26X4Y2Z3X3Y4Z2176X3Y3Z327X4Y2Z2X3Y4Z2X3Y3Z293X2Y3Z310X5YZX3Y3Z26X3Y2Z221X3YZ32X2Y4Z3X2Y3Z22X2Y2Z337XY3Z316X4YZX3Y2Z4X3YZ23X2Y3Z28X2Y2Z23X2YZ3XY4Z2XY2Z341X3YZ4X2Y2Z8X2YZ26XY2Z26XYZ360X2YZXY2Z2XYZ223XYZ64*X^4*Y^6*Z^6+44*X^3*Y^6*Z^6+48*X^2*Y^6*Z^6+4*X*Y^6*Z^6+6*X^4*Y^4*Z^4+2*X^5*Y^4*Z^2+32*X^5*Y^3*Z^3+6*X^3*Y^4*Z^4+4*X^5*Y^3*Z^2+6*X^5*Y^2*Z^3+X^4*Y^4*Z^2+64*X^4*Y^3*Z^3+15*X^5*Y^2*Z^2+3*X^4*Y^3*Z^2+6*X^4*Y^2*Z^3+X^3*Y^4*Z^2+176*X^3*Y^3*Z^3+27*X^4*Y^2*Z^2+X^3*Y^4*Z+2*X^3*Y^3*Z^2+93*X^2*Y^3*Z^3+10*X^5*Y*Z+X^3*Y^3*Z+26*X^3*Y^2*Z^2+21*X^3*Y*Z^3+2*X^2*Y^4*Z+3*X^2*Y^3*Z^2+2*X^2*Y^2*Z^3+37*X*Y^3*Z^3+16*X^4*Y*Z+X^3*Y^2*Z+4*X^3*Y*Z^2+3*X^2*Y^3*Z+28*X^2*Y^2*Z^2+3*X^2*Y*Z^3+X*Y^4*Z+2*X*Y^2*Z^3+41*X^3*Y*Z+4*X^2*Y^2*Z+8*X^2*Y*Z^2+6*X*Y^2*Z^2+6*X*Y*Z^3+60*X^2*Y*Z+X*Y^2*Z+2*X*Y*Z^2+23*X*Y*Z

Algorithm definition

The algorithm ⟨9×10×16:916⟩ is taken from:

Andrew I. Perminov. FastMatrixMultiplication, GitHub, February 2026. [ GitHub repository ]

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.


Back to main table