Description of fast matrix multiplication algorithm: ⟨4×18×20:939⟩

Algorithm type

X2⁢Y14⁢Z2+2⁢X⁢Y15⁢Z+8⁢X4⁢Y8⁢Z4+10⁢X2⁢Y12⁢Z2+2⁢X⁢Y14⁢Z+X2⁢Y12⁢Z+2⁢X2⁢Y10⁢Z2+13⁢X⁢Y12⁢Z+X3⁢Y8⁢Z2+44⁢X4⁢Y4⁢Z4+11⁢X2⁢Y8⁢Z2+2⁢X⁢Y10⁢Z+2⁢X2⁢Y8⁢Z+32⁢X⁢Y9⁢Z+76⁢X2⁢Y6⁢Z2+4⁢X⁢Y8⁢Z+40⁢X2⁢Y4⁢Z2+16⁢X⁢Y6⁢Z+5⁢X2⁢Y4⁢Z+204⁢X2⁢Y2⁢Z2+31⁢X⁢Y4⁢Z+168⁢X⁢Y3⁢Z+48⁢X⁢Y2⁢Z+216⁢X⁢Y⁢ZX2Y14Z22XY15Z8X4Y8Z410X2Y12Z22XY14ZX2Y12Z2X2Y10Z213XY12ZX3Y8Z244X4Y4Z411X2Y8Z22XY10Z2X2Y8Z32XY9Z76X2Y6Z24XY8Z40X2Y4Z216XY6Z5X2Y4Z204X2Y2Z231XY4Z168XY3Z48XY2Z216XYZX^2*Y^14*Z^2+2*X*Y^15*Z+8*X^4*Y^8*Z^4+10*X^2*Y^12*Z^2+2*X*Y^14*Z+X^2*Y^12*Z+2*X^2*Y^10*Z^2+13*X*Y^12*Z+X^3*Y^8*Z^2+44*X^4*Y^4*Z^4+11*X^2*Y^8*Z^2+2*X*Y^10*Z+2*X^2*Y^8*Z+32*X*Y^9*Z+76*X^2*Y^6*Z^2+4*X*Y^8*Z+40*X^2*Y^4*Z^2+16*X*Y^6*Z+5*X^2*Y^4*Z+204*X^2*Y^2*Z^2+31*X*Y^4*Z+168*X*Y^3*Z+48*X*Y^2*Z+216*X*Y*Z

Algorithm definition

The algorithm ⟨4×18×20:939⟩ is serendipitous tensor product (⟨2×6×5:47⟩ - 2) ⊗ ⟨2×3×4:20⟩ +⟨2×6×4:39⟩.

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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