Description of fast matrix multiplication algorithm: ⟨14×18×30:4387⟩

Algorithm type

12⁢X8⁢Y8⁢Z8+6⁢X8⁢Y8⁢Z6+9⁢X8⁢Y6⁢Z8+3⁢X6⁢Y8⁢Z8+9⁢X8⁢Y6⁢Z6+3⁢X8⁢Y4⁢Z8+6⁢X6⁢Y8⁢Z6+6⁢X6⁢Y6⁢Z6+48⁢X4⁢Y8⁢Z4+96⁢X4⁢Y6⁢Z6+18⁢X4⁢Y4⁢Z8+12⁢X4⁢Y8⁢Z3+6⁢X3⁢Y8⁢Z4+6⁢X4⁢Y8⁢Z2+27⁢X4⁢Y6⁢Z4+18⁢X4⁢Y4⁢Z6+9⁢X4⁢Y2⁢Z8+12⁢X3⁢Y8⁢Z3+3⁢X2⁢Y8⁢Z4+144⁢X2⁢Y6⁢Z6+3⁢X2⁢Y4⁢Z8+18⁢X4⁢Y6⁢Z3+3⁢X4⁢Y6⁢Z2+171⁢X4⁢Y4⁢Z4+3⁢X4⁢Y2⁢Z6+12⁢X3⁢Y6⁢Z3+51⁢X2⁢Y8⁢Z2+3⁢X2⁢Y4⁢Z6+12⁢X4⁢Y4⁢Z3+18⁢X4⁢Y3⁢Z4+6⁢X3⁢Y4⁢Z4+12⁢X2⁢Y8⁢Z+192⁢X2⁢Y6⁢Z3+6⁢X⁢Y8⁢Z2+21⁢X6⁢Y2⁢Z2+18⁢X4⁢Y3⁢Z3+18⁢X4⁢Y2⁢Z4+12⁢X3⁢Y4⁢Z3+42⁢X2⁢Y6⁢Z2+54⁢X2⁢Y4⁢Z4+18⁢X2⁢Y2⁢Z6+6⁢X⁢Y8⁢Z+288⁢X⁢Y6⁢Z3+12⁢X3⁢Y3⁢Z3+6⁢X2⁢Y6⁢Z+36⁢X2⁢Y4⁢Z3+2⁢X2⁢Y2⁢Z5+6⁢X⁢Y4⁢Z4+6⁢X4⁢Y2⁢Z2+402⁢X2⁢Y4⁢Z2+192⁢X2⁢Y3⁢Z3+183⁢X2⁢Y2⁢Z4+48⁢X⁢Y6⁢Z+6⁢X⁢Y4⁢Z3+12⁢X2⁢Y4⁢Z+22⁢X2⁢Y3⁢Z2+58⁢X2⁢Y2⁢Z3+23⁢X2⁢Y⁢Z4+42⁢X⁢Y4⁢Z2+288⁢X⁢Y3⁢Z3+6⁢X⁢Y2⁢Z4+10⁢X⁢Y⁢Z5+42⁢X3⁢Y2⁢Z+10⁢X3⁢Y⁢Z2+8⁢X2⁢Y3⁢Z+338⁢X2⁢Y2⁢Z2+16⁢X2⁢Y⁢Z3+150⁢X⁢Y4⁢Z+X⁢Y3⁢Z2+42⁢X⁢Y2⁢Z3+15⁢X⁢Y⁢Z4+48⁢X3⁢Y⁢Z+12⁢X2⁢Y2⁢Z+55⁢X2⁢Y⁢Z2+49⁢X⁢Y3⁢Z+240⁢X⁢Y2⁢Z2+56⁢X⁢Y⁢Z3+20⁢X2⁢Y⁢Z+186⁢X⁢Y2⁢Z+247⁢X⁢Y⁢Z2+52⁢X⁢Y⁢Z12X8Y8Z86X8Y8Z69X8Y6Z83X6Y8Z89X8Y6Z63X8Y4Z86X6Y8Z66X6Y6Z648X4Y8Z496X4Y6Z618X4Y4Z812X4Y8Z36X3Y8Z46X4Y8Z227X4Y6Z418X4Y4Z69X4Y2Z812X3Y8Z33X2Y8Z4144X2Y6Z63X2Y4Z818X4Y6Z33X4Y6Z2171X4Y4Z43X4Y2Z612X3Y6Z351X2Y8Z23X2Y4Z612X4Y4Z318X4Y3Z46X3Y4Z412X2Y8Z192X2Y6Z36XY8Z221X6Y2Z218X4Y3Z318X4Y2Z412X3Y4Z342X2Y6Z254X2Y4Z418X2Y2Z66XY8Z288XY6Z312X3Y3Z36X2Y6Z36X2Y4Z32X2Y2Z56XY4Z46X4Y2Z2402X2Y4Z2192X2Y3Z3183X2Y2Z448XY6Z6XY4Z312X2Y4Z22X2Y3Z258X2Y2Z323X2YZ442XY4Z2288XY3Z36XY2Z410XYZ542X3Y2Z10X3YZ28X2Y3Z338X2Y2Z216X2YZ3150XY4ZXY3Z242XY2Z315XYZ448X3YZ12X2Y2Z55X2YZ249XY3Z240XY2Z256XYZ320X2YZ186XY2Z247XYZ252XYZ12*X^8*Y^8*Z^8+6*X^8*Y^8*Z^6+9*X^8*Y^6*Z^8+3*X^6*Y^8*Z^8+9*X^8*Y^6*Z^6+3*X^8*Y^4*Z^8+6*X^6*Y^8*Z^6+6*X^6*Y^6*Z^6+48*X^4*Y^8*Z^4+96*X^4*Y^6*Z^6+18*X^4*Y^4*Z^8+12*X^4*Y^8*Z^3+6*X^3*Y^8*Z^4+6*X^4*Y^8*Z^2+27*X^4*Y^6*Z^4+18*X^4*Y^4*Z^6+9*X^4*Y^2*Z^8+12*X^3*Y^8*Z^3+3*X^2*Y^8*Z^4+144*X^2*Y^6*Z^6+3*X^2*Y^4*Z^8+18*X^4*Y^6*Z^3+3*X^4*Y^6*Z^2+171*X^4*Y^4*Z^4+3*X^4*Y^2*Z^6+12*X^3*Y^6*Z^3+51*X^2*Y^8*Z^2+3*X^2*Y^4*Z^6+12*X^4*Y^4*Z^3+18*X^4*Y^3*Z^4+6*X^3*Y^4*Z^4+12*X^2*Y^8*Z+192*X^2*Y^6*Z^3+6*X*Y^8*Z^2+21*X^6*Y^2*Z^2+18*X^4*Y^3*Z^3+18*X^4*Y^2*Z^4+12*X^3*Y^4*Z^3+42*X^2*Y^6*Z^2+54*X^2*Y^4*Z^4+18*X^2*Y^2*Z^6+6*X*Y^8*Z+288*X*Y^6*Z^3+12*X^3*Y^3*Z^3+6*X^2*Y^6*Z+36*X^2*Y^4*Z^3+2*X^2*Y^2*Z^5+6*X*Y^4*Z^4+6*X^4*Y^2*Z^2+402*X^2*Y^4*Z^2+192*X^2*Y^3*Z^3+183*X^2*Y^2*Z^4+48*X*Y^6*Z+6*X*Y^4*Z^3+12*X^2*Y^4*Z+22*X^2*Y^3*Z^2+58*X^2*Y^2*Z^3+23*X^2*Y*Z^4+42*X*Y^4*Z^2+288*X*Y^3*Z^3+6*X*Y^2*Z^4+10*X*Y*Z^5+42*X^3*Y^2*Z+10*X^3*Y*Z^2+8*X^2*Y^3*Z+338*X^2*Y^2*Z^2+16*X^2*Y*Z^3+150*X*Y^4*Z+X*Y^3*Z^2+42*X*Y^2*Z^3+15*X*Y*Z^4+48*X^3*Y*Z+12*X^2*Y^2*Z+55*X^2*Y*Z^2+49*X*Y^3*Z+240*X*Y^2*Z^2+56*X*Y*Z^3+20*X^2*Y*Z+186*X*Y^2*Z+247*X*Y*Z^2+52*X*Y*Z

Algorithm definition

The algorithm ⟨14×18×30:4387⟩ is serendipitous tensor product (⟨7×6×10:293⟩ - 16) ⊗ ⟨2×3×3:15⟩ +8⟨4×3×3:29⟩.

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