Description of fast matrix multiplication algorithm: ⟨16×22×24:4732⟩

Algorithm type

6X8Y10Z8+30X8Y8Z8+2X12Y6Z4+X8Y6Z8+4X4Y10Z8+5X4Y6Z12+7X12Y4Z4+7X8Y4Z8+19X4Y12Z4+7X4Y8Z8+12X4Y4Z12+X8Y6Z4+55X4Y10Z4+7X4Y6Z8+4X8Y4Z4+65X4Y8Z4+14X4Y4Z8+6X2Y12Z2+7X2Y10Z4+6X6Y6Z2+47X4Y6Z4+6X2Y10Z2+2X2Y8Z4+5X2Y6Z6+36X4Y5Z4+5X6Y4Z2+2X4Y6Z2+207X4Y4Z4+4X2Y8Z2+12X2Y6Z4+8X2Y4Z6+12X6Y3Z2+6X4Y3Z4+24X2Y5Z4+30X2Y3Z6+43X6Y2Z2+2X4Y4Z2+42X4Y2Z4+234X2Y6Z2+56X2Y4Z4+74X2Y2Z6+6X4Y3Z2+330X2Y5Z2+42X2Y3Z4+24X4Y2Z2+490X2Y4Z2+88X2Y2Z4+36XY6Z+42XY5Z2+36X3Y3Z+282X2Y3Z2+36XY5Z+12XY4Z2+30XY3Z3+30X3Y2Z+12X2Y3Z+212X2Y2Z2+24XY4Z+72XY3Z2+48XY2Z3+6X3YZ+12X2Y2Z+720XY3Z+84XY2Z2+12XYZ3+600XY2Z+24XYZ2+300XYZ6X8Y10Z830X8Y8Z82X12Y6Z4X8Y6Z84X4Y10Z85X4Y6Z127X12Y4Z47X8Y4Z819X4Y12Z47X4Y8Z812X4Y4Z12X8Y6Z455X4Y10Z47X4Y6Z84X8Y4Z465X4Y8Z414X4Y4Z86X2Y12Z27X2Y10Z46X6Y6Z247X4Y6Z46X2Y10Z22X2Y8Z45X2Y6Z636X4Y5Z45X6Y4Z22X4Y6Z2207X4Y4Z44X2Y8Z212X2Y6Z48X2Y4Z612X6Y3Z26X4Y3Z424X2Y5Z430X2Y3Z643X6Y2Z22X4Y4Z242X4Y2Z4234X2Y6Z256X2Y4Z474X2Y2Z66X4Y3Z2330X2Y5Z242X2Y3Z424X4Y2Z2490X2Y4Z288X2Y2Z436XY6Z42XY5Z236X3Y3Z282X2Y3Z236XY5Z12XY4Z230XY3Z330X3Y2Z12X2Y3Z212X2Y2Z224XY4Z72XY3Z248XY2Z36X3YZ12X2Y2Z720XY3Z84XY2Z212XYZ3600XY2Z24XYZ2300XYZ6*X^8*Y^10*Z^8+30*X^8*Y^8*Z^8+2*X^12*Y^6*Z^4+X^8*Y^6*Z^8+4*X^4*Y^10*Z^8+5*X^4*Y^6*Z^12+7*X^12*Y^4*Z^4+7*X^8*Y^4*Z^8+19*X^4*Y^12*Z^4+7*X^4*Y^8*Z^8+12*X^4*Y^4*Z^12+X^8*Y^6*Z^4+55*X^4*Y^10*Z^4+7*X^4*Y^6*Z^8+4*X^8*Y^4*Z^4+65*X^4*Y^8*Z^4+14*X^4*Y^4*Z^8+6*X^2*Y^12*Z^2+7*X^2*Y^10*Z^4+6*X^6*Y^6*Z^2+47*X^4*Y^6*Z^4+6*X^2*Y^10*Z^2+2*X^2*Y^8*Z^4+5*X^2*Y^6*Z^6+36*X^4*Y^5*Z^4+5*X^6*Y^4*Z^2+2*X^4*Y^6*Z^2+207*X^4*Y^4*Z^4+4*X^2*Y^8*Z^2+12*X^2*Y^6*Z^4+8*X^2*Y^4*Z^6+12*X^6*Y^3*Z^2+6*X^4*Y^3*Z^4+24*X^2*Y^5*Z^4+30*X^2*Y^3*Z^6+43*X^6*Y^2*Z^2+2*X^4*Y^4*Z^2+42*X^4*Y^2*Z^4+234*X^2*Y^6*Z^2+56*X^2*Y^4*Z^4+74*X^2*Y^2*Z^6+6*X^4*Y^3*Z^2+330*X^2*Y^5*Z^2+42*X^2*Y^3*Z^4+24*X^4*Y^2*Z^2+490*X^2*Y^4*Z^2+88*X^2*Y^2*Z^4+36*X*Y^6*Z+42*X*Y^5*Z^2+36*X^3*Y^3*Z+282*X^2*Y^3*Z^2+36*X*Y^5*Z+12*X*Y^4*Z^2+30*X*Y^3*Z^3+30*X^3*Y^2*Z+12*X^2*Y^3*Z+212*X^2*Y^2*Z^2+24*X*Y^4*Z+72*X*Y^3*Z^2+48*X*Y^2*Z^3+6*X^3*Y*Z+12*X^2*Y^2*Z+720*X*Y^3*Z+84*X*Y^2*Z^2+12*X*Y*Z^3+600*X*Y^2*Z+24*X*Y*Z^2+300*X*Y*Z

Algorithm definition

The algorithm ⟨16×22×24:4732⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×12:676⟩.

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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