Description of fast matrix multiplication algorithm: ⟨8×20×30:2860⟩

Algorithm type

12⁢X6⁢Y8⁢Z4+2⁢X4⁢Y8⁢Z6+2⁢X2⁢Y8⁢Z8+4⁢X6⁢Y8⁢Z2+18⁢X4⁢Y8⁢Z4+4⁢X2⁢Y12⁢Z2+2⁢X2⁢Y8⁢Z6+66⁢X6⁢Y4⁢Z4+15⁢X4⁢Y4⁢Z6+2⁢X2⁢Y9⁢Z3+8⁢X2⁢Y8⁢Z4+11⁢X2⁢Y4⁢Z8+4⁢X⁢Y12⁢Z+12⁢X3⁢Y8⁢Z2+8⁢X2⁢Y9⁢Z2+10⁢X2⁢Y8⁢Z3+2⁢X⁢Y8⁢Z4+38⁢X6⁢Y4⁢Z2+107⁢X4⁢Y4⁢Z4+22⁢X4⁢Y2⁢Z6+4⁢X3⁢Y8⁢Z+47⁢X2⁢Y8⁢Z2+11⁢X2⁢Y4⁢Z6+X⁢Y10⁢Z+5⁢X⁢Y9⁢Z2+2⁢X⁢Y8⁢Z3+48⁢X3⁢Y6⁢Z2+8⁢X2⁢Y6⁢Z3+24⁢X⁢Y9⁢Z+11⁢X⁢Y8⁢Z2+8⁢X⁢Y6⁢Z4+88⁢X6⁢Y2⁢Z2+20⁢X4⁢Y4⁢Z2+44⁢X4⁢Y2⁢Z4+16⁢X3⁢Y6⁢Z+96⁢X2⁢Y6⁢Z2+44⁢X2⁢Y4⁢Z4+16⁢X⁢Y8⁢Z+8⁢X⁢Y6⁢Z3+24⁢X3⁢Y4⁢Z2+8⁢X2⁢Y4⁢Z3+32⁢X⁢Y6⁢Z2+5⁢X⁢Y5⁢Z3+5⁢X⁢Y4⁢Z4+110⁢X4⁢Y2⁢Z2+24⁢X3⁢Y4⁢Z+84⁢X2⁢Y4⁢Z2+16⁢X2⁢Y3⁢Z3+25⁢X⁢Y6⁢Z+3⁢X⁢Y5⁢Z2+12⁢X⁢Y4⁢Z3+64⁢X3⁢Y3⁢Z+108⁢X3⁢Y2⁢Z2+20⁢X2⁢Y4⁢Z+32⁢X2⁢Y3⁢Z2+26⁢X2⁢Y2⁢Z3+3⁢X⁢Y5⁢Z+32⁢X⁢Y4⁢Z2+18⁢X⁢Y2⁢Z4+68⁢X3⁢Y2⁢Z+80⁢X2⁢Y3⁢Z+277⁢X2⁢Y2⁢Z2+36⁢X2⁢Y⁢Z3+30⁢X⁢Y4⁢Z+18⁢X⁢Y2⁢Z3+144⁢X3⁢Y⁢Z+40⁢X2⁢Y2⁢Z+72⁢X2⁢Y⁢Z2+108⁢X⁢Y3⁢Z+72⁢X⁢Y2⁢Z2+180⁢X2⁢Y⁢Z+72⁢X⁢Y2⁢Z+162⁢X⁢Y⁢Z12X6Y8Z42X4Y8Z62X2Y8Z84X6Y8Z218X4Y8Z44X2Y12Z22X2Y8Z666X6Y4Z415X4Y4Z62X2Y9Z38X2Y8Z411X2Y4Z84XY12Z12X3Y8Z28X2Y9Z210X2Y8Z32XY8Z438X6Y4Z2107X4Y4Z422X4Y2Z64X3Y8Z47X2Y8Z211X2Y4Z6XY10Z5XY9Z22XY8Z348X3Y6Z28X2Y6Z324XY9Z11XY8Z28XY6Z488X6Y2Z220X4Y4Z244X4Y2Z416X3Y6Z96X2Y6Z244X2Y4Z416XY8Z8XY6Z324X3Y4Z28X2Y4Z332XY6Z25XY5Z35XY4Z4110X4Y2Z224X3Y4Z84X2Y4Z216X2Y3Z325XY6Z3XY5Z212XY4Z364X3Y3Z108X3Y2Z220X2Y4Z32X2Y3Z226X2Y2Z33XY5Z32XY4Z218XY2Z468X3Y2Z80X2Y3Z277X2Y2Z236X2YZ330XY4Z18XY2Z3144X3YZ40X2Y2Z72X2YZ2108XY3Z72XY2Z2180X2YZ72XY2Z162XYZ12*X^6*Y^8*Z^4+2*X^4*Y^8*Z^6+2*X^2*Y^8*Z^8+4*X^6*Y^8*Z^2+18*X^4*Y^8*Z^4+4*X^2*Y^12*Z^2+2*X^2*Y^8*Z^6+66*X^6*Y^4*Z^4+15*X^4*Y^4*Z^6+2*X^2*Y^9*Z^3+8*X^2*Y^8*Z^4+11*X^2*Y^4*Z^8+4*X*Y^12*Z+12*X^3*Y^8*Z^2+8*X^2*Y^9*Z^2+10*X^2*Y^8*Z^3+2*X*Y^8*Z^4+38*X^6*Y^4*Z^2+107*X^4*Y^4*Z^4+22*X^4*Y^2*Z^6+4*X^3*Y^8*Z+47*X^2*Y^8*Z^2+11*X^2*Y^4*Z^6+X*Y^10*Z+5*X*Y^9*Z^2+2*X*Y^8*Z^3+48*X^3*Y^6*Z^2+8*X^2*Y^6*Z^3+24*X*Y^9*Z+11*X*Y^8*Z^2+8*X*Y^6*Z^4+88*X^6*Y^2*Z^2+20*X^4*Y^4*Z^2+44*X^4*Y^2*Z^4+16*X^3*Y^6*Z+96*X^2*Y^6*Z^2+44*X^2*Y^4*Z^4+16*X*Y^8*Z+8*X*Y^6*Z^3+24*X^3*Y^4*Z^2+8*X^2*Y^4*Z^3+32*X*Y^6*Z^2+5*X*Y^5*Z^3+5*X*Y^4*Z^4+110*X^4*Y^2*Z^2+24*X^3*Y^4*Z+84*X^2*Y^4*Z^2+16*X^2*Y^3*Z^3+25*X*Y^6*Z+3*X*Y^5*Z^2+12*X*Y^4*Z^3+64*X^3*Y^3*Z+108*X^3*Y^2*Z^2+20*X^2*Y^4*Z+32*X^2*Y^3*Z^2+26*X^2*Y^2*Z^3+3*X*Y^5*Z+32*X*Y^4*Z^2+18*X*Y^2*Z^4+68*X^3*Y^2*Z+80*X^2*Y^3*Z+277*X^2*Y^2*Z^2+36*X^2*Y*Z^3+30*X*Y^4*Z+18*X*Y^2*Z^3+144*X^3*Y*Z+40*X^2*Y^2*Z+72*X^2*Y*Z^2+108*X*Y^3*Z+72*X*Y^2*Z^2+180*X^2*Y*Z+72*X*Y^2*Z+162*X*Y*Z

Algorithm definition

The algorithm ⟨8×20×30:2860⟩ is serendipitous tensor product (⟨2×5×6:47⟩ - 2) ⊗ ⟨4×4×5:61⟩ +⟨4×4×10:115⟩.

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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