Description of fast matrix multiplication algorithm: ⟨10×20×30:3508⟩

Algorithm type

320X4Y8Z4+24X2Y12Z2+8X2Y8Z4+24XY12Z+X3Y2Z7+432X2Y8Z2+16X2Y4Z6+X2Y2Z8+6X7Y2Z2+X6Y2Z3+2X4Y2Z5+X3Y2Z6+8XY8Z2+2X7Y2Z+5X6Y2Z2+80X4Y4Z2+3X4Y2Z4+2X3Y2Z5+104X2Y4Z4+2X2Y2Z6+X2YZ7+112XY8Z+XY2Z7+8X7YZ+4X6YZ2+X4Y2Z3+X4YZ4+2X3Y2Z4+X3YZ5+X2Y2Z5+2X2YZ6+XY2Z6+10X6YZ+16X4Y2Z2+5X4YZ3+2X3Y2Z3+X3YZ4+152X2Y4Z2+6X2Y2Z4+16XY4Z3+2X4Y2Z+8X4YZ2+2X3Y3Z+10X3Y2Z2+2X3YZ3+80X2Y4Z+X2Y3Z2+2X2Y2Z3+104XY4Z2+XY3Z3+2XY2Z4+18X4YZ+4X3Y2Z+6X3YZ2+2X2Y3Z+657X2Y2Z2+5X2YZ3+152XY4Z+XY2Z3+17X3YZ+2X2Y2Z+11X2YZ2+50XY3Z+22XY2Z2+36XYZ3+179X2YZ+226XY2Z+208XYZ2+313XYZ320X4Y8Z424X2Y12Z28X2Y8Z424XY12ZX3Y2Z7432X2Y8Z216X2Y4Z6X2Y2Z86X7Y2Z2X6Y2Z32X4Y2Z5X3Y2Z68XY8Z22X7Y2Z5X6Y2Z280X4Y4Z23X4Y2Z42X3Y2Z5104X2Y4Z42X2Y2Z6X2YZ7112XY8ZXY2Z78X7YZ4X6YZ2X4Y2Z3X4YZ42X3Y2Z4X3YZ5X2Y2Z52X2YZ6XY2Z610X6YZ16X4Y2Z25X4YZ32X3Y2Z3X3YZ4152X2Y4Z26X2Y2Z416XY4Z32X4Y2Z8X4YZ22X3Y3Z10X3Y2Z22X3YZ380X2Y4ZX2Y3Z22X2Y2Z3104XY4Z2XY3Z32XY2Z418X4YZ4X3Y2Z6X3YZ22X2Y3Z657X2Y2Z25X2YZ3152XY4ZXY2Z317X3YZ2X2Y2Z11X2YZ250XY3Z22XY2Z236XYZ3179X2YZ226XY2Z208XYZ2313XYZ320*X^4*Y^8*Z^4+24*X^2*Y^12*Z^2+8*X^2*Y^8*Z^4+24*X*Y^12*Z+X^3*Y^2*Z^7+432*X^2*Y^8*Z^2+16*X^2*Y^4*Z^6+X^2*Y^2*Z^8+6*X^7*Y^2*Z^2+X^6*Y^2*Z^3+2*X^4*Y^2*Z^5+X^3*Y^2*Z^6+8*X*Y^8*Z^2+2*X^7*Y^2*Z+5*X^6*Y^2*Z^2+80*X^4*Y^4*Z^2+3*X^4*Y^2*Z^4+2*X^3*Y^2*Z^5+104*X^2*Y^4*Z^4+2*X^2*Y^2*Z^6+X^2*Y*Z^7+112*X*Y^8*Z+X*Y^2*Z^7+8*X^7*Y*Z+4*X^6*Y*Z^2+X^4*Y^2*Z^3+X^4*Y*Z^4+2*X^3*Y^2*Z^4+X^3*Y*Z^5+X^2*Y^2*Z^5+2*X^2*Y*Z^6+X*Y^2*Z^6+10*X^6*Y*Z+16*X^4*Y^2*Z^2+5*X^4*Y*Z^3+2*X^3*Y^2*Z^3+X^3*Y*Z^4+152*X^2*Y^4*Z^2+6*X^2*Y^2*Z^4+16*X*Y^4*Z^3+2*X^4*Y^2*Z+8*X^4*Y*Z^2+2*X^3*Y^3*Z+10*X^3*Y^2*Z^2+2*X^3*Y*Z^3+80*X^2*Y^4*Z+X^2*Y^3*Z^2+2*X^2*Y^2*Z^3+104*X*Y^4*Z^2+X*Y^3*Z^3+2*X*Y^2*Z^4+18*X^4*Y*Z+4*X^3*Y^2*Z+6*X^3*Y*Z^2+2*X^2*Y^3*Z+657*X^2*Y^2*Z^2+5*X^2*Y*Z^3+152*X*Y^4*Z+X*Y^2*Z^3+17*X^3*Y*Z+2*X^2*Y^2*Z+11*X^2*Y*Z^2+50*X*Y^3*Z+22*X*Y^2*Z^2+36*X*Y*Z^3+179*X^2*Y*Z+226*X*Y^2*Z+208*X*Y*Z^2+313*X*Y*Z

Algorithm definition

The algorithm ⟨10×20×30:3508⟩ is serendipitous tensor product (⟨5×5×6:110⟩ - 8) ⊗ ⟨2×4×5:32⟩ +4⟨4×4×5:61⟩.

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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