Description of fast matrix multiplication algorithm: ⟨14×20×21:3520⟩

Algorithm type

4XY15Z+4X6Y4Z4+40X4Y4Z6+4X2Y10Z2+12XY12Z+232X4Y4Z4+12X2Y8Z2+4X3Y6Z2+40X2Y6Z3+4XY9Z+16X6Y2Z2+4X4Y2Z4+236X2Y6Z2+28X2Y4Z4+32X2Y2Z6+28XY6Z2+76X4Y2Z2+60X2Y4Z2+100X2Y2Z4+60XY6Z+16X3Y3Z+12X3Y2Z2+4X2Y3Z2+120X2Y2Z3+12XY5Z+32XY3Z3+76X2Y3Z+788X2Y2Z2+36XY4Z+100XY3Z2+48X3YZ+12X2YZ2+104XY3Z+84XY2Z2+96XYZ3+228X2YZ+180XY2Z+300XYZ2+276XYZ4XY15Z4X6Y4Z440X4Y4Z64X2Y10Z212XY12Z232X4Y4Z412X2Y8Z24X3Y6Z240X2Y6Z34XY9Z16X6Y2Z24X4Y2Z4236X2Y6Z228X2Y4Z432X2Y2Z628XY6Z276X4Y2Z260X2Y4Z2100X2Y2Z460XY6Z16X3Y3Z12X3Y2Z24X2Y3Z2120X2Y2Z312XY5Z32XY3Z376X2Y3Z788X2Y2Z236XY4Z100XY3Z248X3YZ12X2YZ2104XY3Z84XY2Z296XYZ3228X2YZ180XY2Z300XYZ2276XYZ4*X*Y^15*Z+4*X^6*Y^4*Z^4+40*X^4*Y^4*Z^6+4*X^2*Y^10*Z^2+12*X*Y^12*Z+232*X^4*Y^4*Z^4+12*X^2*Y^8*Z^2+4*X^3*Y^6*Z^2+40*X^2*Y^6*Z^3+4*X*Y^9*Z+16*X^6*Y^2*Z^2+4*X^4*Y^2*Z^4+236*X^2*Y^6*Z^2+28*X^2*Y^4*Z^4+32*X^2*Y^2*Z^6+28*X*Y^6*Z^2+76*X^4*Y^2*Z^2+60*X^2*Y^4*Z^2+100*X^2*Y^2*Z^4+60*X*Y^6*Z+16*X^3*Y^3*Z+12*X^3*Y^2*Z^2+4*X^2*Y^3*Z^2+120*X^2*Y^2*Z^3+12*X*Y^5*Z+32*X*Y^3*Z^3+76*X^2*Y^3*Z+788*X^2*Y^2*Z^2+36*X*Y^4*Z+100*X*Y^3*Z^2+48*X^3*Y*Z+12*X^2*Y*Z^2+104*X*Y^3*Z+84*X*Y^2*Z^2+96*X*Y*Z^3+228*X^2*Y*Z+180*X*Y^2*Z+300*X*Y*Z^2+276*X*Y*Z

Algorithm definition

The algorithm ⟨14×20×21:3520⟩ is the (Kronecker) tensor product of ⟨2×4×3:20⟩ with ⟨7×5×7:176⟩.

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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