Description of fast matrix multiplication algorithm: ⟨20×21×30:6840⟩

Algorithm type

3X6Y4Z4+18X4Y4Z6+6X6Y4Z2+861X4Y4Z4+6X6Y2Z2+12X4Y4Z2+18X4Y2Z4+72X2Y2Z6+6X3Y4Z2+18X2Y4Z3+312X4Y2Z2+12X3Y4Z+1206X2Y4Z2+1008X2Y2Z4+54XYZ6+6X3Y2Z2+24X2Y4Z+18X2YZ4+24X3Y2Z+462X2Y2Z2+354XY4Z+54XY2Z3+162XYZ4+12X3YZ+360X2Y2Z+288X2YZ2+468XY2Z2+48X2YZ+498XY2Z+378XYZ2+72XYZ3X6Y4Z418X4Y4Z66X6Y4Z2861X4Y4Z46X6Y2Z212X4Y4Z218X4Y2Z472X2Y2Z66X3Y4Z218X2Y4Z3312X4Y2Z212X3Y4Z1206X2Y4Z21008X2Y2Z454XYZ66X3Y2Z224X2Y4Z18X2YZ424X3Y2Z462X2Y2Z2354XY4Z54XY2Z3162XYZ412X3YZ360X2Y2Z288X2YZ2468XY2Z248X2YZ498XY2Z378XYZ272XYZ3*X^6*Y^4*Z^4+18*X^4*Y^4*Z^6+6*X^6*Y^4*Z^2+861*X^4*Y^4*Z^4+6*X^6*Y^2*Z^2+12*X^4*Y^4*Z^2+18*X^4*Y^2*Z^4+72*X^2*Y^2*Z^6+6*X^3*Y^4*Z^2+18*X^2*Y^4*Z^3+312*X^4*Y^2*Z^2+12*X^3*Y^4*Z+1206*X^2*Y^4*Z^2+1008*X^2*Y^2*Z^4+54*X*Y*Z^6+6*X^3*Y^2*Z^2+24*X^2*Y^4*Z+18*X^2*Y*Z^4+24*X^3*Y^2*Z+462*X^2*Y^2*Z^2+354*X*Y^4*Z+54*X*Y^2*Z^3+162*X*Y*Z^4+12*X^3*Y*Z+360*X^2*Y^2*Z+288*X^2*Y*Z^2+468*X*Y^2*Z^2+48*X^2*Y*Z+498*X*Y^2*Z+378*X*Y*Z^2+72*X*Y*Z

Algorithm definition

The algorithm ⟨20×21×30:6840⟩ is serendipitous tensor product (⟨5×7×5:127⟩ - 13) ⊗ ⟨4×3×6:54⟩ +⟨4×9×6:159⟩ +5⟨4×6×6:105⟩.

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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