Description of fast matrix multiplication algorithm: ⟨4×16×28:1166⟩

Algorithm type

X2⁢Y16⁢Z2+X⁢Y16⁢Z+2⁢X2⁢Y13⁢Z2+6⁢X4⁢Y8⁢Z4+2⁢X2⁢Y12⁢Z2+3⁢X⁢Y13⁢Z+6⁢X4⁢Y6⁢Z4+X2⁢Y10⁢Z2+X2⁢Y8⁢Z4+6⁢X⁢Y12⁢Z+2⁢X2⁢Y9⁢Z2+54⁢X4⁢Y4⁢Z4+26⁢X2⁢Y8⁢Z2+X2⁢Y6⁢Z4+4⁢X⁢Y10⁢Z+5⁢X⁢Y9⁢Z2+X2⁢Y7⁢Z2+2⁢X2⁢Y5⁢Z4+13⁢X⁢Y9⁢Z+55⁢X2⁢Y6⁢Z2+2⁢X2⁢Y4⁢Z4+24⁢X⁢Y8⁢Z+5⁢X⁢Y7⁢Z2+10⁢X2⁢Y5⁢Z2+7⁢X⁢Y7⁢Z+112⁢X2⁢Y4⁢Z2+38⁢X⁢Y6⁢Z+10⁢X2⁢Y3⁢Z2+6⁢X⁢Y5⁢Z+7⁢X⁢Y4⁢Z2+200⁢X2⁢Y2⁢Z2+73⁢X⁢Y4⁢Z+7⁢X⁢Y3⁢Z2+101⁢X⁢Y3⁢Z+164⁢X⁢Y2⁢Z+8⁢X⁢Y⁢Z2+200⁢X⁢Y⁢ZX2Y16Z2XY16Z2X2Y13Z26X4Y8Z42X2Y12Z23XY13Z6X4Y6Z4X2Y10Z2X2Y8Z46XY12Z2X2Y9Z254X4Y4Z426X2Y8Z2X2Y6Z44XY10Z5XY9Z2X2Y7Z22X2Y5Z413XY9Z55X2Y6Z22X2Y4Z424XY8Z5XY7Z210X2Y5Z27XY7Z112X2Y4Z238XY6Z10X2Y3Z26XY5Z7XY4Z2200X2Y2Z273XY4Z7XY3Z2101XY3Z164XY2Z8XYZ2200XYZX^2*Y^16*Z^2+X*Y^16*Z+2*X^2*Y^13*Z^2+6*X^4*Y^8*Z^4+2*X^2*Y^12*Z^2+3*X*Y^13*Z+6*X^4*Y^6*Z^4+X^2*Y^10*Z^2+X^2*Y^8*Z^4+6*X*Y^12*Z+2*X^2*Y^9*Z^2+54*X^4*Y^4*Z^4+26*X^2*Y^8*Z^2+X^2*Y^6*Z^4+4*X*Y^10*Z+5*X*Y^9*Z^2+X^2*Y^7*Z^2+2*X^2*Y^5*Z^4+13*X*Y^9*Z+55*X^2*Y^6*Z^2+2*X^2*Y^4*Z^4+24*X*Y^8*Z+5*X*Y^7*Z^2+10*X^2*Y^5*Z^2+7*X*Y^7*Z+112*X^2*Y^4*Z^2+38*X*Y^6*Z+10*X^2*Y^3*Z^2+6*X*Y^5*Z+7*X*Y^4*Z^2+200*X^2*Y^2*Z^2+73*X*Y^4*Z+7*X*Y^3*Z^2+101*X*Y^3*Z+164*X*Y^2*Z+8*X*Y*Z^2+200*X*Y*Z

Algorithm definition

The algorithm ⟨4×16×28:1166⟩ is serendipitous tensor product (⟨2×4×7:45⟩ - 8) ⊗ ⟨2×4×4:26⟩ +4⟨2×4×8:51⟩.

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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