Description of fast matrix multiplication algorithm: ⟨4×16×32:1318⟩

Algorithm type

X2⁢Y16⁢Z2+X4⁢Y11⁢Z4+X2⁢Y15⁢Z2+X⁢Y16⁢Z2+X⁢Y16⁢Z+3⁢X⁢Y15⁢Z+6⁢X4⁢Y8⁢Z4+4⁢X2⁢Y12⁢Z2+X⁢Y14⁢Z+X2⁢Y11⁢Z2+2⁢X4⁢Y6⁢Z4+X2⁢Y10⁢Z2+10⁢X⁢Y12⁢Z+X⁢Y11⁢Z2+2⁢X⁢Y11⁢Z+70⁢X4⁢Y4⁢Z4+31⁢X2⁢Y8⁢Z2+4⁢X2⁢Y7⁢Z3+5⁢X⁢Y10⁢Z+16⁢X2⁢Y7⁢Z2+14⁢X⁢Y9⁢Z+62⁢X2⁢Y6⁢Z2+2⁢X2⁢Y4⁢Z4+27⁢X⁢Y8⁢Z+X⁢Y7⁢Z2+5⁢X⁢Y7⁢Z+102⁢X2⁢Y4⁢Z2+X2⁢Y2⁢Z4+42⁢X⁢Y6⁢Z+4⁢X⁢Y5⁢Z2+10⁢X2⁢Y3⁢Z2+X⁢Y5⁢Z+8⁢X⁢Y4⁢Z2+257⁢X2⁢Y2⁢Z2+67⁢X⁢Y4⁢Z+10⁢X⁢Y3⁢Z2+129⁢X⁢Y3⁢Z+148⁢X⁢Y2⁢Z+5⁢X⁢Y⁢Z2+261⁢X⁢Y⁢ZX2Y16Z2X4Y11Z4X2Y15Z2XY16Z2XY16Z3XY15Z6X4Y8Z44X2Y12Z2XY14ZX2Y11Z22X4Y6Z4X2Y10Z210XY12ZXY11Z22XY11Z70X4Y4Z431X2Y8Z24X2Y7Z35XY10Z16X2Y7Z214XY9Z62X2Y6Z22X2Y4Z427XY8ZXY7Z25XY7Z102X2Y4Z2X2Y2Z442XY6Z4XY5Z210X2Y3Z2XY5Z8XY4Z2257X2Y2Z267XY4Z10XY3Z2129XY3Z148XY2Z5XYZ2261XYZX^2*Y^16*Z^2+X^4*Y^11*Z^4+X^2*Y^15*Z^2+X*Y^16*Z^2+X*Y^16*Z+3*X*Y^15*Z+6*X^4*Y^8*Z^4+4*X^2*Y^12*Z^2+X*Y^14*Z+X^2*Y^11*Z^2+2*X^4*Y^6*Z^4+X^2*Y^10*Z^2+10*X*Y^12*Z+X*Y^11*Z^2+2*X*Y^11*Z+70*X^4*Y^4*Z^4+31*X^2*Y^8*Z^2+4*X^2*Y^7*Z^3+5*X*Y^10*Z+16*X^2*Y^7*Z^2+14*X*Y^9*Z+62*X^2*Y^6*Z^2+2*X^2*Y^4*Z^4+27*X*Y^8*Z+X*Y^7*Z^2+5*X*Y^7*Z+102*X^2*Y^4*Z^2+X^2*Y^2*Z^4+42*X*Y^6*Z+4*X*Y^5*Z^2+10*X^2*Y^3*Z^2+X*Y^5*Z+8*X*Y^4*Z^2+257*X^2*Y^2*Z^2+67*X*Y^4*Z+10*X*Y^3*Z^2+129*X*Y^3*Z+148*X*Y^2*Z+5*X*Y*Z^2+261*X*Y*Z

Algorithm definition

The algorithm ⟨4×16×32:1318⟩ is serendipitous tensor product (⟨2×4×8:51⟩ - 17) ⊗ ⟨2×4×4:26⟩ +⟨2×4×12:77⟩ +7⟨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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