Description of fast matrix multiplication algorithm: ⟨20×20×27:6032⟩

Algorithm type

4X6Y12Z3+68X6Y8Z6+8X12Y4Z3+4X6Y4Z9+20X3Y12Z3+8X6Y8Z3+4X9Y4Z3+8X6Y4Z6+20X3Y4Z9+4X2Y12Z+4X3Y8Z3+20XY12Z+52X6Y4Z3+4X3Y4Z6+64X8Y2Z2+32X4Y6Z2+544X4Y4Z4+32X4Y2Z6+68X2Y8Z2+8X2Y8Z+32X6Y2Z2+64X4Y4Z2+64X4Y2Z4+28X3Y4Z3+160X2Y6Z2+160X2Y2Z6+4XY8Z+8X4Y4Z+4X2Y4Z3+416X4Y2Z2+4X3Y4Z+40X2Y4Z2+32X2Y2Z4+20XY4Z3+52X2Y4Z+4XY4Z2+128X4YZ+64X2Y3Z+1312X2Y2Z2+64X2YZ3+28XY4Z+64X3YZ+128X2Y2Z+128X2YZ2+320XY3Z+320XYZ3+832X2YZ+64XY2Z+64XYZ2+448XYZ4X6Y12Z368X6Y8Z68X12Y4Z34X6Y4Z920X3Y12Z38X6Y8Z34X9Y4Z38X6Y4Z620X3Y4Z94X2Y12Z4X3Y8Z320XY12Z52X6Y4Z34X3Y4Z664X8Y2Z232X4Y6Z2544X4Y4Z432X4Y2Z668X2Y8Z28X2Y8Z32X6Y2Z264X4Y4Z264X4Y2Z428X3Y4Z3160X2Y6Z2160X2Y2Z64XY8Z8X4Y4Z4X2Y4Z3416X4Y2Z24X3Y4Z40X2Y4Z232X2Y2Z420XY4Z352X2Y4Z4XY4Z2128X4YZ64X2Y3Z1312X2Y2Z264X2YZ328XY4Z64X3YZ128X2Y2Z128X2YZ2320XY3Z320XYZ3832X2YZ64XY2Z64XYZ2448XYZ4*X^6*Y^12*Z^3+68*X^6*Y^8*Z^6+8*X^12*Y^4*Z^3+4*X^6*Y^4*Z^9+20*X^3*Y^12*Z^3+8*X^6*Y^8*Z^3+4*X^9*Y^4*Z^3+8*X^6*Y^4*Z^6+20*X^3*Y^4*Z^9+4*X^2*Y^12*Z+4*X^3*Y^8*Z^3+20*X*Y^12*Z+52*X^6*Y^4*Z^3+4*X^3*Y^4*Z^6+64*X^8*Y^2*Z^2+32*X^4*Y^6*Z^2+544*X^4*Y^4*Z^4+32*X^4*Y^2*Z^6+68*X^2*Y^8*Z^2+8*X^2*Y^8*Z+32*X^6*Y^2*Z^2+64*X^4*Y^4*Z^2+64*X^4*Y^2*Z^4+28*X^3*Y^4*Z^3+160*X^2*Y^6*Z^2+160*X^2*Y^2*Z^6+4*X*Y^8*Z+8*X^4*Y^4*Z+4*X^2*Y^4*Z^3+416*X^4*Y^2*Z^2+4*X^3*Y^4*Z+40*X^2*Y^4*Z^2+32*X^2*Y^2*Z^4+20*X*Y^4*Z^3+52*X^2*Y^4*Z+4*X*Y^4*Z^2+128*X^4*Y*Z+64*X^2*Y^3*Z+1312*X^2*Y^2*Z^2+64*X^2*Y*Z^3+28*X*Y^4*Z+64*X^3*Y*Z+128*X^2*Y^2*Z+128*X^2*Y*Z^2+320*X*Y^3*Z+320*X*Y*Z^3+832*X^2*Y*Z+64*X*Y^2*Z+64*X*Y*Z^2+448*X*Y*Z

Algorithm definition

The algorithm ⟨20×20×27:6032⟩ is the (Kronecker) tensor product of ⟨5×5×3:58⟩ with ⟨4×4×9:104⟩.

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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