Description of fast matrix multiplication algorithm: ⟨15×25×25:5394⟩

Algorithm type

2XY12Z2+X9Y4Z+X2Y2Z9+XY6Z6+5X9Y2Z+49X6Y4Z2+544X4Y4Z4+17X4Y2Z6+2X3Y8Z+64X2Y8Z2+17X2Y6Z4+32X2Y4Z6+5X2YZ9+XY9Z2+3X6Y4Z+X6Y2Z3+X3Y6Z2+2X2Y8Z+2XY8Z2+2XY6Z4+XY4Z6+161X6Y2Z2+5X6YZ3+81X4Y4Z2+17X4Y2Z4+X3Y6Z+X3Y4Z3+34X2Y6Z2+81X2Y4Z4+163X2Y2Z6+22XY8Z+5XY3Z6+17X6Y2Z+5X6YZ2+2X4Y4Z+2X4Y2Z3+3X3Y4Z2+X2Y6Z+3X2Y4Z3+6X2YZ6+14XY6Z2+2XY4Z4+16XY2Z6+55X6YZ+221X4Y2Z2+X4YZ3+24X3Y4Z+5X3Y3Z2+5X3Y2Z3+609X2Y4Z2+X2Y3Z3+221X2Y2Z4+11XY6Z+11XY4Z3+XY3Z4+55XYZ6+23X4Y2Z+X4YZ2+17X3Y2Z2+57X2Y4Z+2X2Y3Z2+29X2Y2Z3+X2YZ4+57XY4Z2+23XY2Z4+11X4YZ+84X3Y2Z+55X3YZ2+11X2Y3Z+657X2Y2Z2+62X2YZ3+187XY4Z+18XY3Z2+77XY2Z3+11XYZ4+110X3YZ+205X2Y2Z+29X2YZ2+22XY3Z+205XY2Z2+110XYZ3+99X2YZ+363XY2Z+99XYZ2+154XYZ2XY12Z2X9Y4ZX2Y2Z9XY6Z65X9Y2Z49X6Y4Z2544X4Y4Z417X4Y2Z62X3Y8Z64X2Y8Z217X2Y6Z432X2Y4Z65X2YZ9XY9Z23X6Y4ZX6Y2Z3X3Y6Z22X2Y8Z2XY8Z22XY6Z4XY4Z6161X6Y2Z25X6YZ381X4Y4Z217X4Y2Z4X3Y6ZX3Y4Z334X2Y6Z281X2Y4Z4163X2Y2Z622XY8Z5XY3Z617X6Y2Z5X6YZ22X4Y4Z2X4Y2Z33X3Y4Z2X2Y6Z3X2Y4Z36X2YZ614XY6Z22XY4Z416XY2Z655X6YZ221X4Y2Z2X4YZ324X3Y4Z5X3Y3Z25X3Y2Z3609X2Y4Z2X2Y3Z3221X2Y2Z411XY6Z11XY4Z3XY3Z455XYZ623X4Y2ZX4YZ217X3Y2Z257X2Y4Z2X2Y3Z229X2Y2Z3X2YZ457XY4Z223XY2Z411X4YZ84X3Y2Z55X3YZ211X2Y3Z657X2Y2Z262X2YZ3187XY4Z18XY3Z277XY2Z311XYZ4110X3YZ205X2Y2Z29X2YZ222XY3Z205XY2Z2110XYZ399X2YZ363XY2Z99XYZ2154XYZ2*X*Y^12*Z^2+X^9*Y^4*Z+X^2*Y^2*Z^9+X*Y^6*Z^6+5*X^9*Y^2*Z+49*X^6*Y^4*Z^2+544*X^4*Y^4*Z^4+17*X^4*Y^2*Z^6+2*X^3*Y^8*Z+64*X^2*Y^8*Z^2+17*X^2*Y^6*Z^4+32*X^2*Y^4*Z^6+5*X^2*Y*Z^9+X*Y^9*Z^2+3*X^6*Y^4*Z+X^6*Y^2*Z^3+X^3*Y^6*Z^2+2*X^2*Y^8*Z+2*X*Y^8*Z^2+2*X*Y^6*Z^4+X*Y^4*Z^6+161*X^6*Y^2*Z^2+5*X^6*Y*Z^3+81*X^4*Y^4*Z^2+17*X^4*Y^2*Z^4+X^3*Y^6*Z+X^3*Y^4*Z^3+34*X^2*Y^6*Z^2+81*X^2*Y^4*Z^4+163*X^2*Y^2*Z^6+22*X*Y^8*Z+5*X*Y^3*Z^6+17*X^6*Y^2*Z+5*X^6*Y*Z^2+2*X^4*Y^4*Z+2*X^4*Y^2*Z^3+3*X^3*Y^4*Z^2+X^2*Y^6*Z+3*X^2*Y^4*Z^3+6*X^2*Y*Z^6+14*X*Y^6*Z^2+2*X*Y^4*Z^4+16*X*Y^2*Z^6+55*X^6*Y*Z+221*X^4*Y^2*Z^2+X^4*Y*Z^3+24*X^3*Y^4*Z+5*X^3*Y^3*Z^2+5*X^3*Y^2*Z^3+609*X^2*Y^4*Z^2+X^2*Y^3*Z^3+221*X^2*Y^2*Z^4+11*X*Y^6*Z+11*X*Y^4*Z^3+X*Y^3*Z^4+55*X*Y*Z^6+23*X^4*Y^2*Z+X^4*Y*Z^2+17*X^3*Y^2*Z^2+57*X^2*Y^4*Z+2*X^2*Y^3*Z^2+29*X^2*Y^2*Z^3+X^2*Y*Z^4+57*X*Y^4*Z^2+23*X*Y^2*Z^4+11*X^4*Y*Z+84*X^3*Y^2*Z+55*X^3*Y*Z^2+11*X^2*Y^3*Z+657*X^2*Y^2*Z^2+62*X^2*Y*Z^3+187*X*Y^4*Z+18*X*Y^3*Z^2+77*X*Y^2*Z^3+11*X*Y*Z^4+110*X^3*Y*Z+205*X^2*Y^2*Z+29*X^2*Y*Z^2+22*X*Y^3*Z+205*X*Y^2*Z^2+110*X*Y*Z^3+99*X^2*Y*Z+363*X*Y^2*Z+99*X*Y*Z^2+154*X*Y*Z

Algorithm definition

The algorithm ⟨15×25×25:5394⟩ is the (Kronecker) tensor product of ⟨3×5×5:58⟩ with ⟨5×5×5:93⟩.

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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