Description of fast matrix multiplication algorithm: ⟨12 × 32 × 32:6916⟩

Algorithm type

[[1, 1, 1]$252,[1, 1, 2]$84,[1, 1, 3]$252,[1, 2, 1]$1032,[1, 2, 2]$204,[1, 2, 3]$108,[1, 3, 1]$168,[1, 4, 1]$396,[1, 4, 2]$72,[1, 6, 1]$72,[2, 1, 1]$84,[2, 2, 1]$204,[2, 2, 2]$990,[2, 2, 4]$50,[2, 2, 6]$150,[2, 4, 1]$72,[2, 4, 2]$928,[2, 4, 4]$106,[2, 4, 6]$18,[2, 6, 2]$100,[2, 8, 2]$66,[2, 8, 4]$12,[2, 12, 2]$12,[3, 1, 1]$252,[3, 2, 1]$108,[4, 2, 2]$50,[4, 4, 2]$106,[4, 4, 4]$518,[4, 4, 8]$6,[4, 4, 12]$18,[4, 8, 2]$12,[4, 8, 4]$126,[4, 8, 8]$12,[4, 12, 4]$12,[6, 2, 2]$150,[6, 4, 2]$18,[8, 4, 4]$6,[8, 8, 4]$12,[8, 8, 8]$60,[12, 4, 4]$18]

Algorithm definition

The algorithm ⟨12 × 32 × 32:6916⟩ is the (Kronecker) tensor product of ⟨2 × 2 × 2:7⟩ with ⟨6 × 16 × 16:988⟩.

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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