Description of fast matrix multiplication algorithm: ⟨21 × 32 × 32:11780⟩
Algorithm type
[[1, 1, 1]$351,[1, 1, 2]$126,[1, 1, 3]$378,[1, 1, 4]$3,[1, 1, 6]$18,[1, 1, 9]$27,[1, 2, 1]$1389,[1, 2, 2]$328,[1, 2, 3]$201,[1, 2, 4]$15,[1, 2, 6]$45,[1, 3, 1]$252,[1, 3, 2]$12,[1, 3, 3]$36,[1, 4, 1]$374,[1, 4, 2]$167,[1, 4, 4]$18,[1, 6, 1]$134,[1, 6, 2]$30,[1, 9, 1]$12,[2, 1, 1]$126,[2, 1, 2]$6,[2, 1, 3]$18,[2, 2, 1]$328,[2, 2, 2]$1485,[2, 2, 3]$45,[2, 2, 4]$125,[2, 2, 6]$375,[2, 3, 1]$12,[2, 4, 1]$167,[2, 4, 2]$1421,[2, 4, 4]$280,[2, 6, 1]$30,[2, 6, 2]$250,[3, 1, 1]$378,[3, 1, 2]$18,[3, 1, 3]$54,[3, 2, 1]$201,[3, 2, 2]$45,[3, 3, 1]$36,[3, 4, 3]$6,[3, 4, 4]$6,[3, 4, 6]$2,[3, 4, 8]$2,[3, 4, 9]$6,[3, 4, 12]$6,[3, 8, 3]$22,[3, 8, 4]$22,[3, 8, 6]$4,[3, 8, 8]$4,[3, 12, 3]$4,[3, 12, 4]$4,[4, 1, 1]$3,[4, 2, 1]$15,[4, 2, 2]$125,[4, 4, 1]$18,[4, 4, 2]$280,[4, 4, 3]$6,[4, 4, 4]$977,[4, 4, 6]$2,[4, 4, 8]$9,[4, 4, 9]$6,[4, 4, 12]$27,[4, 8, 3]$22,[4, 8, 4]$99,[4, 8, 6]$4,[4, 8, 8]$18,[4, 12, 3]$4,[4, 12, 4]$18,[6, 1, 1]$18,[6, 2, 1]$45,[6, 2, 2]$375,[6, 4, 3]$2,[6, 4, 4]$2,[6, 8, 3]$4,[6, 8, 4]$4,[6, 8, 6]$20,[6, 8, 8]$20,[7, 8, 7]$3,[7, 8, 14]$1,[7, 8, 21]$3,[7, 16, 7]$11,[7, 16, 14]$2,[7, 24, 7]$2,[8, 4, 3]$2,[8, 4, 4]$9,[8, 8, 3]$4,[8, 8, 4]$18,[8, 8, 6]$20,[8, 8, 8]$90,[9, 1, 1]$27,[9, 4, 3]$6,[9, 4, 4]$6,[12, 4, 3]$6,[12, 4, 4]$27,[14, 8, 7]$1,[14, 16, 7]$2,[14, 16, 14]$10,[21, 8, 7]$3]Algorithm definition
The algorithm ⟨21 × 32 × 32:11780⟩ is the (Kronecker) tensor product of ⟨3 × 4 × 4:38⟩ with ⟨7 × 8 × 8:310⟩.
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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