Description of fast matrix multiplication algorithm: ⟨5×6×8:176⟩

Algorithm type

2X4Y4Z4+5X3Y4Z3+X2Y6Z2+X5Y2Z2+X2Y6Z+X2Y4Z3+X2Y2Z5+2X2Y4Z2+2X2Y2Z4+XY4Z3+XY2Z5+X2Y4Z+X2Y2Z3+39X2Y2Z2+XY4Z+XY2Z3+3X3YZ+X2Y2Z+18XY3Z+6XY2Z2+6XYZ3+12XY2Z+12XYZ2+57XYZ2X4Y4Z45X3Y4Z3X2Y6Z2X5Y2Z2X2Y6ZX2Y4Z3X2Y2Z52X2Y4Z22X2Y2Z4XY4Z3XY2Z5X2Y4ZX2Y2Z339X2Y2Z2XY4ZXY2Z33X3YZX2Y2Z18XY3Z6XY2Z26XYZ312XY2Z12XYZ257XYZ2*X^4*Y^4*Z^4+5*X^3*Y^4*Z^3+X^2*Y^6*Z^2+X^5*Y^2*Z^2+X^2*Y^6*Z+X^2*Y^4*Z^3+X^2*Y^2*Z^5+2*X^2*Y^4*Z^2+2*X^2*Y^2*Z^4+X*Y^4*Z^3+X*Y^2*Z^5+X^2*Y^4*Z+X^2*Y^2*Z^3+39*X^2*Y^2*Z^2+X*Y^4*Z+X*Y^2*Z^3+3*X^3*Y*Z+X^2*Y^2*Z+18*X*Y^3*Z+6*X*Y^2*Z^2+6*X*Y*Z^3+12*X*Y^2*Z+12*X*Y*Z^2+57*X*Y*Z

Algorithm definition

The algorithm ⟨5×6×8:176⟩ could be constructed using the following decomposition:

⟨5×6×8:176⟩ = ⟨3×3×4:29⟩ + ⟨3×3×4:29⟩ + ⟨2×3×4:20⟩ + ⟨3×3×4:29⟩ + ⟨2×3×4:20⟩ + ⟨2×3×4:20⟩ + ⟨3×3×4:29⟩.

This decomposition is defined by the following equality:

TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8C_1_1C_1_2C_1_3C_1_4C_1_5C_2_1C_2_2C_2_3C_2_4C_2_5C_3_1C_3_2C_3_3C_3_4C_3_5C_4_1C_4_2C_4_3C_4_4C_4_5C_5_1C_5_2C_5_3C_5_4C_5_5C_6_1C_6_2C_6_3C_6_4C_6_5C_7_1C_7_2C_7_3C_7_4C_7_5C_8_1C_8_2C_8_3C_8_4C_8_5=TraceMulA_3_3-A_3_4A_3_1-A_3_5A_3_2-A_3_6A_4_3-A_4_4A_4_1-A_4_5A_4_2-A_4_6A_5_3-A_5_4A_5_1-A_5_5A_5_2-A_5_6-B_3_2+B_3_1B_3_5-B_3_6B_3_3-B_3_7B_3_4-B_3_8B_1_1-B_1_2B_1_5-B_1_6B_1_3-B_1_7B_1_4-B_1_8B_2_1-B_2_2B_2_5-B_2_6B_2_3-B_2_7B_2_4-B_2_8C_1_3-C_1_2C_1_4-C_1_1+C_1_5-C_5_2+C_5_3C_5_4-C_5_1+C_5_5-C_3_2+C_3_3C_3_4-C_3_1+C_3_5-C_4_2+C_4_3C_4_4-C_4_1+C_4_5+TraceMulA_3_3+A_2_3A_3_1+A_2_1A_2_2+A_3_2A_4_3A_4_1A_4_2A_1_3+A_5_3A_1_1+A_5_1A_1_2+A_5_2B_3_1+B_4_1B_3_5+B_4_5B_3_3+B_4_3B_4_4+B_3_4B_1_1+B_5_1B_1_5+B_5_5B_1_3+B_5_3B_1_4+B_5_4B_2_1+B_6_1B_2_5+B_6_5B_2_3+B_6_3B_2_4+B_6_4C_1_3+C_2_3C_1_4+C_2_4C_1_5+C_2_5C_5_3+C_6_3C_5_4+C_6_4C_5_5+C_6_5C_3_3+C_7_3C_3_4+C_7_4C_3_5+C_7_5C_4_3+C_8_3C_4_4+C_8_4C_4_5+C_8_5+TraceMulA_2_4A_2_5A_2_6A_1_4A_1_5A_1_6B_4_2B_4_6B_4_7B_4_8B_5_2B_5_6B_5_7B_5_8B_6_2B_6_6B_6_7B_6_8C_2_2C_2_1C_6_2C_6_1C_7_2C_7_1C_8_2C_8_1+TraceMulA_3_4A_3_5A_3_6A_4_4A_4_5A_4_6A_5_4A_5_5A_5_6-B_3_1-B_4_1+B_3_2+B_4_2-B_3_5-B_4_5+B_3_6+B_4_6-B_3_3-B_4_3+B_3_7+B_4_7-B_3_4-B_4_4+B_3_8+B_4_8-B_1_1-B_5_1+B_1_2+B_5_2-B_1_5-B_5_5+B_1_6+B_5_6-B_1_3-B_5_3+B_1_7+B_5_7-B_1_4-B_5_4+B_1_8+B_5_8-B_2_1-B_6_1+B_2_2+B_6_2-B_2_5-B_6_5+B_2_6+B_6_6-B_2_3-B_6_3+B_2_7+B_6_7-B_2_4-B_6_4+B_2_8+B_6_8C_2_3C_2_4C_2_5C_6_3C_6_4C_6_5C_7_3C_7_4C_7_5C_8_3C_8_4C_8_5+TraceMul-A_2_3-A_3_3+A_2_4+A_3_4-A_2_1-A_3_1+A_2_5+A_3_5-A_2_2-A_3_2+A_2_6+A_3_6-A_1_3-A_5_3+A_1_4+A_5_4-A_1_1-A_5_1+A_1_5+A_5_5-A_1_2-A_5_2+A_1_6+A_5_6B_4_1B_4_5B_4_3B_4_4B_5_1B_5_5B_5_3B_5_4B_6_1B_6_5B_6_3B_6_4C_1_2C_1_1C_5_2C_5_1C_3_2C_3_1C_4_2C_4_1+TraceMulA_2_3A_2_1A_2_2A_1_3A_1_1A_1_2B_3_2B_3_6B_3_7B_3_8B_1_2B_1_6B_1_7B_1_8B_2_2B_2_6B_2_7B_2_8-C_1_3-C_2_3+C_2_2+C_1_2C_1_1+C_2_1-C_1_5-C_2_5C_5_2+C_6_2-C_5_3-C_6_3C_5_1+C_6_1-C_5_5-C_6_5C_3_2+C_7_2-C_3_3-C_7_3C_3_1+C_7_1-C_3_5-C_7_5C_4_2+C_8_2-C_4_3-C_8_3C_4_1+C_8_1-C_4_5-C_8_5+TraceMul-A_2_3-A_3_3+A_3_4-A_2_1-A_3_1+A_3_5-A_2_2-A_3_2+A_3_6-A_4_3+A_4_4-A_4_1+A_4_5-A_4_2+A_4_6-A_1_3-A_5_3+A_5_4-A_1_1-A_5_1+A_5_5-A_1_2-A_5_2+A_5_6B_3_1+B_4_1-B_3_2B_3_5+B_4_5-B_3_6B_3_3+B_4_3-B_3_7B_4_4+B_3_4-B_3_8B_1_1+B_5_1-B_1_2B_1_5+B_5_5-B_1_6B_1_3+B_5_3-B_1_7B_1_4+B_5_4-B_1_8B_2_1+B_6_1-B_2_2B_2_5+B_6_5-B_2_6B_2_3+B_6_3-B_2_7B_2_4+B_6_4-B_2_8C_1_3-C_1_2+C_2_3C_1_4+C_2_4-C_1_1+C_1_5+C_2_5-C_5_2+C_5_3+C_6_3C_5_4+C_6_4-C_5_1+C_5_5+C_6_5-C_3_2+C_3_3+C_7_3C_3_4+C_7_4-C_3_1+C_3_5+C_7_5-C_4_2+C_4_3+C_8_3C_4_4+C_8_4-C_4_1+C_4_5+C_8_5TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8C_1_1C_1_2C_1_3C_1_4C_1_5C_2_1C_2_2C_2_3C_2_4C_2_5C_3_1C_3_2C_3_3C_3_4C_3_5C_4_1C_4_2C_4_3C_4_4C_4_5C_5_1C_5_2C_5_3C_5_4C_5_5C_6_1C_6_2C_6_3C_6_4C_6_5C_7_1C_7_2C_7_3C_7_4C_7_5C_8_1C_8_2C_8_3C_8_4C_8_5TraceMulA_3_3A_3_4A_3_1A_3_5A_3_2A_3_6A_4_3A_4_4A_4_1A_4_5A_4_2A_4_6A_5_3A_5_4A_5_1A_5_5A_5_2A_5_6B_3_2B_3_1B_3_5B_3_6B_3_3B_3_7B_3_4B_3_8B_1_1B_1_2B_1_5B_1_6B_1_3B_1_7B_1_4B_1_8B_2_1B_2_2B_2_5B_2_6B_2_3B_2_7B_2_4B_2_8C_1_3C_1_2C_1_4C_1_1C_1_5C_5_2C_5_3C_5_4C_5_1C_5_5C_3_2C_3_3C_3_4C_3_1C_3_5C_4_2C_4_3C_4_4C_4_1C_4_5TraceMulA_3_3A_2_3A_3_1A_2_1A_2_2A_3_2A_4_3A_4_1A_4_2A_1_3A_5_3A_1_1A_5_1A_1_2A_5_2B_3_1B_4_1B_3_5B_4_5B_3_3B_4_3B_4_4B_3_4B_1_1B_5_1B_1_5B_5_5B_1_3B_5_3B_1_4B_5_4B_2_1B_6_1B_2_5B_6_5B_2_3B_6_3B_2_4B_6_4C_1_3C_2_3C_1_4C_2_4C_1_5C_2_5C_5_3C_6_3C_5_4C_6_4C_5_5C_6_5C_3_3C_7_3C_3_4C_7_4C_3_5C_7_5C_4_3C_8_3C_4_4C_8_4C_4_5C_8_5TraceMulA_2_4A_2_5A_2_6A_1_4A_1_5A_1_6B_4_2B_4_6B_4_7B_4_8B_5_2B_5_6B_5_7B_5_8B_6_2B_6_6B_6_7B_6_8C_2_2C_2_1C_6_2C_6_1C_7_2C_7_1C_8_2C_8_1TraceMulA_3_4A_3_5A_3_6A_4_4A_4_5A_4_6A_5_4A_5_5A_5_6B_3_1B_4_1B_3_2B_4_2B_3_5B_4_5B_3_6B_4_6B_3_3B_4_3B_3_7B_4_7B_3_4B_4_4B_3_8B_4_8B_1_1B_5_1B_1_2B_5_2B_1_5B_5_5B_1_6B_5_6B_1_3B_5_3B_1_7B_5_7B_1_4B_5_4B_1_8B_5_8B_2_1B_6_1B_2_2B_6_2B_2_5B_6_5B_2_6B_6_6B_2_3B_6_3B_2_7B_6_7B_2_4B_6_4B_2_8B_6_8C_2_3C_2_4C_2_5C_6_3C_6_4C_6_5C_7_3C_7_4C_7_5C_8_3C_8_4C_8_5TraceMulA_2_3A_3_3A_2_4A_3_4A_2_1A_3_1A_2_5A_3_5A_2_2A_3_2A_2_6A_3_6A_1_3A_5_3A_1_4A_5_4A_1_1A_5_1A_1_5A_5_5A_1_2A_5_2A_1_6A_5_6B_4_1B_4_5B_4_3B_4_4B_5_1B_5_5B_5_3B_5_4B_6_1B_6_5B_6_3B_6_4C_1_2C_1_1C_5_2C_5_1C_3_2C_3_1C_4_2C_4_1TraceMulA_2_3A_2_1A_2_2A_1_3A_1_1A_1_2B_3_2B_3_6B_3_7B_3_8B_1_2B_1_6B_1_7B_1_8B_2_2B_2_6B_2_7B_2_8C_1_3C_2_3C_2_2C_1_2C_1_1C_2_1C_1_5C_2_5C_5_2C_6_2C_5_3C_6_3C_5_1C_6_1C_5_5C_6_5C_3_2C_7_2C_3_3C_7_3C_3_1C_7_1C_3_5C_7_5C_4_2C_8_2C_4_3C_8_3C_4_1C_8_1C_4_5C_8_5TraceMulA_2_3A_3_3A_3_4A_2_1A_3_1A_3_5A_2_2A_3_2A_3_6A_4_3A_4_4A_4_1A_4_5A_4_2A_4_6A_1_3A_5_3A_5_4A_1_1A_5_1A_5_5A_1_2A_5_2A_5_6B_3_1B_4_1B_3_2B_3_5B_4_5B_3_6B_3_3B_4_3B_3_7B_4_4B_3_4B_3_8B_1_1B_5_1B_1_2B_1_5B_5_5B_1_6B_1_3B_5_3B_1_7B_1_4B_5_4B_1_8B_2_1B_6_1B_2_2B_2_5B_6_5B_2_6B_2_3B_6_3B_2_7B_2_4B_6_4B_2_8C_1_3C_1_2C_2_3C_1_4C_2_4C_1_1C_1_5C_2_5C_5_2C_5_3C_6_3C_5_4C_6_4C_5_1C_5_5C_6_5C_3_2C_3_3C_7_3C_3_4C_7_4C_3_1C_3_5C_7_5C_4_2C_4_3C_8_3C_4_4C_8_4C_4_1C_4_5C_8_5Trace(Mul(Matrix(5, 6, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6]]),Matrix(6, 8, [[B_1_1,B_1_2,B_1_3,B_1_4,B_1_5,B_1_6,B_1_7,B_1_8],[B_2_1,B_2_2,B_2_3,B_2_4,B_2_5,B_2_6,B_2_7,B_2_8],[B_3_1,B_3_2,B_3_3,B_3_4,B_3_5,B_3_6,B_3_7,B_3_8],[B_4_1,B_4_2,B_4_3,B_4_4,B_4_5,B_4_6,B_4_7,B_4_8],[B_5_1,B_5_2,B_5_3,B_5_4,B_5_5,B_5_6,B_5_7,B_5_8],[B_6_1,B_6_2,B_6_3,B_6_4,B_6_5,B_6_6,B_6_7,B_6_8]]),Matrix(8, 5, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5],[C_8_1,C_8_2,C_8_3,C_8_4,C_8_5]]))) = Trace(Mul(Matrix(3, 3, [[A_3_3-A_3_4,A_3_1-A_3_5,A_3_2-A_3_6],[A_4_3-A_4_4,A_4_1-A_4_5,A_4_2-A_4_6],[A_5_3-A_5_4,A_5_1-A_5_5,A_5_2-A_5_6]]),Matrix(3, 4, [[-B_3_2+B_3_1,B_3_5-B_3_6,B_3_3-B_3_7,B_3_4-B_3_8],[B_1_1-B_1_2,B_1_5-B_1_6,B_1_3-B_1_7,B_1_4-B_1_8],[B_2_1-B_2_2,B_2_5-B_2_6,B_2_3-B_2_7,B_2_4-B_2_8]]),Matrix(4, 3, [[C_1_3-C_1_2,C_1_4,-C_1_1+C_1_5],[-C_5_2+C_5_3,C_5_4,-C_5_1+C_5_5],[-C_3_2+C_3_3,C_3_4,-C_3_1+C_3_5],[-C_4_2+C_4_3,C_4_4,-C_4_1+C_4_5]])))+Trace(Mul(Matrix(3, 3, [[A_3_3+A_2_3,A_3_1+A_2_1,A_2_2+A_3_2],[A_4_3,A_4_1,A_4_2],[A_1_3+A_5_3,A_1_1+A_5_1,A_1_2+A_5_2]]),Matrix(3, 4, [[B_3_1+B_4_1,B_3_5+B_4_5,B_3_3+B_4_3,B_4_4+B_3_4],[B_1_1+B_5_1,B_1_5+B_5_5,B_1_3+B_5_3,B_1_4+B_5_4],[B_2_1+B_6_1,B_2_5+B_6_5,B_2_3+B_6_3,B_2_4+B_6_4]]),Matrix(4, 3, [[C_1_3+C_2_3,C_1_4+C_2_4,C_1_5+C_2_5],[C_5_3+C_6_3,C_5_4+C_6_4,C_5_5+C_6_5],[C_3_3+C_7_3,C_3_4+C_7_4,C_3_5+C_7_5],[C_4_3+C_8_3,C_4_4+C_8_4,C_4_5+C_8_5]])))+Trace(Mul(Matrix(2, 3, [[A_2_4,A_2_5,A_2_6],[A_1_4,A_1_5,A_1_6]]),Matrix(3, 4, [[B_4_2,B_4_6,B_4_7,B_4_8],[B_5_2,B_5_6,B_5_7,B_5_8],[B_6_2,B_6_6,B_6_7,B_6_8]]),Matrix(4, 2, [[C_2_2,C_2_1],[C_6_2,C_6_1],[C_7_2,C_7_1],[C_8_2,C_8_1]])))+Trace(Mul(Matrix(3, 3, [[A_3_4,A_3_5,A_3_6],[A_4_4,A_4_5,A_4_6],[A_5_4,A_5_5,A_5_6]]),Matrix(3, 4, [[-B_3_1-B_4_1+B_3_2+B_4_2,-B_3_5-B_4_5+B_3_6+B_4_6,-B_3_3-B_4_3+B_3_7+B_4_7,-B_3_4-B_4_4+B_3_8+B_4_8],[-B_1_1-B_5_1+B_1_2+B_5_2,-B_1_5-B_5_5+B_1_6+B_5_6,-B_1_3-B_5_3+B_1_7+B_5_7,-B_1_4-B_5_4+B_1_8+B_5_8],[-B_2_1-B_6_1+B_2_2+B_6_2,-B_2_5-B_6_5+B_2_6+B_6_6,-B_2_3-B_6_3+B_2_7+B_6_7,-B_2_4-B_6_4+B_2_8+B_6_8]]),Matrix(4, 3, [[C_2_3,C_2_4,C_2_5],[C_6_3,C_6_4,C_6_5],[C_7_3,C_7_4,C_7_5],[C_8_3,C_8_4,C_8_5]])))+Trace(Mul(Matrix(2, 3, [[-A_2_3-A_3_3+A_2_4+A_3_4,-A_2_1-A_3_1+A_2_5+A_3_5,-A_2_2-A_3_2+A_2_6+A_3_6],[-A_1_3-A_5_3+A_1_4+A_5_4,-A_1_1-A_5_1+A_1_5+A_5_5,-A_1_2-A_5_2+A_1_6+A_5_6]]),Matrix(3, 4, [[B_4_1,B_4_5,B_4_3,B_4_4],[B_5_1,B_5_5,B_5_3,B_5_4],[B_6_1,B_6_5,B_6_3,B_6_4]]),Matrix(4, 2, [[C_1_2,C_1_1],[C_5_2,C_5_1],[C_3_2,C_3_1],[C_4_2,C_4_1]])))+Trace(Mul(Matrix(2, 3, [[A_2_3,A_2_1,A_2_2],[A_1_3,A_1_1,A_1_2]]),Matrix(3, 4, [[B_3_2,B_3_6,B_3_7,B_3_8],[B_1_2,B_1_6,B_1_7,B_1_8],[B_2_2,B_2_6,B_2_7,B_2_8]]),Matrix(4, 2, [[-C_1_3-C_2_3+C_2_2+C_1_2,C_1_1+C_2_1-C_1_5-C_2_5],[C_5_2+C_6_2-C_5_3-C_6_3,C_5_1+C_6_1-C_5_5-C_6_5],[C_3_2+C_7_2-C_3_3-C_7_3,C_3_1+C_7_1-C_3_5-C_7_5],[C_4_2+C_8_2-C_4_3-C_8_3,C_4_1+C_8_1-C_4_5-C_8_5]])))+Trace(Mul(Matrix(3, 3, [[-A_2_3-A_3_3+A_3_4,-A_2_1-A_3_1+A_3_5,-A_2_2-A_3_2+A_3_6],[-A_4_3+A_4_4,-A_4_1+A_4_5,-A_4_2+A_4_6],[-A_1_3-A_5_3+A_5_4,-A_1_1-A_5_1+A_5_5,-A_1_2-A_5_2+A_5_6]]),Matrix(3, 4, [[B_3_1+B_4_1-B_3_2,B_3_5+B_4_5-B_3_6,B_3_3+B_4_3-B_3_7,B_4_4+B_3_4-B_3_8],[B_1_1+B_5_1-B_1_2,B_1_5+B_5_5-B_1_6,B_1_3+B_5_3-B_1_7,B_1_4+B_5_4-B_1_8],[B_2_1+B_6_1-B_2_2,B_2_5+B_6_5-B_2_6,B_2_3+B_6_3-B_2_7,B_2_4+B_6_4-B_2_8]]),Matrix(4, 3, [[C_1_3-C_1_2+C_2_3,C_1_4+C_2_4,-C_1_1+C_1_5+C_2_5],[-C_5_2+C_5_3+C_6_3,C_5_4+C_6_4,-C_5_1+C_5_5+C_6_5],[-C_3_2+C_3_3+C_7_3,C_3_4+C_7_4,-C_3_1+C_3_5+C_7_5],[-C_4_2+C_4_3+C_8_3,C_4_4+C_8_4,-C_4_1+C_4_5+C_8_5]])))

N.B.: for any matrices A, B and C such that the expression Tr(Mul(A,B,C)) is defined, one can construct several trilinear homogeneous polynomials P(A,B,C) such that P(A,B,C)=Tr(Mul(A,B,C)) (P(A,B,C) variables are A,B and C's coefficients). Each trilinear P expression encodes a matrix multiplication algorithm: the coefficient in C_i_j of P(A,B,C) is the (i,j)-th entry of the matrix product Mul(A,B)=Transpose(C).

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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