Description of fast matrix multiplication algorithm: ⟨3×20×24:1068⟩

Algorithm type

X2Y12Z2+XY12Z2+6X3Y8Z3+6XY12Z+5X2Y9Z2+30X3Y6Z3+22X2Y8Z2+5XY9Z2+2X2Y8Z+10XY9Z+36X3Y4Z3+56X2Y6Z2+26XY8Z+10X2Y6Z+6XY6Z2+53X2Y4Z2+58XY6Z+13X2Y4Z+25X2Y3Z2+16XY5Z+3XY4Z2+5X2Y3Z+66X2Y2Z2+123XY4Z+15XY3Z2+6X2Y2Z+115XY3Z+18XY2Z2+158XY2Z+172XYZX2Y12Z2XY12Z26X3Y8Z36XY12Z5X2Y9Z230X3Y6Z322X2Y8Z25XY9Z22X2Y8Z10XY9Z36X3Y4Z356X2Y6Z226XY8Z10X2Y6Z6XY6Z253X2Y4Z258XY6Z13X2Y4Z25X2Y3Z216XY5Z3XY4Z25X2Y3Z66X2Y2Z2123XY4Z15XY3Z26X2Y2Z115XY3Z18XY2Z2158XY2Z172XYZX^2*Y^12*Z^2+X*Y^12*Z^2+6*X^3*Y^8*Z^3+6*X*Y^12*Z+5*X^2*Y^9*Z^2+30*X^3*Y^6*Z^3+22*X^2*Y^8*Z^2+5*X*Y^9*Z^2+2*X^2*Y^8*Z+10*X*Y^9*Z+36*X^3*Y^4*Z^3+56*X^2*Y^6*Z^2+26*X*Y^8*Z+10*X^2*Y^6*Z+6*X*Y^6*Z^2+53*X^2*Y^4*Z^2+58*X*Y^6*Z+13*X^2*Y^4*Z+25*X^2*Y^3*Z^2+16*X*Y^5*Z+3*X*Y^4*Z^2+5*X^2*Y^3*Z+66*X^2*Y^2*Z^2+123*X*Y^4*Z+15*X*Y^3*Z^2+6*X^2*Y^2*Z+115*X*Y^3*Z+18*X*Y^2*Z^2+158*X*Y^2*Z+172*X*Y*Z

Algorithm definition

The algorithm ⟨3×20×24:1068⟩ could be constructed using the following decomposition:

⟨3×20×24:1068⟩ = ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨1×4×4:16⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨1×4×4:16⟩ + ⟨2×4×4:26⟩ + ⟨2×4×4:26⟩ + ⟨1×4×4:16⟩ + ⟨1×4×4:16⟩.

This decomposition is defined by the following equality:

TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_1_7A_1_8A_1_9A_1_10A_1_11A_1_12A_1_13A_1_14A_1_15A_1_16A_1_17A_1_18A_1_19A_1_20A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_2_7A_2_8A_2_9A_2_10A_2_11A_2_12A_2_13A_2_14A_2_15A_2_16A_2_17A_2_18A_2_19A_2_20A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_3_7A_3_8A_3_9A_3_10A_3_11A_3_12A_3_13A_3_14A_3_15A_3_16A_3_17A_3_18A_3_19A_3_20B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_9B_1_10B_1_11B_1_12B_1_13B_1_14B_1_15B_1_16B_1_17B_1_18B_1_19B_1_20B_1_21B_1_22B_1_23B_1_24B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_9B_2_10B_2_11B_2_12B_2_13B_2_14B_2_15B_2_16B_2_17B_2_18B_2_19B_2_20B_2_21B_2_22B_2_23B_2_24B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_9B_3_10B_3_11B_3_12B_3_13B_3_14B_3_15B_3_16B_3_17B_3_18B_3_19B_3_20B_3_21B_3_22B_3_23B_3_24B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_9B_4_10B_4_11B_4_12B_4_13B_4_14B_4_15B_4_16B_4_17B_4_18B_4_19B_4_20B_4_21B_4_22B_4_23B_4_24B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_9B_5_10B_5_11B_5_12B_5_13B_5_14B_5_15B_5_16B_5_17B_5_18B_5_19B_5_20B_5_21B_5_22B_5_23B_5_24B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8B_6_9B_6_10B_6_11B_6_12B_6_13B_6_14B_6_15B_6_16B_6_17B_6_18B_6_19B_6_20B_6_21B_6_22B_6_23B_6_24B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_7_7B_7_8B_7_9B_7_10B_7_11B_7_12B_7_13B_7_14B_7_15B_7_16B_7_17B_7_18B_7_19B_7_20B_7_21B_7_22B_7_23B_7_24B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_8_7B_8_8B_8_9B_8_10B_8_11B_8_12B_8_13B_8_14B_8_15B_8_16B_8_17B_8_18B_8_19B_8_20B_8_21B_8_22B_8_23B_8_24B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_9B_9_10B_9_11B_9_12B_9_13B_9_14B_9_15B_9_16B_9_17B_9_18B_9_19B_9_20B_9_21B_9_22B_9_23B_9_24B_10_1B_10_2B_10_3B_10_4B_10_5B_10_6B_10_7B_10_8B_10_9B_10_10B_10_11B_10_12B_10_13B_10_14B_10_15B_10_16B_10_17B_10_18B_10_19B_10_20B_10_21B_10_22B_10_23B_10_24B_11_1B_11_2B_11_3B_11_4B_11_5B_11_6B_11_7B_11_8B_11_9B_11_10B_11_11B_11_12B_11_13B_11_14B_11_15B_11_16B_11_17B_11_18B_11_19B_11_20B_11_21B_11_22B_11_23B_11_24B_12_1B_12_2B_12_3B_12_4B_12_5B_12_6B_12_7B_12_8B_12_9B_12_10B_12_11B_12_12B_12_13B_12_14B_12_15B_12_16B_12_17B_12_18B_12_19B_12_20B_12_21B_12_22B_12_23B_12_24B_13_1B_13_2B_13_3B_13_4B_13_5B_13_6B_13_7B_13_8B_13_9B_13_10B_13_11B_13_12B_13_13B_13_14B_13_15B_13_16B_13_17B_13_18B_13_19B_13_20B_13_21B_13_22B_13_23B_13_24B_14_1B_14_2B_14_3B_14_4B_14_5B_14_6B_14_7B_14_8B_14_9B_14_10B_14_11B_14_12B_14_13B_14_14B_14_15B_14_16B_14_17B_14_18B_14_19B_14_20B_14_21B_14_22B_14_23B_14_24B_15_1B_15_2B_15_3B_15_4B_15_5B_15_6B_15_7B_15_8B_15_9B_15_10B_15_11B_15_12B_15_13B_15_14B_15_15B_15_16B_15_17B_15_18B_15_19B_15_20B_15_21B_15_22B_15_23B_15_24B_16_1B_16_2B_16_3B_16_4B_16_5B_16_6B_16_7B_16_8B_16_9B_16_10B_16_11B_16_12B_16_13B_16_14B_16_15B_16_16B_16_17B_16_18B_16_19B_16_20B_16_21B_16_22B_16_23B_16_24B_17_1B_17_2B_17_3B_17_4B_17_5B_17_6B_17_7B_17_8B_17_9B_17_10B_17_11B_17_12B_17_13B_17_14B_17_15B_17_16B_17_17B_17_18B_17_19B_17_20B_17_21B_17_22B_17_23B_17_24B_18_1B_18_2B_18_3B_18_4B_18_5B_18_6B_18_7B_18_8B_18_9B_18_10B_18_11B_18_12B_18_13B_18_14B_18_15B_18_16B_18_17B_18_18B_18_19B_18_20B_18_21B_18_22B_18_23B_18_24B_19_1B_19_2B_19_3B_19_4B_19_5B_19_6B_19_7B_19_8B_19_9B_19_10B_19_11B_19_12B_19_13B_19_14B_19_15B_19_16B_19_17B_19_18B_19_19B_19_20B_19_21B_19_22B_19_23B_19_24B_20_1B_20_2B_20_3B_20_4B_20_5B_20_6B_20_7B_20_8B_20_9B_20_10B_20_11B_20_12B_20_13B_20_14B_20_15B_20_16B_20_17B_20_18B_20_19B_20_20B_20_21B_20_22B_20_23B_20_24C_1_1C_1_2C_1_3C_2_1C_2_2C_2_3C_3_1C_3_2C_3_3C_4_1C_4_2C_4_3C_5_1C_5_2C_5_3C_6_1C_6_2C_6_3C_7_1C_7_2C_7_3C_8_1C_8_2C_8_3C_9_1C_9_2C_9_3C_10_1C_10_2C_10_3C_11_1C_11_2C_11_3C_12_1C_12_2C_12_3C_13_1C_13_2C_13_3C_14_1C_14_2C_14_3C_15_1C_15_2C_15_3C_16_1C_16_2C_16_3C_17_1C_17_2C_17_3C_18_1C_18_2C_18_3C_19_1C_19_2C_19_3C_20_1C_20_2C_20_3C_21_1C_21_2C_21_3C_22_1C_22_2C_22_3C_23_1C_23_2C_23_3C_24_1C_24_2C_24_3=TraceMulA_2_1A_2_2A_2_3A_2_4A_3_1A_3_2A_3_3A_3_4-B_5_1+B_1_1+a11+a21+1B_13_1a41B_1_2-B_5_2+a11+a21+1B_13_2a41B_1_3-B_5_3+a11+a21+1B_13_3a41B_1_4-B_5_4+a11+a21+1B_13_4a41B_2_1-B_6_1+a11+a21+1B_14_1a41B_2_2-B_6_2+a11+a21+1B_14_2a41B_2_3-B_6_3+a11+a21+1B_14_3a41B_2_4-B_6_4+a11+a21+1B_14_4a41B_3_1-B_7_1+a11+a21+1B_15_1a41B_3_2-B_7_2+a11+a21+1B_15_2a41B_3_3-B_7_3+a11+a21+1B_15_3a41B_3_4-B_7_4+a11+a21+1B_15_4a41B_4_1-B_8_1+a11+a21+1B_16_1a41B_4_2-B_8_2+a11+a21+1B_16_2a41B_4_3-B_8_3+a11+a21+1B_16_3a41B_4_4-B_8_4+a11+a21+1B_16_4a41C_1_2C_1_1+C_1_3C_2_2C_2_1+C_2_3C_3_2C_3_1+C_3_3C_4_2C_4_1+C_4_3+TraceMulA_1_5A_1_6A_1_7A_1_8B_9_1-a21+a11B_13_1a41-a21+a11+a31B_17_1a51-B_1_5+B_5_5-B_9_5+a21+a11+a31B_17_5a51B_9_2-a21+a11B_13_2a41-a21+a11+a31B_17_2a51-B_1_6+B_5_6-B_9_6+a21+a11+a31B_17_6a51B_9_3-a21+a11B_13_3a41-a21+a11+a31B_17_3a51-B_1_7+B_5_7-B_9_7+a21+a11+a31B_17_7a51B_9_4-a21+a11B_13_4a41-a21+a11+a31B_17_4a51-B_1_8+B_5_8-B_9_8+a21+a11+a31B_17_8a51B_10_1-a21+a11B_14_1a41-a21+a11+a31B_18_1a51-B_2_5+B_6_5-B_10_5+a21+a11+a31B_18_5a51B_10_2-a21+a11B_14_2a41-a21+a11+a31B_18_2a51-B_2_6+B_6_6-B_10_6+a21+a11+a31B_18_6a51B_10_3-a21+a11B_14_3a41-a21+a11+a31B_18_3a51-B_2_7+B_6_7-B_10_7+a21+a11+a31B_18_7a51B_10_4-a21+a11B_14_4a41-a21+a11+a31B_18_4a51-B_2_8+B_6_8-B_10_8+a21+a11+a31B_18_8a51B_1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