Description of fast matrix multiplication algorithm: ⟨5×13×15:675⟩

Algorithm type

10⁢X4⁢Y4⁢Z4+X4⁢Y4⁢Z3+2⁢X2⁢Y7⁢Z2+2⁢X5⁢Y3⁢Z2+3⁢X4⁢Y4⁢Z2+22⁢X3⁢Y4⁢Z3+4⁢X3⁢Y3⁢Z4+2⁢X2⁢Y7⁢Z+X2⁢Y6⁢Z2+2⁢X2⁢Y4⁢Z4+2⁢X⁢Y4⁢Z5+5⁢X5⁢Y2⁢Z2+10⁢X3⁢Y3⁢Z3+X2⁢Y6⁢Z+2⁢X2⁢Y5⁢Z2+X2⁢Y4⁢Z3+10⁢X2⁢Y2⁢Z5+2⁢X⁢Y7⁢Z+2⁢X5⁢Y2⁢Z+4⁢X5⁢Y⁢Z2+2⁢X4⁢Y2⁢Z2+2⁢X3⁢Y4⁢Z+77⁢X2⁢Y4⁢Z2+3⁢X2⁢Y2⁢Z4+16⁢X⁢Y6⁢Z+4⁢X⁢Y4⁢Z3+4⁢X⁢Y2⁢Z5+2⁢X5⁢Y⁢Z+X3⁢Y3⁢Z+3⁢X3⁢Y2⁢Z2+5⁢X2⁢Y4⁢Z+11⁢X2⁢Y3⁢Z2+2⁢X2⁢Y2⁢Z3+3⁢X⁢Y5⁢Z+8⁢X⁢Y4⁢Z2+8⁢X3⁢Y2⁢Z+78⁢X2⁢Y2⁢Z2+44⁢X⁢Y4⁢Z+4⁢X⁢Y3⁢Z2+16⁢X⁢Y2⁢Z3+12⁢X3⁢Y⁢Z+11⁢X2⁢Y2⁢Z+2⁢X2⁢Y⁢Z2+28⁢X⁢Y3⁢Z+21⁢X⁢Y2⁢Z2+12⁢X⁢Y⁢Z3+11⁢X2⁢Y⁢Z+110⁢X⁢Y2⁢Z+18⁢X⁢Y⁢Z2+69⁢X⁢Y⁢Z10X4Y4Z4X4Y4Z32X2Y7Z22X5Y3Z23X4Y4Z222X3Y4Z34X3Y3Z42X2Y7ZX2Y6Z22X2Y4Z42XY4Z55X5Y2Z210X3Y3Z3X2Y6Z2X2Y5Z2X2Y4Z310X2Y2Z52XY7Z2X5Y2Z4X5YZ22X4Y2Z22X3Y4Z77X2Y4Z23X2Y2Z416XY6Z4XY4Z34XY2Z52X5YZX3Y3Z3X3Y2Z25X2Y4Z11X2Y3Z22X2Y2Z33XY5Z8XY4Z28X3Y2Z78X2Y2Z244XY4Z4XY3Z216XY2Z312X3YZ11X2Y2Z2X2YZ228XY3Z21XY2Z212XYZ311X2YZ110XY2Z18XYZ269XYZ10*X^4*Y^4*Z^4+X^4*Y^4*Z^3+2*X^2*Y^7*Z^2+2*X^5*Y^3*Z^2+3*X^4*Y^4*Z^2+22*X^3*Y^4*Z^3+4*X^3*Y^3*Z^4+2*X^2*Y^7*Z+X^2*Y^6*Z^2+2*X^2*Y^4*Z^4+2*X*Y^4*Z^5+5*X^5*Y^2*Z^2+10*X^3*Y^3*Z^3+X^2*Y^6*Z+2*X^2*Y^5*Z^2+X^2*Y^4*Z^3+10*X^2*Y^2*Z^5+2*X*Y^7*Z+2*X^5*Y^2*Z+4*X^5*Y*Z^2+2*X^4*Y^2*Z^2+2*X^3*Y^4*Z+77*X^2*Y^4*Z^2+3*X^2*Y^2*Z^4+16*X*Y^6*Z+4*X*Y^4*Z^3+4*X*Y^2*Z^5+2*X^5*Y*Z+X^3*Y^3*Z+3*X^3*Y^2*Z^2+5*X^2*Y^4*Z+11*X^2*Y^3*Z^2+2*X^2*Y^2*Z^3+3*X*Y^5*Z+8*X*Y^4*Z^2+8*X^3*Y^2*Z+78*X^2*Y^2*Z^2+44*X*Y^4*Z+4*X*Y^3*Z^2+16*X*Y^2*Z^3+12*X^3*Y*Z+11*X^2*Y^2*Z+2*X^2*Y*Z^2+28*X*Y^3*Z+21*X*Y^2*Z^2+12*X*Y*Z^3+11*X^2*Y*Z+110*X*Y^2*Z+18*X*Y*Z^2+69*X*Y*Z

Algorithm definition

The algorithm ⟨5×13×15:675⟩ could be constructed using the following decomposition:

⟨5×13×15:675⟩ = ⟨3×5×5:58⟩ + ⟨3×5×5:58⟩ + ⟨2×4×5:33⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨2×4×5:33⟩ + ⟨3×5×5:58⟩ + ⟨3×4×5:47⟩ + ⟨3×4×5:47⟩ + ⟨3×4×5:47⟩ + ⟨2×5×5:40⟩ + ⟨3×4×5:47⟩ + ⟨2×4×5:33⟩ + ⟨3×4×5:47⟩ + ⟨3×4×5:47⟩.

This decomposition is defined by the following equality:

Trace⁡Mul⁡A_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_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_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_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_4_7A_4_8A_4_9A_4_10A_4_11A_4_12A_4_13A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_5_7A_5_8A_5_9A_5_10A_5_11A_5_12A_5_13B_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_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_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_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_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_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_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_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_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_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_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_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_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_15C_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_5C_9_1C_9_2C_9_3C_9_4C_9_5C_10_1C_10_2C_10_3C_10_4C_10_5C_11_1C_11_2C_11_3C_11_4C_11_5C_12_1C_12_2C_12_3C_12_4C_12_5C_13_1C_13_2C_13_3C_13_4C_13_5C_14_1C_14_2C_14_3C_14_4C_14_5C_15_1C_15_2C_15_3C_15_4C_15_5=Trace⁡Mul⁡A_3_9A_3_10A_3_11A_3_12A_3_13A_4_9A_4_10A_4_11A_4_12A_4_13A_5_9A_5_10A_5_11A_5_12A_5_13B_9_1+B_9_6B_9_2+B_9_7B_9_3+B_9_8B_9_4+B_9_9B_9_5+B_9_10B_4_1+B_10_1+B_10_6B_4_2+B_10_2+B_10_7B_4_3+B_10_3+B_10_8B_4_4+B_10_4+B_10_9B_4_5+B_10_5+B_10_10B_1_1+B_11_1+B_11_6B_1_2+B_11_2+B_11_7B_1_3+B_11_3+B_11_8B_1_4+B_11_4+B_11_9B_1_5+B_11_5+B_11_10B_2_1+B_12_1+B_12_6B_2_2+B_12_2+B_12_7B_2_3+B_12_3+B_12_8B_2_4+B_12_4+B_12_9B_2_5+B_12_5+B_12_10B_3_1+B_13_1+B_13_6B_3_2+B_13_2+B_13_7B_3_3+B_13_3+B_13_8B_3_4+B_13_4+B_13_9B_3_5+B_13_5+B_13_10C_1_3C_1_1+C_1_4C_1_2+C_1_5C_2_3C_2_1+C_2_4C_2_2+C_2_5C_3_3C_3_1+C_3_4C_3_2+C_3_5C_4_3C_4_1+C_4_4C_4_2+C_4_5C_5_3C_5_1+C_5_4C_5_2+C_5_5+Trace⁡Mul⁡-A_3_9-A_3_10-A_3_11-A_3_12-A_3_13-A_4_9A_1_4-A_4_10A_1_1-A_4_11A_1_2-A_4_12A_1_3-A_4_13-A_5_9A_2_4-A_5_10A_2_1-A_5_11A_2_2-A_5_12A_2_3-A_5_13B_9_11B_9_12B_9_13B_9_14B_9_15B_4_1+B_10_11B_4_2+B_10_12B_4_3+B_10_13B_4_4+B_10_14B_4_5+B_10_15B_1_1+B_11_11B_1_2+B_11_12B_1_3+B_11_13B_1_4+B_11_14B_1_5+B_11_15B_2_1+B_12_11B_2_2+B_12_12B_2_3+B_12_13B_2_4+B_12_14B_2_5+B_12_15B_3_1+B_13_11B_3_2+B_13_12B_3_3+B_13_13B_3_4+B_13_14B_3_5+B_13_15-C_11_3C_1_1-C_11_4C_1_2-C_11_5-C_12_3C_2_1-C_12_4C_2_2-C_12_5-C_13_3C_3_1-C_13_4C_3_2-C_13_5-C_14_3C_4_1-C_14_4C_4_2-C_14_5-C_15_3C_5_1-C_15_4C_5_2-C_15_5+Trace⁡Mul⁡A_1_4A_1_1A_1_2A_1_3A_2_4A_2_1A_2_2A_2_3B_4_6-B_4_11-B_10_11B_4_7-B_4_12-B_10_12B_4_8-B_4_13-B_10_13B_4_9-B_4_14-B_10_14-B_4_15+B_4_10-B_10_15B_1_6-B_1_11-B_11_11B_1_7-B_1_12-B_11_12B_1_8-B_1_13-B_11_13B_1_9-B_1_14-B_11_14B_1_10-B_1_15-B_11_15B_2_6-B_2_11-B_12_11B_2_7-B_2_12-B_12_12B_2_8-B_2_13-B_12_13B_2_9-B_2_14-B_12_14B_2_10-B_2_15-B_12_15B_3_6-B_3_11-B_13_11B_3_7-B_3_12-B_13_12B_3_8-B_3_13-B_13_13B_3_9-B_3_14-B_13_14B_3_10-B_3_15-B_13_15-C_11_1-C_11_4-C_11_2-C_11_5-C_12_1-C_12_4-C_12_2-C_12_5-C_13_1-C_13_4-C_13_2-C_13_5-C_14_1-C_14_4-C_14_2-C_14_5-C_15_1-C_15_4-C_15_2-C_15_5+Trace⁡Mul⁡-A_1_9A_1_4-A_1_10A_1_1-A_1_11A_1_2-A_1_12A_1_3-A_1_13-A_2_9A_2_4-A_2_10A_2_1-A_2_11A_2_2-A_2_12A_2_3-A_2_13B_9_11B_9_12B_9_13B_9_14B_9_15B_10_11B_10_12B_10_13B_10_14B_10_15B_11_11B_11_12B_11_13B_11_14B_11_15B_12_11B_12_12B_12_13B_12_14B_12_15B_13_11B_13_12B_13_13B_13_14B_13_15-C_1_1-C_11_1-C_1_2-C_11_2-C_2_1-C_12_1-C_2_2-C_12_2-C_3_1-C_13_1-C_3_2-C_13_2-C_4_1-C_14_1-C_4_2-C_14_2-C_5_1-C_15_1-C_5_2-C_15_2+Trace⁡Mul⁡A_1_9-A_4_9A_1_10-A_4_10A_1_11-A_4_11A_1_12-A_4_12A_1_13-A_4_13A_2_9-A_5_9A_2_10-A_5_10A_2_11-A_5_11A_2_12-A_5_12A_2_13-A_5_13B_9_1-B_9_11B_9_2-B_9_12B_9_3-B_9_13B_9_4-B_9_14B_9_5-B_9_15B_5_1+B_10_1-B_10_11B_5_2+B_10_2-B_10_12B_5_3+B_10_3-B_10_13B_5_4+B_10_4-B_10_14B_5_5+B_10_5-B_10_15B_6_1+B_11_1-B_11_11B_6_2+B_11_2-B_11_12B_6_3+B_11_3-B_11_13B_6_4+B_11_4-B_11_14B_6_5+B_11_5-B_11_15B_7_1+B_12_1-B_12_11B_7_2+B_12_2-B_12_12B_7_3+B_12_3-B_12_13B_7_4+B_12_4-B_12_14B_7_5+B_12_5-B_12_15B_8_1+B_13_1-B_13_11B_8_2+B_13_2-B_13_12B_8_3+B_13_3-B_13_13B_8_4+B_13_4-B_13_14B_8_5+B_13_5-B_13_15C_1_1C_1_2C_2_1C_2_2C_3_1C_3_2C_4_1C_4_2C_5_1C_5_2+Trace⁡Mul⁡A_1_5A_1_6A_1_7A_1_8A_2_5A_2_6A_2_7A_2_8B_5_6+B_10_6-B_5_11B_5_7+B_10_7-B_5_12B_5_8+B_10_8-B_5_13B_5_9+B_10_9-B_5_14B_5_10+B_10_10-B_5_15B_6_6+B_11_6-B_6_11B_6_7+B_11_7-B_6_12B_6_8+B_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1_9B_6_14B_6_10B_11_10B_6_15B_7_6B_12_6B_7_11B_7_7B_12_7B_7_12B_7_8B_12_8B_7_13B_7_9B_12_9B_7_14B_7_10B_12_10B_7_15B_8_6B_13_6B_8_11B_8_7B_13_7B_8_12B_8_8B_13_8B_8_13B_8_9B_13_9B_8_14B_8_10B_13_10B_8_15C_6_1C_6_2C_7_1C_7_2C_8_1C_8_2C_9_1C_9_2C_10_1C_10_2TraceMulA_3_9A_3_10A_3_11A_3_12A_3_13A_1_9A_4_9A_1_10A_1_5A_4_10A_1_6A_1_11A_4_11A_1_7A_1_12A_4_12A_1_8A_1_13A_4_13A_2_9A_5_9A_2_10A_2_5A_5_10A_2_6A_2_11A_5_11A_2_7A_2_12A_5_12A_2_8A_2_13A_5_13B_9_6B_9_7B_9_8B_9_9B_9_10B_5_1B_10_6B_5_2B_10_7B_5_3B_10_8B_5_4B_10_9B_5_5B_10_10B_6_1B_11_6B_6_2B_11_7B_6_3B_11_8B_6_4B_11_9B_6_5B_11_10B_7_1B_12_6B_7_2B_12_7B_7_3B_12_8B_7_4B_12_9B_7_5B_12_10B_8_1B_13_6B_8_2B_13_7B_8_3B_13_8B_8_4B_13_9B_8_5B_13_10C_1_3C_6_3C_1_1C_1_4C_6_4C_1_2C_1_5C_6_5C_2_3C_7_3C_2_1C_2_4C_7_4C_2_2C_2_5C_7_5C_3_3C_8_3C_3_1C_3_4C_8_4C_3_2C_3_5C_8_5C_9_3C_4_3C_4_1C_4_4C_9_4C_4_2C_4_5C_9_5C_5_3C_10_3C_5_1C_5_4C_10_4C_5_2C_5_5C_10_5TraceMulA_3_4A_3_5A_3_1A_3_6A_3_2A_3_7A_3_3A_3_8A_1_4A_4_4A_4_5A_1_1A_4_1A_4_6A_1_2A_4_2A_4_7A_1_3A_4_3A_4_8A_2_4A_5_4A_5_5A_2_1A_5_1A_5_6A_2_2A_5_2A_5_7A_2_3A_5_3A_5_8B_4_6B_5_11B_4_7B_5_12B_4_8B_5_13B_4_9B_5_14B_4_10B_5_15B_1_6B_6_11B_1_7B_6_12B_1_8B_6_13B_1_9B_6_14B_1_10B_6_15B_2_6B_7_11B_2_7B_7_12B_2_8B_7_13B_2_9B_7_14B_2_10B_7_15B_3_6B_8_11B_3_7B_8_12B_3_8B_8_13B_3_9B_8_14B_3_10B_8_15C_11_3C_6_1C_11_1C_11_4C_6_2C_11_2C_11_5C_12_3C_7_1C_12_1C_12_4C_7_2C_12_2C_12_5C_13_3C_8_1C_13_1C_13_4C_8_2C_13_2C_13_5C_14_3C_9_1C_14_1C_14_4C_9_2C_14_2C_14_5C_15_3C_10_1C_15_1C_15_4C_10_2C_15_2C_15_5TraceMulA_3_4A_3_5A_3_1A_3_6A_3_2A_3_7A_3_8A_3_3A_4_4A_4_5A_4_1A_4_6A_4_2A_4_7A_4_3A_4_8A_5_4A_5_5A_5_1A_5_6A_5_2A_5_7A_5_3A_5_8B_4_6B_4_7B_4_8B_4_9B_4_10B_1_6B_1_7B_1_8B_1_9B_1_10B_2_6B_2_7B_2_8B_2_9B_2_10B_3_6B_3_7B_3_8B_3_9B_3_10C_6_3C_11_3C_6_1C_11_1C_6_4C_11_4C_6_2C_11_2C_6_5C_11_5C_7_3C_12_3C_7_1C_12_1C_7_4C_12_4C_7_2C_12_2C_7_5C_12_5C_8_3C_13_3C_8_1C_13_1C_8_4C_13_4C_8_2C_13_2C_8_5C_13_5C_9_3C_14_3C_9_1C_14_1C_9_4C_14_4C_9_2C_14_2C_9_5C_14_5C_10_3C_15_3C_10_1C_15_1C_10_4C_15_4C_10_2C_15_2C_10_5C_15_5TraceMulA_3_5A_3_10A_3_6A_3_11A_3_7A_3_12A_3_8A_3_13A_1_5A_4_5A_1_10A_4_10A_1_6A_4_6A_1_11A_4_11A_1_7A_4_7A_1_12A_4_12A_1_8A_4_8A_1_13A_4_13A_2_5A_5_5A_2_10A_5_10A_2_6A_5_6A_2_11A_5_11A_2_7A_5_7A_2_12A_5_12A_2_8A_5_8A_2_13A_5_13B_5_1B_5_2B_5_3B_5_4B_5_5B_6_1B_6_2B_6_3B_6_4B_6_5B_7_1B_7_2B_7_3B_7_4B_7_5B_8_1B_8_2B_8_3B_8_4B_8_5C_1_3C_6_3C_1_4C_6_4C_1_5C_6_5C_2_3C_7_3C_2_4C_7_4C_2_5C_7_5C_3_3C_8_3C_3_4C_8_4C_3_5C_8_5C_4_3C_9_3C_4_4C_9_4C_4_5C_9_5C_5_3C_10_3C_5_4C_10_4C_5_5C_10_5TraceMulA_1_9A_1_10A_1_5A_1_6A_1_11A_1_7A_1_12A_1_8A_1_13A_2_9A_2_10A_2_5A_2_6A_2_11A_2_7A_2_12A_2_8A_2_13B_9_6B_9_7B_9_8B_9_9B_9_10B_10_6B_10_7B_10_8B_10_9B_10_10B_11_6B_11_7B_11_8B_11_9B_11_10B_12_6B_12_7B_12_8B_12_9B_12_10B_13_6B_13_7B_13_8B_13_9B_13_10C_1_1C_6_1C_1_4C_6_4C_1_2C_6_2C_1_5C_6_5C_2_1C_7_1C_2_4C_7_4C_2_2C_7_2C_2_5C_7_5C_3_1C_8_1C_3_4C_8_4C_3_2C_8_2C_3_5C_8_5C_9_1C_4_1C_4_4C_9_4C_9_2C_4_2C_4_5C_9_5C_5_1C_10_1C_5_4C_10_4C_5_2C_10_2C_5_5C_10_5TraceMulA_3_5A_3_6A_3_7A_3_8A_4_5A_4_6A_4_7A_4_8A_5_5A_5_6A_5_7A_5_8B_5_1B_4_6B_5_6B_5_2B_4_7B_5_7B_5_3B_4_8B_5_8B_5_4B_4_9B_5_9B_5_5B_4_10B_5_10B_6_1B_1_6B_6_6B_6_2B_1_7B_6_7B_6_3B_1_8B_6_8B_6_4B_1_9B_6_9B_6_5B_1_10B_6_10B_7_1B_2_6B_7_6B_7_2B_2_7B_7_7B_7_3B_2_8B_7_8B_7_4B_2_9B_7_9B_7_5B_2_10B_7_10B_8_1B_3_6B_8_6B_8_2B_3_7B_8_7B_8_3B_3_8B_8_8B_8_4B_3_9B_8_9B_8_5B_3_10B_8_10C_6_3C_6_4C_6_5C_7_3C_7_4C_7_5C_8_3C_8_4C_8_5C_9_3C_9_4C_9_5C_10_3C_10_4C_10_5TraceMulA_1_4A_4_4A_1_5A_4_5A_1_1A_4_1A_1_6A_4_6A_1_2A_4_2A_1_7A_4_7A_1_3A_4_3A_1_8A_4_8A_2_4A_5_4A_2_5A_5_5A_2_1A_5_1A_2_6A_5_6A_2_2A_5_2A_2_7A_5_7A_2_3A_5_3A_2_8A_5_8B_5_11B_5_12B_5_13B_5_14B_5_15B_6_11B_6_12B_6_13B_6_14B_6_15B_7_11B_7_12B_7_13B_7_14B_7_15B_8_11B_8_12B_8_13B_8_14B_8_15C_6_1C_11_1C_6_2C_11_2C_7_1C_12_1C_7_2C_12_2C_8_1C_13_1C_8_2C_13_2C_9_1C_14_1C_9_2C_14_2C_10_1C_15_1C_10_2C_15_2TraceMulA_3_4A_3_10A_3_1A_3_11A_3_2A_3_12A_3_3A_3_13A_4_4A_4_10A_4_1A_4_11A_4_2A_4_12A_4_3A_4_13A_5_4A_5_10A_5_1A_5_11A_5_2A_5_12A_5_3A_5_13B_4_1B_4_2B_4_3B_4_4B_4_5B_1_1B_1_2B_1_3B_1_4B_1_5B_2_1B_2_2B_2_3B_2_4B_2_5B_3_1B_3_2B_3_3B_3_4B_3_5C_1_3C_11_3C_1_4C_11_4C_1_5C_11_5C_2_3C_12_3C_2_4C_12_4C_2_5C_12_5C_3_3C_13_3C_3_4C_13_4C_3_5C_13_5C_4_3C_14_3C_4_4C_14_4C_4_5C_14_5C_5_3C_15_3C_5_4C_15_4C_5_5C_15_5TraceMulA_3_4A_3_1A_3_2A_3_3A_1_4A_4_4A_1_1A_4_1A_1_2A_4_2A_1_3A_4_3A_2_4A_5_4A_2_1A_5_1A_2_2A_5_2A_2_3A_5_3B_4_1B_4_11B_5_11B_4_2B_4_12B_5_12B_4_3B_4_13B_5_13B_4_4B_4_14B_5_14B_4_5B_4_15B_5_15B_1_1B_1_11B_6_11B_1_2B_1_12B_6_12B_1_3B_1_13B_6_13B_1_4B_1_14B_6_14B_1_5B_1_15B_6_15B_2_1B_2_11B_7_11B_2_2B_2_12B_7_12B_2_3B_2_13B_7_13B_2_4B_2_14B_7_14B_2_5B_2_15B_7_15B_3_1B_3_11B_8_11B_3_2B_3_12B_8_12B_3_3B_3_13B_8_13B_3_4B_3_14B_8_14B_3_5B_3_15B_8_15C_11_3C_11_4C_11_5C_12_3C_12_4C_12_5C_13_3C_13_4C_13_5C_14_3C_14_4C_14_5C_15_3C_15_4C_15_5Trace(Mul(Matrix(5, 13, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6,A_1_7,A_1_8,A_1_9,A_1_10,A_1_11,A_1_12,A_1_13],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8,A_2_9,A_2_10,A_2_11,A_2_12,A_2_13],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6,A_3_7,A_3_8,A_3_9,A_3_10,A_3_11,A_3_12,A_3_13],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6,A_4_7,A_4_8,A_4_9,A_4_10,A_4_11,A_4_12,A_4_13],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6,A_5_7,A_5_8,A_5_9,A_5_10,A_5_11,A_5_12,A_5_13]]),Matrix(13, 15, [[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_1_9,B_1_10,B_1_11,B_1_12,B_1_13,B_1_14,B_1_15],[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_2_9,B_2_10,B_2_11,B_2_12,B_2_13,B_2_14,B_2_15],[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_3_9,B_3_10,B_3_11,B_3_12,B_3_13,B_3_14,B_3_15],[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_4_9,B_4_10,B_4_11,B_4_12,B_4_13,B_4_14,B_4_15],[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_5_9,B_5_10,B_5_11,B_5_12,B_5_13,B_5_14,B_5_15],[B_6_1,B_6_2,B_6_3,B_6_4,B_6_5,B_6_6,B_6_7,B_6_8,B_6_9,B_6_10,B_6_11,B_6_12,B_6_13,B_6_14,B_6_15],[B_7_1,B_7_2,B_7_3,B_7_4,B_7_5,B_7_6,B_7_7,B_7_8,B_7_9,B_7_10,B_7_11,B_7_12,B_7_13,B_7_14,B_7_15],[B_8_1,B_8_2,B_8_3,B_8_4,B_8_5,B_8_6,B_8_7,B_8_8,B_8_9,B_8_10,B_8_11,B_8_12,B_8_13,B_8_14,B_8_15],[B_9_1,B_9_2,B_9_3,B_9_4,B_9_5,B_9_6,B_9_7,B_9_8,B_9_9,B_9_10,B_9_11,B_9_12,B_9_13,B_9_14,B_9_15],[B_10_1,B_10_2,B_10_3,B_10_4,B_10_5,B_10_6,B_10_7,B_10_8,B_10_9,B_10_10,B_10_11,B_10_12,B_10_13,B_10_14,B_10_15],[B_11_1,B_11_2,B_11_3,B_11_4,B_11_5,B_11_6,B_11_7,B_11_8,B_11_9,B_11_10,B_11_11,B_11_12,B_11_13,B_11_14,B_11_15],[B_12_1,B_12_2,B_12_3,B_12_4,B_12_5,B_12_6,B_12_7,B_12_8,B_12_9,B_12_10,B_12_11,B_12_12,B_12_13,B_12_14,B_12_15],[B_13_1,B_13_2,B_13_3,B_13_4,B_13_5,B_13_6,B_13_7,B_13_8,B_13_9,B_13_10,B_13_11,B_13_12,B_13_13,B_13_14,B_13_15]]),Matrix(15, 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],[C_9_1,C_9_2,C_9_3,C_9_4,C_9_5],[C_10_1,C_10_2,C_10_3,C_10_4,C_10_5],[C_11_1,C_11_2,C_11_3,C_11_4,C_11_5],[C_12_1,C_12_2,C_12_3,C_12_4,C_12_5],[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5],[C_14_1,C_14_2,C_14_3,C_14_4,C_14_5],[C_15_1,C_15_2,C_15_3,C_15_4,C_15_5]]))) = Trace(Mul(Matrix(3, 5, [[A_3_9,A_3_10,A_3_11,A_3_12,A_3_13],[A_4_9,A_4_10,A_4_11,A_4_12,A_4_13],[A_5_9,A_5_10,A_5_11,A_5_12,A_5_13]]),Matrix(5, 5, [[B_9_1+B_9_6,B_9_2+B_9_7,B_9_3+B_9_8,B_9_4+B_9_9,B_9_5+B_9_10],[B_4_1+B_10_1+B_10_6,B_4_2+B_10_2+B_10_7,B_4_3+B_10_3+B_10_8,B_4_4+B_10_4+B_10_9,B_4_5+B_10_5+B_10_10],[B_1_1+B_11_1+B_11_6,B_1_2+B_11_2+B_11_7,B_1_3+B_11_3+B_11_8,B_1_4+B_11_4+B_11_9,B_1_5+B_11_5+B_11_10],[B_2_1+B_12_1+B_12_6,B_2_2+B_12_2+B_12_7,B_2_3+B_12_3+B_12_8,B_2_4+B_12_4+B_12_9,B_2_5+B_12_5+B_12_10],[B_3_1+B_13_1+B_13_6,B_3_2+B_13_2+B_13_7,B_3_3+B_13_3+B_13_8,B_3_4+B_13_4+B_13_9,B_3_5+B_13_5+B_13_10]]),Matrix(5, 3, [[C_1_3,C_1_1+C_1_4,C_1_2+C_1_5],[C_2_3,C_2_1+C_2_4,C_2_2+C_2_5],[C_3_3,C_3_1+C_3_4,C_3_2+C_3_5],[C_4_3,C_4_1+C_4_4,C_4_2+C_4_5],[C_5_3,C_5_1+C_5_4,C_5_2+C_5_5]])))+Trace(Mul(Matrix(3, 5, [[-A_3_9,-A_3_10,-A_3_11,-A_3_12,-A_3_13],[-A_4_9,A_1_4-A_4_10,A_1_1-A_4_11,A_1_2-A_4_12,A_1_3-A_4_13],[-A_5_9,A_2_4-A_5_10,A_2_1-A_5_11,A_2_2-A_5_12,A_2_3-A_5_13]]),Matrix(5, 5, [[B_9_11,B_9_12,B_9_13,B_9_14,B_9_15],[B_4_1+B_10_11,B_4_2+B_10_12,B_4_3+B_10_13,B_4_4+B_10_14,B_4_5+B_10_15],[B_1_1+B_11_11,B_1_2+B_11_12,B_1_3+B_11_13,B_1_4+B_11_14,B_1_5+B_11_15],[B_2_1+B_12_11,B_2_2+B_12_12,B_2_3+B_12_13,B_2_4+B_12_14,B_2_5+B_12_15],[B_3_1+B_13_11,B_3_2+B_13_12,B_3_3+B_13_13,B_3_4+B_13_14,B_3_5+B_13_15]]),Matrix(5, 3, [[-C_11_3,C_1_1-C_11_4,C_1_2-C_11_5],[-C_12_3,C_2_1-C_12_4,C_2_2-C_12_5],[-C_13_3,C_3_1-C_13_4,C_3_2-C_13_5],[-C_14_3,C_4_1-C_14_4,C_4_2-C_14_5],[-C_15_3,C_5_1-C_15_4,C_5_2-C_15_5]])))+Trace(Mul(Matrix(2, 4, [[A_1_4,A_1_1,A_1_2,A_1_3],[A_2_4,A_2_1,A_2_2,A_2_3]]),Matrix(4, 5, [[B_4_6-B_4_11-B_10_11,B_4_7-B_4_12-B_10_12,B_4_8-B_4_13-B_10_13,B_4_9-B_4_14-B_10_14,-B_4_15+B_4_10-B_10_15],[B_1_6-B_1_11-B_11_11,B_1_7-B_1_12-B_11_12,B_1_8-B_1_13-B_11_13,B_1_9-B_1_14-B_11_14,B_1_10-B_1_15-B_11_15],[B_2_6-B_2_11-B_12_11,B_2_7-B_2_12-B_12_12,B_2_8-B_2_13-B_12_13,B_2_9-B_2_14-B_12_14,B_2_10-B_2_15-B_12_15],[B_3_6-B_3_11-B_13_11,B_3_7-B_3_12-B_13_12,B_3_8-B_3_13-B_13_13,B_3_9-B_3_14-B_13_14,B_3_10-B_3_15-B_13_15]]),Matrix(5, 2, [[-C_11_1-C_11_4,-C_11_2-C_11_5],[-C_12_1-C_12_4,-C_12_2-C_12_5],[-C_13_1-C_13_4,-C_13_2-C_13_5],[-C_14_1-C_14_4,-C_14_2-C_14_5],[-C_15_1-C_15_4,-C_15_2-C_15_5]])))+Trace(Mul(Matrix(2, 5, [[-A_1_9,A_1_4-A_1_10,A_1_1-A_1_11,A_1_2-A_1_12,A_1_3-A_1_13],[-A_2_9,A_2_4-A_2_10,A_2_1-A_2_11,A_2_2-A_2_12,A_2_3-A_2_13]]),Matrix(5, 5, [[B_9_11,B_9_12,B_9_13,B_9_14,B_9_15],[B_10_11,B_10_12,B_10_13,B_10_14,B_10_15],[B_11_11,B_11_12,B_11_13,B_11_14,B_11_15],[B_12_11,B_12_12,B_12_13,B_12_14,B_12_15],[B_13_11,B_13_12,B_13_13,B_13_14,B_13_15]]),Matrix(5, 2, [[-C_1_1-C_11_1,-C_1_2-C_11_2],[-C_2_1-C_12_1,-C_2_2-C_12_2],[-C_3_1-C_13_1,-C_3_2-C_13_2],[-C_4_1-C_14_1,-C_4_2-C_14_2],[-C_5_1-C_15_1,-C_5_2-C_15_2]])))+Trace(Mul(Matrix(2, 5, [[A_1_9-A_4_9,A_1_10-A_4_10,A_1_11-A_4_11,A_1_12-A_4_12,A_1_13-A_4_13],[A_2_9-A_5_9,A_2_10-A_5_10,A_2_11-A_5_11,A_2_12-A_5_12,A_2_13-A_5_13]]),Matrix(5, 5, [[B_9_1-B_9_11,B_9_2-B_9_12,B_9_3-B_9_13,B_9_4-B_9_14,B_9_5-B_9_15],[B_5_1+B_10_1-B_10_11,B_5_2+B_10_2-B_10_12,B_5_3+B_10_3-B_10_13,B_5_4+B_10_4-B_10_14,B_5_5+B_10_5-B_10_15],[B_6_1+B_11_1-B_11_11,B_6_2+B_11_2-B_11_12,B_6_3+B_11_3-B_11_13,B_6_4+B_11_4-B_11_14,B_6_5+B_11_5-B_11_15],[B_7_1+B_12_1-B_12_11,B_7_2+B_12_2-B_12_12,B_7_3+B_12_3-B_12_13,B_7_4+B_12_4-B_12_14,B_7_5+B_12_5-B_12_15],[B_8_1+B_13_1-B_13_11,B_8_2+B_13_2-B_13_12,B_8_3+B_13_3-B_13_13,B_8_4+B_13_4-B_13_14,B_8_5+B_13_5-B_13_15]]),Matrix(5, 2, [[C_1_1,C_1_2],[C_2_1,C_2_2],[C_3_1,C_3_2],[C_4_1,C_4_2],[C_5_1,C_5_2]])))+Trace(Mul(Matrix(2, 4, [[A_1_5,A_1_6,A_1_7,A_1_8],[A_2_5,A_2_6,A_2_7,A_2_8]]),Matrix(4, 5, [[B_5_6+B_10_6-B_5_11,B_5_7+B_10_7-B_5_12,B_5_8+B_10_8-B_5_13,B_5_9+B_10_9-B_5_14,B_5_10+B_10_10-B_5_15],[B_6_6+B_11_6-B_6_11,B_6_7+B_11_7-B_6_12,B_6_8+B_11_8-B_6_13,B_6_9+B_11_9-B_6_14,B_6_10+B_11_10-B_6_15],[B_7_6+B_12_6-B_7_11,B_7_7+B_12_7-B_7_12,B_7_8+B_12_8-B_7_13,B_7_9+B_12_9-B_7_14,B_7_10+B_12_10-B_7_15],[B_8_6+B_13_6-B_8_11,B_8_7+B_13_7-B_8_12,B_8_8+B_13_8-B_8_13,B_8_9+B_13_9-B_8_14,B_8_10+B_13_10-B_8_15]]),Matrix(5, 2, [[C_6_1,C_6_2],[C_7_1,C_7_2],[C_8_1,C_8_2],[C_9_1,C_9_2],[C_10_1,C_10_2]])))+Trace(Mul(Matrix(3, 5, [[A_3_9,A_3_10,A_3_11,A_3_12,A_3_13],[-A_1_9+A_4_9,-A_1_10+A_1_5+A_4_10,A_1_6-A_1_11+A_4_11,A_1_7-A_1_12+A_4_12,A_1_8-A_1_13+A_4_13],[-A_2_9+A_5_9,-A_2_10+A_2_5+A_5_10,A_2_6-A_2_11+A_5_11,A_2_7-A_2_12+A_5_12,A_2_8-A_2_13+A_5_13]]),Matrix(5, 5, [[-B_9_6,-B_9_7,-B_9_8,-B_9_9,-B_9_10],[B_5_1-B_10_6,B_5_2-B_10_7,B_5_3-B_10_8,B_5_4-B_10_9,B_5_5-B_10_10],[B_6_1-B_11_6,B_6_2-B_11_7,B_6_3-B_11_8,B_6_4-B_11_9,B_6_5-B_11_10],[B_7_1-B_12_6,B_7_2-B_12_7,B_7_3-B_12_8,B_7_4-B_12_9,B_7_5-B_12_10],[B_8_1-B_13_6,B_8_2-B_13_7,B_8_3-B_13_8,B_8_4-B_13_9,B_8_5-B_13_10]]),Matrix(5, 3, [[C_1_3-C_6_3,C_1_1+C_1_4-C_6_4,C_1_2+C_1_5-C_6_5],[C_2_3-C_7_3,C_2_1+C_2_4-C_7_4,C_2_2+C_2_5-C_7_5],[C_3_3-C_8_3,C_3_1+C_3_4-C_8_4,C_3_2+C_3_5-C_8_5],[-C_9_3+C_4_3,C_4_1+C_4_4-C_9_4,C_4_2+C_4_5-C_9_5],[C_5_3-C_10_3,C_5_1+C_5_4-C_10_4,C_5_2+C_5_5-C_10_5]])))+Trace(Mul(Matrix(3, 4, [[-A_3_4+A_3_5,-A_3_1+A_3_6,-A_3_2+A_3_7,-A_3_3+A_3_8],[A_1_4-A_4_4+A_4_5,A_1_1-A_4_1+A_4_6,A_1_2-A_4_2+A_4_7,A_1_3-A_4_3+A_4_8],[A_2_4-A_5_4+A_5_5,A_2_1-A_5_1+A_5_6,A_2_2-A_5_2+A_5_7,A_2_3-A_5_3+A_5_8]]),Matrix(4, 5, [[B_4_6+B_5_11,B_4_7+B_5_12,B_4_8+B_5_13,B_4_9+B_5_14,B_4_10+B_5_15],[B_1_6+B_6_11,B_1_7+B_6_12,B_1_8+B_6_13,B_1_9+B_6_14,B_1_10+B_6_15],[B_2_6+B_7_11,B_2_7+B_7_12,B_2_8+B_7_13,B_2_9+B_7_14,B_2_10+B_7_15],[B_3_6+B_8_11,B_3_7+B_8_12,B_3_8+B_8_13,B_3_9+B_8_14,B_3_10+B_8_15]]),Matrix(5, 3, [[C_11_3,C_6_1+C_11_1+C_11_4,C_6_2+C_11_2+C_11_5],[C_12_3,C_7_1+C_12_1+C_12_4,C_7_2+C_12_2+C_12_5],[C_13_3,C_8_1+C_13_1+C_13_4,C_8_2+C_13_2+C_13_5],[C_14_3,C_9_1+C_14_1+C_14_4,C_9_2+C_14_2+C_14_5],[C_15_3,C_10_1+C_15_1+C_15_4,C_10_2+C_15_2+C_15_5]])))+Trace(Mul(Matrix(3, 4, [[A_3_4-A_3_5,A_3_1-A_3_6,A_3_2-A_3_7,-A_3_8+A_3_3],[A_4_4-A_4_5,A_4_1-A_4_6,A_4_2-A_4_7,A_4_3-A_4_8],[A_5_4-A_5_5,A_5_1-A_5_6,A_5_2-A_5_7,A_5_3-A_5_8]]),Matrix(4, 5, [[B_4_6,B_4_7,B_4_8,B_4_9,B_4_10],[B_1_6,B_1_7,B_1_8,B_1_9,B_1_10],[B_2_6,B_2_7,B_2_8,B_2_9,B_2_10],[B_3_6,B_3_7,B_3_8,B_3_9,B_3_10]]),Matrix(5, 3, [[C_6_3+C_11_3,C_6_1+C_11_1+C_6_4+C_11_4,C_6_2+C_11_2+C_6_5+C_11_5],[C_7_3+C_12_3,C_7_1+C_12_1+C_7_4+C_12_4,C_7_2+C_12_2+C_7_5+C_12_5],[C_8_3+C_13_3,C_8_1+C_13_1+C_8_4+C_13_4,C_8_2+C_13_2+C_8_5+C_13_5],[C_9_3+C_14_3,C_9_1+C_14_1+C_9_4+C_14_4,C_9_2+C_14_2+C_9_5+C_14_5],[C_10_3+C_15_3,C_10_1+C_15_1+C_10_4+C_15_4,C_10_2+C_15_2+C_10_5+C_15_5]])))+Trace(Mul(Matrix(3, 4, [[-A_3_5+A_3_10,-A_3_6+A_3_11,-A_3_7+A_3_12,-A_3_8+A_3_13],[A_1_5-A_4_5-A_1_10+A_4_10,A_1_6-A_4_6-A_1_11+A_4_11,A_1_7-A_4_7-A_1_12+A_4_12,A_1_8-A_4_8-A_1_13+A_4_13],[A_2_5-A_5_5-A_2_10+A_5_10,A_2_6-A_5_6-A_2_11+A_5_11,A_2_7-A_5_7-A_2_12+A_5_12,A_2_8-A_5_8-A_2_13+A_5_13]]),Matrix(4, 5, [[B_5_1,B_5_2,B_5_3,B_5_4,B_5_5],[B_6_1,B_6_2,B_6_3,B_6_4,B_6_5],[B_7_1,B_7_2,B_7_3,B_7_4,B_7_5],[B_8_1,B_8_2,B_8_3,B_8_4,B_8_5]]),Matrix(5, 3, [[-C_1_3+C_6_3,-C_1_4+C_6_4,-C_1_5+C_6_5],[-C_2_3+C_7_3,-C_2_4+C_7_4,-C_2_5+C_7_5],[-C_3_3+C_8_3,-C_3_4+C_8_4,-C_3_5+C_8_5],[-C_4_3+C_9_3,-C_4_4+C_9_4,-C_4_5+C_9_5],[-C_5_3+C_10_3,-C_5_4+C_10_4,-C_5_5+C_10_5]])))+Trace(Mul(Matrix(2, 5, [[-A_1_9,-A_1_10+A_1_5,A_1_6-A_1_11,A_1_7-A_1_12,A_1_8-A_1_13],[-A_2_9,-A_2_10+A_2_5,A_2_6-A_2_11,A_2_7-A_2_12,A_2_8-A_2_13]]),Matrix(5, 5, [[B_9_6,B_9_7,B_9_8,B_9_9,B_9_10],[B_10_6,B_10_7,B_10_8,B_10_9,B_10_10],[B_11_6,B_11_7,B_11_8,B_11_9,B_11_10],[B_12_6,B_12_7,B_12_8,B_12_9,B_12_10],[B_13_6,B_13_7,B_13_8,B_13_9,B_13_10]]),Matrix(5, 2, [[C_1_1-C_6_1+C_1_4-C_6_4,C_1_2-C_6_2+C_1_5-C_6_5],[C_2_1-C_7_1+C_2_4-C_7_4,C_2_2-C_7_2+C_2_5-C_7_5],[C_3_1-C_8_1+C_3_4-C_8_4,C_3_2-C_8_2+C_3_5-C_8_5],[-C_9_1+C_4_1+C_4_4-C_9_4,-C_9_2+C_4_2+C_4_5-C_9_5],[C_5_1-C_10_1+C_5_4-C_10_4,C_5_2-C_10_2+C_5_5-C_10_5]])))+Trace(Mul(Matrix(3, 4, [[A_3_5,A_3_6,A_3_7,A_3_8],[A_4_5,A_4_6,A_4_7,A_4_8],[A_5_5,A_5_6,A_5_7,A_5_8]]),Matrix(4, 5, [[B_5_1+B_4_6+B_5_6,B_5_2+B_4_7+B_5_7,B_5_3+B_4_8+B_5_8,B_5_4+B_4_9+B_5_9,B_5_5+B_4_10+B_5_10],[B_6_1+B_1_6+B_6_6,B_6_2+B_1_7+B_6_7,B_6_3+B_1_8+B_6_8,B_6_4+B_1_9+B_6_9,B_6_5+B_1_10+B_6_10],[B_7_1+B_2_6+B_7_6,B_7_2+B_2_7+B_7_7,B_7_3+B_2_8+B_7_8,B_7_4+B_2_9+B_7_9,B_7_5+B_2_10+B_7_10],[B_8_1+B_3_6+B_8_6,B_8_2+B_3_7+B_8_7,B_8_3+B_3_8+B_8_8,B_8_4+B_3_9+B_8_9,B_8_5+B_3_10+B_8_10]]),Matrix(5, 3, [[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],[C_9_3,C_9_4,C_9_5],[C_10_3,C_10_4,C_10_5]])))+Trace(Mul(Matrix(2, 4, [[A_1_4-A_4_4-A_1_5+A_4_5,A_1_1-A_4_1-A_1_6+A_4_6,A_1_2-A_4_2-A_1_7+A_4_7,A_1_3-A_4_3-A_1_8+A_4_8],[A_2_4-A_5_4-A_2_5+A_5_5,A_2_1-A_5_1-A_2_6+A_5_6,A_2_2-A_5_2-A_2_7+A_5_7,A_2_3-A_5_3-A_2_8+A_5_8]]),Matrix(4, 5, [[B_5_11,B_5_12,B_5_13,B_5_14,B_5_15],[B_6_11,B_6_12,B_6_13,B_6_14,B_6_15],[B_7_11,B_7_12,B_7_13,B_7_14,B_7_15],[B_8_11,B_8_12,B_8_13,B_8_14,B_8_15]]),Matrix(5, 2, [[-C_6_1-C_11_1,-C_6_2-C_11_2],[-C_7_1-C_12_1,-C_7_2-C_12_2],[-C_8_1-C_13_1,-C_8_2-C_13_2],[-C_9_1-C_14_1,-C_9_2-C_14_2],[-C_10_1-C_15_1,-C_10_2-C_15_2]])))+Trace(Mul(Matrix(3, 4, [[A_3_4-A_3_10,A_3_1-A_3_11,A_3_2-A_3_12,A_3_3-A_3_13],[A_4_4-A_4_10,A_4_1-A_4_11,A_4_2-A_4_12,A_4_3-A_4_13],[A_5_4-A_5_10,A_5_1-A_5_11,A_5_2-A_5_12,A_5_3-A_5_13]]),Matrix(4, 5, [[B_4_1,B_4_2,B_4_3,B_4_4,B_4_5],[B_1_1,B_1_2,B_1_3,B_1_4,B_1_5],[B_2_1,B_2_2,B_2_3,B_2_4,B_2_5],[B_3_1,B_3_2,B_3_3,B_3_4,B_3_5]]),Matrix(5, 3, [[C_1_3+C_11_3,C_1_4+C_11_4,C_1_5+C_11_5],[C_2_3+C_12_3,C_2_4+C_12_4,C_2_5+C_12_5],[C_3_3+C_13_3,C_3_4+C_13_4,C_3_5+C_13_5],[C_4_3+C_14_3,C_4_4+C_14_4,C_4_5+C_14_5],[C_5_3+C_15_3,C_5_4+C_15_4,C_5_5+C_15_5]])))+Trace(Mul(Matrix(3, 4, [[-A_3_4,-A_3_1,-A_3_2,-A_3_3],[A_1_4-A_4_4,A_1_1-A_4_1,A_1_2-A_4_2,A_1_3-A_4_3],[A_2_4-A_5_4,A_2_1-A_5_1,A_2_2-A_5_2,A_2_3-A_5_3]]),Matrix(4, 5, [[B_4_1-B_4_11-B_5_11,B_4_2-B_4_12-B_5_12,B_4_3-B_4_13-B_5_13,B_4_4-B_4_14-B_5_14,B_4_5-B_4_15-B_5_15],[B_1_1-B_1_11-B_6_11,B_1_2-B_1_12-B_6_12,B_1_3-B_1_13-B_6_13,B_1_4-B_1_14-B_6_14,B_1_5-B_1_15-B_6_15],[B_2_1-B_2_11-B_7_11,B_2_2-B_2_12-B_7_12,B_2_3-B_2_13-B_7_13,B_2_4-B_2_14-B_7_14,B_2_5-B_2_15-B_7_15],[B_3_1-B_3_11-B_8_11,B_3_2-B_3_12-B_8_12,B_3_3-B_3_13-B_8_13,B_3_4-B_3_14-B_8_14,B_3_5-B_3_15-B_8_15]]),Matrix(5, 3, [[C_11_3,C_11_4,C_11_5],[C_12_3,C_12_4,C_12_5],[C_13_3,C_13_4,C_13_5],[C_14_3,C_14_4,C_14_5],[C_15_3,C_15_4,C_15_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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