User:B jonas/Sandbox

Strange cascading formula errors
From Pfister's sixteen-square identity


 * $$u_1 = (1/c)\bigl((ax_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2)x_9 - 2x_1(bx_1 x_9 +x_2 x_{10} +x_3 x_{11} +x_4 x_{12} +x_5 x_{13} +x_6 x_{14} +x_7 x_{15} +x_8 x_{16})\bigr)$$
 * $$u_2 = (1/c)\bigl((x_1^2+ax_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2)x_{10} - 2x_2(x_1 x_9 +bx_2 x_{10} +x_3 x_{11} +x_4 x_{12} +x_5 x_{13} +x_6 x_{14} +x_7 x_{15} +x_8 x_{16})\bigr)$$
 * $$u_3 = (1/c)\bigl((x_1^2+x_2^2+ax_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2)x_{11} - 2x_3(x_1 x_9 +x_2 x_{10} +bx_3 x_{11} +x_4 x_{12} +x_5 x_{13} +x_6 x_{14} +x_7 x_{15} +x_8 x_{16})\bigr)$$
 * $$u_4 = (1/c)\bigl((x_1^2+x_2^2+x_3^2+ax_4^2+x_5^2+x_6^2+x_7^2+x_8^2)x_{12} - 2x_4(x_1 x_9 +x_2 x_{10} +x_3 x_{11} +bx_4 x_{12} +x_5 x_{13} +x_6 x_{14} +x_7 x_{15} +x_8 x_{16})\bigr)$$
 * $$u_5 = (1/c)\bigl((x_1^2+x_2^2+x_3^2+x_4^2+ax_5^2+x_6^2+x_7^2+x_8^2)x_{13} - 2x_5(x_1 x_9 +x_2 x_{10} +x_3 x_{11} +x_4 x_{12} +bx_5 x_{13} +x_6 x_{14} +x_7 x_{15} +x_8 x_{16})\bigr)$$
 * $$u_6 = (1/c)\bigl((x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+ax_6^2+x_7^2+x_8^2)x_{14} - 2x_6(x_1 x_9 +x_2 x_{10} +x_3 x_{11} +x_4 x_{12} +x_5 x_{13} +bx_6 x_{14} +x_7 x_{15} +x_8 x_{16})\bigr)$$
 * $$u_7 = (1/c)\bigl((x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+ax_7^2+x_8^2)x_{15} - 2x_7(x_1 x_9 +x_2 x_{10} +x_3 x_{11} +x_4 x_{12} +x_5 x_{13} +x_6 x_{14} +bx_7 x_{15} +x_8 x_{16})\bigr)$$
 * $$u_8 = (1/c)\bigl((x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+ax_8^2)x_{16} - 2x_8(x_1 x_9 +x_2 x_{10} +x_3 x_{11} +x_4 x_{12} +x_5 x_{13} +x_6 x_{14} +x_7 x_{15} +bx_8 x_{16})\bigr)$$

$$a^2 + b^2 = c^2$$


 * u1 = (1/c) ( (ax12 + x22 + x32 + x42 + x52 + x62 + x72 + x82)x9 &#x2212;
 * 2x1(bx1x9 + x2x10 + x3x11 + x4x12 + x5x13 + x6x14 + x7x15 + x8x16) )
 * u2 = (1/c) ( (x12 + ax22 + x32 + x42 + x52 + x62 + x72 + x82)x10 &#x2212;
 * 2x2(x1x9 + bx2x10 + x3x11 + x4x12 + x5x13 + x6x14 + x7x15 + x8x16) )
 * u3 = (1/c) ( (x12 + x22 + ax32 + x42 + x52 + x62 + x72 + x82)x11 &#x2212;
 * 2x3(x1x9 + x2x10 + bx3x11 + x4x12 + x5x13 + x6x14 + x7x15 + x8x16) )
 * u4 = (1/c) ( (x12 + x22 + x32 + ax42 + x52 + x62 + x72 + x82)x12 &#x2212;
 * 2x4(x1x9 + x2x10 + x3x11 + bx4x12 + x5x13 + x6x14 + x7x15 + x8x16) )
 * u5 = (1/c) ( (x12 + x22 + x32 + x42 + ax52 + x62 + x72 + x82)x13 &#x2212;
 * 2x5(x1x9 + x2x10 + x3x11 + x4x12 + bx5x13 + x6x14 + x7x15 + x8x16) )
 * u6 = (1/c) ( (x12 + x22 + x32 + x42 + x52 + ax62 + x72 + x82)x14 &#x2212;
 * 2x6(x1x9 + x2x10 + x3x11 + x4x12 + x5x13 + bx6x14 + x7x15 + x8x16) )
 * u7 = (1/c) ( (x12 + x22 + x32 + x42 + x52 + x62 + ax72 + x82)x15 &#x2212;
 * 2x7(x1x9 + x2x10 + x3x11 + x4x12 + x5x13 + x6x14 + bx7x15 + x8x16) )
 * u8 = (1/c) ( (x12 + x22 + x32 + x42 + x52 + x62 + x72 + ax82)x16 &#x2212;
 * 2x8(x1x9 + x2x10 + x3x11 + x4x12 + x5x13 + x6x14 + x7x15 + bx8x16) )