Source code for diatomic_fits

[docs]def function_5pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] result = (y1 + (x - x1)*((-y1 + y2)/(-x1 + x2) + (x - x2)*((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3) + (x - x3)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4) + ((x - x4)* (-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5)))/(-x1 + x5))))) return result
[docs]def first_deriv_5pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] result = ((-y1 + y2)/(-x1 + x2) + (x - x2)*((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3) + (x - x3)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4) + ((x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5))) + (x - x1)*((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3) + (x - x3)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4)\ + ((x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5)) + (x - x2)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4)\ + ((x - x3)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5) + ((x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5)))) return result
[docs]def second_deriv_5pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] result = ((2.0*(-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3)))/(-x1 + x3) + 2.0*(x - x3)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4) + ((x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5)) + 2.0*(x - x2)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4) + ((x - x3)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5) + ((x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5)) + (x - x1)*((2.0*(-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)))/(-x1 + x4)\ + (2.0*(x - x2)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5) ))/(-x1 + x5) + (2.0*(x - x3)* (-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5) + (2.0*(x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5) ))/(-x1 + x5))) return result
[docs]def third_deriv_5pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] result = ((2.0*(-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)))/(-x1 + x4) + (6.0*(x - x1)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5)))/ (-x1 + x5) + (6.0*(x - x2)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5)))/ (-x1 + x5) + (4.0*(x - x3)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5)))/ (-x1 + x5) + (2.0*(x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5)))/ (-x1 + x5) + 2.0*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4) )/(-x1 + x4) + ((x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5)) + 2.0*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4) + ((x - x3)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5) + ((x - x4)*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)))/(-x1 + x5))) return result
[docs]def fourth_deriv_5pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] result = ((24.0*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4))\ + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5)))/ (-x1 + x5)) return result
[docs]def function_9pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] x6 = xa[5] x7 = xa[6] x8 = xa[7] x9 = xa[8] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] y6 = ya[5] y7 = ya[6] y8 = ya[7] y9 = ya[8] result = (y1 + (x - x1)*((-y1 + y2)/(-x1 + x2) + (x - x2)*((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3) + (x - x3)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4)\ + (x - x4)*((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5))/(-x1 + x5) + (x - x5)*((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6)) /(-x3 + x6))/(-x2 + x6))/(-x1 + x6) + (x - x6)*((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) + (x - x7)*((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) )/(-x1 + x8) + ((x - x8)*(-((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) )/(-x1 + x8)) + (-((-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) ) + (-((-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8)) + (-((-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9))))))))) return result
[docs]def first_deriv_9pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] x6 = xa[5] x7 = xa[6] x8 = xa[7] x9 = xa[8] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] y6 = ya[5] y7 = ya[6] y8 = ya[7] y9 = ya[8] result = ((-y1 + y2)/(-x1 + x2) + (x - x2)*((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3) + (x - x3)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4) + (x - x4)*((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5) + (x - x5)*((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4) )/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6))/(-x2 + x6))/(-x1 + x6) + (x - x6)*((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) + (x - x7)*((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + 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y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9) + ((x - x8)*(-((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) )/(-x1 + x8)) + (-((-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) ) + (-((-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8)) + (-((-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9)))))))) return result
[docs]def second_deriv_9pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] x6 = xa[5] x7 = xa[6] x8 = xa[7] x9 = xa[8] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] y6 = ya[5] y7 = ya[6] y8 = ya[7] y9 = ya[8] result = ((2*(-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3)))/(-x1 + x3) + 2*(x - x3)*((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4) + (x - x4)*((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5) + (x - x5)*((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6))/(-x2 + x6))/(-x1 + x6) + (x - x6)*((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/(-x5 + x7)) /(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) + (x - x7)*((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 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+ (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8)) + (-((-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9) + (2*(x - x8)*(-((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) )/(-x1 + x8)) + (-((-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) ) + (-((-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8)) + (-((-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9))))))) return result
[docs]def third_deriv_9pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] x6 = xa[5] x7 = xa[6] x8 = xa[7] x9 = xa[8] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] y6 = ya[5] y7 = ya[6] y8 = ya[7] y9 = ya[8] result = ((2*(-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)))/(-x1 + x4) + 2*(x - x4)*((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4))\ + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5))/ (-x1 + x5) + (x - x5)*((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6) + (x - x6)*((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5) )/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5) )/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5) )/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/(-x5 + x7))/ (-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) + (x - x7)*((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ 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(-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) )/(-x1 + x8)) + (-((-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) ) + (-((-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8)) + (-((-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9))))))) return result
[docs]def fourth_deriv_9pt(xa, ya, x): x1 = xa[0] x2 = xa[1] x3 = xa[2] x4 = xa[3] x5 = xa[4] x6 = xa[5] x7 = xa[6] x8 = xa[7] x9 = xa[8] y1 = ya[0] y2 = ya[1] y3 = ya[2] y4 = ya[3] y5 = ya[4] y6 = ya[5] y7 = ya[6] y8 = ya[7] y9 = ya[8] result = ((2*(-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/(-x1 + x4))\ + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/(-x2 + x5)))/ (-x1 + x5) + 2*(x - x5)*((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4))/ (-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6) + (x - x6)*((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) /(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5))/ (-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/(-x4 + x6))/ (-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/(-x5 + x7))/ (-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) + (x - x7)*((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/ (-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7)) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + 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(-((-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9) + (2*(x - x8)*(-((-((-((-((-((-((-((-y1 + y2)/(-x1 + x2)) + (-y2 + y3)/(-x2 + x3))/(-x1 + x3)) + (-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4))/(-x1 + x4)) + (-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5))/(-x1 + x5)) + (-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/ (-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6))/(-x1 + x6)) + (-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7))/(-x1 + x7) ) + (-((-((-((-((-((-y2 + y3)/(-x2 + x3)) + (-y3 + y4)/(-x3 + x4))/(-x2 + x4)) + (-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5))/(-x2 + x5)) + (-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6))/(-x2 + x6)) + (-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7))/(-x2 + x7)) + (-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/ (-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + 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x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8))/(-x2 + x8) ) + (-((-((-((-((-((-y3 + y4)/(-x3 + x4)) + (-y4 + y5)/(-x4 + x5))/(-x3 + x5)) + (-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6))/(-x3 + x6)) + (-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7))/(-x3 + x7)) + (-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8))/(-x3 + x8)) + (-((-((-((-((-y4 + y5)/(-x4 + x5)) + (-y5 + y6)/(-x5 + x6))/ (-x4 + x6)) + (-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7))/(-x4 + x7)) + (-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8))/(-x4 + x8)) + (-((-((-((-y5 + y6)/(-x5 + x6)) + (-y6 + y7)/(-x6 + x7))/ (-x5 + x7)) + (-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8))/(-x5 + x8)) + (-((-((-y6 + y7)/(-x6 + x7)) + (-y7 + y8)/(-x7 + x8))/ (-x6 + x8)) + (-((-y7 + y8)/(-x7 + x8)) + (-y8 + y9)/(-x8 + x9))/ (-x7 + x9))/(-x6 + x9))/(-x5 + x9))/(-x4 + x9))/(-x3 + x9) )/(-x2 + x9)))/(-x1 + x9)))))) return result