📄 program4.m
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((a[2] - ((a[2]^2 + b[2]^2)* Sin[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[2] - b[3])/(a[2] - a[3])] + ArcTan[(b[2] + b[3])/(a[2] - a[3])] + ArcTan[(b[2] - b[4])/(a[2] - a[4])] + ArcTan[(b[2] + b[4])/(a[2] - a[4])] - ArcTan[(b[2] - d[1])/(a[2] - c[1])] - ArcTan[(b[2] + d[1])/(a[2] - c[1])] - ArcTan[(b[2] - d[2])/(a[2] - c[2])] - ArcTan[(b[2] + d[2])/(a[2] - c[2])] - ArcTan[(b[2] - d[3])/(a[2] - c[3])] - ArcTan[(b[2] + d[3])/(a[2] - c[3])] - ArcTan[(b[2] - d[4])/(a[2] - c[4])] - ArcTan[(b[2] + d[4])/(a[2] - c[4])]])/ (b[2]*Cos[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[2] - b[3])/(a[2] - a[3])] + ArcTan[(b[2] + b[3])/(a[2] - a[3])] + ArcTan[(b[2] - b[4])/(a[2] - a[4])] + ArcTan[(b[2] + b[4])/(a[2] - a[4])] - ArcTan[(b[2] - d[1])/(a[2] - c[1])] - ArcTan[(b[2] + d[1])/(a[2] - c[1])] - ArcTan[(b[2] - d[2])/(a[2] - c[2])] - ArcTan[(b[2] + d[2])/(a[2] - c[2])] - ArcTan[(b[2] - d[3])/(a[2] - c[3])] - ArcTan[(b[2] + d[3])/(a[2] - c[3])] - ArcTan[(b[2] - d[4])/(a[2] - c[4])] - ArcTan[(b[2] + d[4])/(a[2] - c[4])]] + a[2]*Sin[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[2] - b[3])/(a[2] - a[3])] + ArcTan[(b[2] + b[3])/(a[2] - a[3])] + ArcTan[(b[2] - b[4])/(a[2] - a[4])] + ArcTan[(b[2] + b[4])/(a[2] - a[4])] - ArcTan[(b[2] - d[1])/(a[2] - c[1])] - ArcTan[(b[2] + d[1])/(a[2] - c[1])] - ArcTan[(b[2] - d[2])/(a[2] - c[2])] - ArcTan[(b[2] + d[2])/(a[2] - c[2])] - ArcTan[(b[2] - d[3])/(a[2] - c[3])] - ArcTan[(b[2] + d[3])/(a[2] - c[3])] - ArcTan[(b[2] - d[4])/(a[2] - c[4])] - ArcTan[(b[2] + d[4])/(a[2] - c[4])]]))* Sin[tpeak1*b[2]])/b[2])))/ (b[2]*Sqrt[((-a[1] + a[2])^2 + (-b[1] + b[2])^2)* ((-a[1] + a[2])^2 + (b[1] + b[2])^2)* ((a[2] - a[3])^2 + (b[2] - b[3])^2)* ((a[2] - a[3])^2 + (b[2] + b[3])^2)* ((a[2] - a[4])^2 + (b[2] - b[4])^2)* ((a[2] - a[4])^2 + (b[2] + b[4])^2)]*(c[1]^2 + d[1]^2)* (c[2]^2 + d[2]^2)*(c[3]^2 + d[3]^2)*(c[4]^2 + d[4]^2)) + ((a[1]^2 + b[1]^2)*(a[2]^2 + b[2]^2)*(a[4]^2 + b[4]^2)* Sqrt[((a[3] - c[1])^2 + (b[3] - d[1])^2)* ((a[3] - c[1])^2 + (b[3] + d[1])^2)* ((a[3] - c[2])^2 + (b[3] - d[2])^2)* ((a[3] - c[2])^2 + (b[3] + d[2])^2)* ((a[3] - c[3])^2 + (b[3] - d[3])^2)* ((a[3] - c[3])^2 + (b[3] + d[3])^2)* ((a[3] - c[4])^2 + (b[3] - d[4])^2)* ((a[3] - c[4])^2 + (b[3] + d[4])^2)]* (b[3]*Cos[ArcTan[(-b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(-b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[3] - b[4])/(a[3] - a[4])] + ArcTan[(b[3] + b[4])/(a[3] - a[4])] - ArcTan[(b[3] - d[1])/(a[3] - c[1])] - ArcTan[(b[3] + d[1])/(a[3] - c[1])] - ArcTan[(b[3] - d[2])/(a[3] - c[2])] - ArcTan[(b[3] + d[2])/(a[3] - c[2])] - ArcTan[(b[3] - d[3])/(a[3] - c[3])] - ArcTan[(b[3] + d[3])/(a[3] - c[3])] - ArcTan[(b[3] - d[4])/(a[3] - c[4])] - ArcTan[(b[3] + d[4])/(a[3] - c[4])]] + a[3]*Sin[ArcTan[(-b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(-b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[3] - b[4])/(a[3] - a[4])] + ArcTan[(b[3] + b[4])/(a[3] - a[4])] - ArcTan[(b[3] - d[1])/(a[3] - c[1])] - ArcTan[(b[3] + d[1])/(a[3] - c[1])] - ArcTan[(b[3] - d[2])/(a[3] - c[2])] - ArcTan[(b[3] + d[2])/(a[3] - c[2])] - ArcTan[(b[3] - d[3])/(a[3] - c[3])] - ArcTan[(b[3] + d[3])/(a[3] - c[3])] - ArcTan[(b[3] - d[4])/(a[3] - c[4])] - ArcTan[(b[3] + d[4])/(a[3] - c[4])]])* (1 - E^(tpeak1*a[3])* (Cos[tpeak1*b[3]] - ((a[3] - ((a[3]^2 + b[3]^2)* Sin[ArcTan[(-b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(-b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[3] - b[4])/(a[3] - a[4])] + ArcTan[(b[3] + b[4])/(a[3] - a[4])] - ArcTan[(b[3] - d[1])/(a[3] - c[1])] - ArcTan[(b[3] + d[1])/(a[3] - c[1])] - ArcTan[(b[3] - d[2])/(a[3] - c[2])] - ArcTan[(b[3] + d[2])/(a[3] - c[2])] - ArcTan[(b[3] - d[3])/(a[3] - c[3])] - ArcTan[(b[3] + d[3])/(a[3] - c[3])] - ArcTan[(b[3] - d[4])/(a[3] - c[4])] - ArcTan[(b[3] + d[4])/(a[3] - c[4])]])/ (b[3]*Cos[ArcTan[(-b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(-b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[3] - b[4])/(a[3] - a[4])] + ArcTan[(b[3] + b[4])/(a[3] - a[4])] - ArcTan[(b[3] - d[1])/(a[3] - c[1])] - ArcTan[(b[3] + d[1])/(a[3] - c[1])] - ArcTan[(b[3] - d[2])/(a[3] - c[2])] - ArcTan[(b[3] + d[2])/(a[3] - c[2])] - ArcTan[(b[3] - d[3])/(a[3] - c[3])] - ArcTan[(b[3] + d[3])/(a[3] - c[3])] - ArcTan[(b[3] - d[4])/(a[3] - c[4])] - ArcTan[(b[3] + d[4])/(a[3] - c[4])]] + a[3]*Sin[ArcTan[(-b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(b[1] + b[3])/(-a[1] + a[3])] + ArcTan[(-b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[2] + b[3])/(-a[2] + a[3])] + ArcTan[(b[3] - b[4])/(a[3] - a[4])] + ArcTan[(b[3] + b[4])/(a[3] - a[4])] - ArcTan[(b[3] - d[1])/(a[3] - c[1])] - ArcTan[(b[3] + d[1])/(a[3] - c[1])] - ArcTan[(b[3] - d[2])/(a[3] - c[2])] - ArcTan[(b[3] + d[2])/(a[3] - c[2])] - ArcTan[(b[3] - d[3])/(a[3] - c[3])] - ArcTan[(b[3] + d[3])/(a[3] - c[3])] - ArcTan[(b[3] - d[4])/(a[3] - c[4])] - ArcTan[(b[3] + d[4])/(a[3] - c[4])]]))* Sin[tpeak1*b[3]])/b[3])))/ (b[3]*Sqrt[((-a[1] + a[3])^2 + (-b[1] + b[3])^2)* ((-a[1] + a[3])^2 + (b[1] + b[3])^2)* ((-a[2] + a[3])^2 + (-b[2] + b[3])^2)* ((-a[2] + a[3])^2 + (b[2] + b[3])^2)* ((a[3] - a[4])^2 + (b[3] - b[4])^2)* ((a[3] - a[4])^2 + (b[3] + b[4])^2)]*(c[1]^2 + d[1]^2)* (c[2]^2 + d[2]^2)*(c[3]^2 + d[3]^2)*(c[4]^2 + d[4]^2)) + ((a[1]^2 + b[1]^2)*(a[2]^2 + b[2]^2)*(a[3]^2 + b[3]^2)* Sqrt[((a[4] - c[1])^2 + (b[4] - d[1])^2)* ((a[4] - c[1])^2 + (b[4] + d[1])^2)* ((a[4] - c[2])^2 + (b[4] - d[2])^2)* ((a[4] - c[2])^2 + (b[4] + d[2])^2)* ((a[4] - c[3])^2 + (b[4] - d[3])^2)* ((a[4] - c[3])^2 + (b[4] + d[3])^2)* ((a[4] - c[4])^2 + (b[4] - d[4])^2)* ((a[4] - c[4])^2 + (b[4] + d[4])^2)]* (b[4]*Cos[ArcTan[(-b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(-b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(-b[3] + b[4])/(-a[3] + a[4])] + ArcTan[(b[3] + b[4])/(-a[3] + a[4])] - ArcTan[(b[4] - d[1])/(a[4] - c[1])] - ArcTan[(b[4] + d[1])/(a[4] - c[1])] - ArcTan[(b[4] - d[2])/(a[4] - c[2])] - ArcTan[(b[4] + d[2])/(a[4] - c[2])] - ArcTan[(b[4] - d[3])/(a[4] - c[3])] - ArcTan[(b[4] + d[3])/(a[4] - c[3])] - ArcTan[(b[4] - d[4])/(a[4] - c[4])] - ArcTan[(b[4] + d[4])/(a[4] - c[4])]] + a[4]*Sin[ArcTan[(-b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(-b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(-b[3] + b[4])/(-a[3] + a[4])] + ArcTan[(b[3] + b[4])/(-a[3] + a[4])] - ArcTan[(b[4] - d[1])/(a[4] - c[1])] - ArcTan[(b[4] + d[1])/(a[4] - c[1])] - ArcTan[(b[4] - d[2])/(a[4] - c[2])] - ArcTan[(b[4] + d[2])/(a[4] - c[2])] - ArcTan[(b[4] - d[3])/(a[4] - c[3])] - ArcTan[(b[4] + d[3])/(a[4] - c[3])] - ArcTan[(b[4] - d[4])/(a[4] - c[4])] - ArcTan[(b[4] + d[4])/(a[4] - c[4])]])* (1 - E^(tpeak1*a[4])* (Cos[tpeak1*b[4]] - ((a[4] - ((a[4]^2 + b[4]^2)* Sin[ArcTan[(-b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(-b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(-b[3] + b[4])/(-a[3] + a[4])] + ArcTan[(b[3] + b[4])/(-a[3] + a[4])] - ArcTan[(b[4] - d[1])/(a[4] - c[1])] - ArcTan[(b[4] + d[1])/(a[4] - c[1])] - ArcTan[(b[4] - d[2])/(a[4] - c[2])] - ArcTan[(b[4] + d[2])/(a[4] - c[2])] - ArcTan[(b[4] - d[3])/(a[4] - c[3])] - ArcTan[(b[4] + d[3])/(a[4] - c[3])] - ArcTan[(b[4] - d[4])/(a[4] - c[4])] - ArcTan[(b[4] + d[4])/(a[4] - c[4])]])/ (b[4]*Cos[ArcTan[(-b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(-b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(-b[3] + b[4])/(-a[3] + a[4])] + ArcTan[(b[3] + b[4])/(-a[3] + a[4])] - ArcTan[(b[4] - d[1])/(a[4] - c[1])] - ArcTan[(b[4] + d[1])/(a[4] - c[1])] - ArcTan[(b[4] - d[2])/(a[4] - c[2])] - ArcTan[(b[4] + d[2])/(a[4] - c[2])] - ArcTan[(b[4] - d[3])/(a[4] - c[3])] - ArcTan[(b[4] + d[3])/(a[4] - c[3])] - ArcTan[(b[4] - d[4])/(a[4] - c[4])] - ArcTan[(b[4] + d[4])/(a[4] - c[4])]] + a[4]*Sin[ArcTan[(-b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(b[1] + b[4])/(-a[1] + a[4])] + ArcTan[(-b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(b[2] + b[4])/(-a[2] + a[4])] + ArcTan[(-b[3] + b[4])/(-a[3] + a[4])] + ArcTan[(b[3] + b[4])/(-a[3] + a[4])] - ArcTan[(b[4] - d[1])/(a[4] - c[1])] - ArcTan[(b[4] + d[1])/(a[4] - c[1])] - ArcTan[(b[4] - d[2])/(a[4] - c[2])] - ArcTan[(b[4] + d[2])/(a[4] - c[2])] - ArcTan[(b[4] - d[3])/(a[4] - c[3])] - ArcTan[(b[4] + d[3])/(a[4] - c[3])] - ArcTan[(b[4] - d[4])/(a[4] - c[4])] - ArcTan[(b[4] + d[4])/(a[4] - c[4])]]))* Sin[tpeak1*b[4]])/b[4])))/ (b[4]*Sqrt[((-a[1] + a[4])^2 + (-b[1] + b[4])^2)* ((-a[1] + a[4])^2 + (b[1] + b[4])^2)* ((-a[2] + a[4])^2 + (-b[2] + b[4])^2)* ((-a[2] + a[4])^2 + (b[2] + b[4])^2)* ((-a[3] + a[4])^2 + (-b[3] + b[4])^2)* ((-a[3] + a[4])^2 + (b[3] + b[4])^2)]*(c[1]^2 + d[1]^2)* (c[2]^2 + d[2]^2)*(c[3]^2 + d[3]^2)*(c[4]^2 + d[4]^2)))^2](* Derivatives have been omitted *)
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