CoCalc -- 3314.sagews

All published worksheets from http://sagenb.org

Project: sagenb.org published worksheets

Views: ¹⁶⁸⁷²¹
Image: ubuntu2004

a1,a2,a3,S0,S1,S2,S3,S0t,S1t,S2t,S0t2,S1t2,S2t2 = var('a1,a2,a3,S0,S1,S2,S3,S0t,S1t,S0t2,S2t,S1t2,S2t2')

solve ([S1 == a1*S0 + 2*a2*S0t + 3*a3*S0t2 , S2 == 2*a2*S0 + 6*a3*S0t + a1*S1 + 2*a2*S1t + 3*a3*S1t2 , S3 == 6*a3*S0 + 2*a2*S1 + 6*a3*S1t + a1*S2 + 2*a2*S2t + 3*a3*S2t2 + 2*a2*S1 + 6*a3*S1t],a1,a2,a3)

[[a1 == -(2*(2*S0t + S1t2)*S1^2 - 2*S0t^2*S3 - (S0t2*S2 - S1t*S3)*S2t + (2*S0t*S2 + S2t*S3)*S0 + ((4*S1t + S2t2)*S2 - S1t2*S3)*S0t - ((6*S1t + S2t2)*S0 + 2*S0^2 - 2*S0t*S0t2 - S0t2*S1t2 + 4*S1t^2 + S1t*S2t2 + 2*S2*S2t)*S1)/((6*S1t + S2t2)*S0^2 + 2*S0^3 + 2*S0t^2*S2 + S0t*S1t2*S2 + 2*S1^2*S2t - S1t*S2*S2t - ((4*S1t + S2t2)*S0t + 2*(3*S0t + S1t2)*S0 - S0t2*S2t)*S1 - (2*S0t*S0t2 + S0t2*S1t2 - 4*S1t^2 - S1t*S2t2 + S2*S2t)*S0), a2 == -1/2*((2*S0 + 4*S1t + S2t2)*S1^2 - 2*S0^2*S2 + S2^2*S2t - (2*S0t*S2 + S1t2*S2 + S2t*S3)*S1 - ((4*S1t + S2t2)*S2 - 2*S0t*S3 - S1t2*S3)*S0)/((6*S1t + S2t2)*S0^2 + 2*S0^3 + 2*S0t^2*S2 + S0t*S1t2*S2 + 2*S1^2*S2t - S1t*S2*S2t - ((4*S1t + S2t2)*S0t + 2*(3*S0t + S1t2)*S0 - S0t2*S2t)*S1 - (2*S0t*S0t2 + S0t2*S1t2 - 4*S1t^2 - S1t*S2t2 + S2*S2t)*S0), a3 == 1/3*(S0^2*S3 + S0t*S2^2 + S0t2*S1^2 + 2*S1^3 - (S0t2*S2 - S1t*S3)*S0 - (3*S0*S2 + S0t*S3 + S1t*S2)*S1)/((6*S1t + S2t2)*S0^2 + 2*S0^3 + 2*S0t^2*S2 + S0t*S1t2*S2 + 2*S1^2*S2t - S1t*S2*S2t - ((4*S1t + S2t2)*S0t + 2*(3*S0t + S1t2)*S0 - S0t2*S2t)*S1 - (2*S0t*S0t2 + S0t2*S1t2 - 4*S1t^2 - S1t*S2t2 + S2*S2t)*S0)]]