Extracting coefficients from symbolic expression

syms P121 P131 P151 P122 P132 P152 cosd sind cosdphi12over2 cosdphi13over2 cosdphi15over2 sindphi12over2 sindphi13over2 sindphi15over2 P121raised_to2  P122raised_to2  P131raised_to2 P132raised_to2 P151raised_to2 P152raised_to2 x y 
M4=[P121*cosdphi12over2-y*cosdphi12over2+P122*sindphi12over2+sindphi12over2*x P122*cosdphi12over2+x*cosdphi12over2-P121*sindphi12over2+y*sindphi12over2 P121raised_to2*sindphi12over2+P122raised_to2*sindphi12over2-P121*cosdphi12over2-P122*cosdphi12over2*y+sindphi12over2*P122*x-sindphi12over2*P121*y;
P131*cosdphi13over2-y*cosdphi13over2+P132*sindphi13over2+sindphi13over2*x P132*cosdphi13over2+x*cosdphi13over2-P131*sindphi13over2+y*sindphi13over2 P131raised_to2*sindphi13over2+P132raised_to2*sindphi13over2-P131*cosdphi13over2-P132*cosdphi13over2*y+sindphi13over2*P132*x-sindphi13over2*P131*y;
P151*cosdphi15over2-y*cosdphi15over2+P152*sindphi15over2+sindphi15over2*x P152*cosdphi15over2+x*cosdphi15over2-P151*sindphi15over2+y*sindphi15over2 P151raised_to2*sindphi15over2+P152raised_to2*sindphi15over2-P151*cosdphi15over2-P152*cosdphi15over2*y+sindphi15over2*P152*x-sindphi15over2*P151*y]

det(M4)

ans =
 
P121*cosdphi12over2*cosdphi13over2*sindphi15over2*x^2 - P121*cosdphi12over2*cosdphi15over2*sindphi13over2*x^2 - P131*cosdphi12over2*cosdphi13over2*sindphi15over2*x^2 + P131*cosdphi13over2*cosdphi15over2*sindphi12over2*x^2 + P151*cosdphi12over2*cosdphi15over2*sindphi13over2*x^2 - P151*cosdphi13over2*cosdphi15over2*sindphi12over2*x^2 + P121*cosdphi12over2*cosdphi13over2*sindphi15over2*y^2 - P121*cosdphi12over2*cosdphi15over2*sindphi13over2*y^2 + P122*cosdphi12over2*cosdphi13over2*sindphi15over2*y^3 - P122*cosdphi12over2*cosdphi15over2*sindphi13over2*y^3 - P131*cosdphi12over2*cosdphi13over2*sindphi15over2*y^2 + P131*cosdphi13over2*cosdphi15over2*sindphi12over2*y^2 - P132*cosdphi12over2*cosdphi13over2*sindphi15over2*y^3 + P132*cosdphi13over2*cosdphi15over2*sindphi12over2*y^3 + P151*cosdphi12over2*cosdphi15over2*sindphi13over2*y^2 - P151*cosdphi13over2*cosdphi15over2*sindphi12over2*y^2 + P152*cosdphi12over2*cosdphi15over2*sindphi13over2*y^3 - P152*cosdphi13over2*cosdphi15over2*sindphi12over2*y^3 - P122*cosdphi13over2*sindphi12over2*sindphi15over2*x^3 + P122*cosdphi15over2*sindphi12over2*sindphi13over2*x^3 + P132*cosdphi12over2*sindphi13over2*sindphi15over2*x^3 - P132*cosdphi15over2*sindphi12over2*sindphi13over2*x^3 - P152*cosdphi12over2*sindphi13over2*sindphi15over2*x^3 + P152*cosdphi13over2*sindphi12over2*sindphi15over2*x^3 - P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x^2 + P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x^2 - P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x^2 + P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x^2 + P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x^2 - P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x^2 + P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x^2 - P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x^2 - P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x^2 + P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x^2 - P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x^2 + P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x^2 + P121*cosdphi13over2*sindphi12over2*sindphi15over2*y^3 - P121*cosdphi15over2*sindphi12over2*sindphi13over2*y^3 - P131*cosdphi12over2*sindphi13over2*sindphi15over2*y^3 + P131*cosdphi15over2*sindphi12over2*sindphi13over2*y^3 + P151*cosdphi12over2*sindphi13over2*sindphi15over2*y^3 - P151*cosdphi13over2*sindphi12over2*sindphi15over2*y^3 - P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 + P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 - P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 + P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 + P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 - P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 + P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 - P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 - P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 + P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 - P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 + P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 - P121*P132*cosdphi12over2*cosdphi15over2*sindphi13over2*x^2 + P122*P131*cosdphi13over2*cosdphi15over2*sindphi12over2*x^2 + P121*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x^2 - P122*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*x^2 - P131*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x^2 + P132*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*x^2 + P121*P132*cosdphi12over2*cosdphi13over2*sindphi15over2*y^2 - 2*P121*P132*cosdphi13over2*cosdphi15over2*sindphi12over2*y^2 - P122*P131*cosdphi12over2*cosdphi13over2*sindphi15over2*y^2 + 2*P122*P131*cosdphi12over2*cosdphi15over2*sindphi13over2*y^2 - P121*P152*cosdphi12over2*cosdphi15over2*sindphi13over2*y^2 + 2*P121*P152*cosdphi13over2*cosdphi15over2*sindphi12over2*y^2 - 2*P122*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*y^2 + P122*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*y^2 - 2*P131*P152*cosdphi12over2*cosdphi15over2*sindphi13over2*y^2 + P131*P152*cosdphi13over2*cosdphi15over2*sindphi12over2*y^2 + 2*P132*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*y^2 - P132*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*y^2 + P122*P132*cosdphi12over2*sindphi13over2*sindphi15over2*x^2 - P122*P132*cosdphi13over2*sindphi12over2*sindphi15over2*x^2 - P122*P152*cosdphi12over2*sindphi13over2*sindphi15over2*x^2 + P122*P152*cosdphi15over2*sindphi12over2*sindphi13over2*x^2 + P132*P152*cosdphi13over2*sindphi12over2*sindphi15over2*x^2 - P132*P152*cosdphi15over2*sindphi12over2*sindphi13over2*x^2 + P121*P131*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 - P121*P131*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 - P122*P132*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 + P122*P132*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 - P121*P151*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 + P121*P151*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 + P122*P152*cosdphi12over2*sindphi13over2*sindphi15over2*y^2 - P122*P152*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 + P131*P151*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 - P131*P151*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 - P132*P152*cosdphi13over2*sindphi12over2*sindphi15over2*y^2 + P132*P152*cosdphi15over2*sindphi12over2*sindphi13over2*y^2 - P121*P132*sindphi12over2*sindphi13over2*sindphi15over2*x^2 + P122*P131*sindphi12over2*sindphi13over2*sindphi15over2*x^2 + P121*P152*sindphi12over2*sindphi13over2*sindphi15over2*x^2 - P122*P151*sindphi12over2*sindphi13over2*sindphi15over2*x^2 - P131*P152*sindphi12over2*sindphi13over2*sindphi15over2*x^2 + P132*P151*sindphi12over2*sindphi13over2*sindphi15over2*x^2 - P121*P132*sindphi12over2*sindphi13over2*sindphi15over2*y^2 + P122*P131*sindphi12over2*sindphi13over2*sindphi15over2*y^2 + P121*P152*sindphi12over2*sindphi13over2*sindphi15over2*y^2 - P122*P151*sindphi12over2*sindphi13over2*sindphi15over2*y^2 - P131*P152*sindphi12over2*sindphi13over2*sindphi15over2*y^2 + P132*P151*sindphi12over2*sindphi13over2*sindphi15over2*y^2 + P122*cosdphi12over2*cosdphi13over2*sindphi15over2*x^2*y - P122*cosdphi12over2*cosdphi15over2*sindphi13over2*x^2*y - P132*cosdphi12over2*cosdphi13over2*sindphi15over2*x^2*y + P132*cosdphi13over2*cosdphi15over2*sindphi12over2*x^2*y + P152*cosdphi12over2*cosdphi15over2*sindphi13over2*x^2*y - P152*cosdphi13over2*cosdphi15over2*sindphi12over2*x^2*y + P121*cosdphi13over2*sindphi12over2*sindphi15over2*x^2*y - P121*cosdphi15over2*sindphi12over2*sindphi13over2*x^2*y - P122*cosdphi13over2*sindphi12over2*sindphi15over2*x*y^2 + P122*cosdphi15over2*sindphi12over2*sindphi13over2*x*y^2 - P131*cosdphi12over2*sindphi13over2*sindphi15over2*x^2*y + P131*cosdphi15over2*sindphi12over2*sindphi13over2*x^2*y + P132*cosdphi12over2*sindphi13over2*sindphi15over2*x*y^2 - P132*cosdphi15over2*sindphi12over2*sindphi13over2*x*y^2 + P151*cosdphi12over2*sindphi13over2*sindphi15over2*x^2*y - P151*cosdphi13over2*sindphi12over2*sindphi15over2*x^2*y - P152*cosdphi12over2*sindphi13over2*sindphi15over2*x*y^2 + P152*cosdphi13over2*sindphi12over2*sindphi15over2*x*y^2 + P121*P132*P152*cosdphi12over2*cosdphi13over2*sindphi15over2 - P121*P132*P152*cosdphi12over2*cosdphi15over2*sindphi13over2 - P122*P131*P152*cosdphi12over2*cosdphi13over2*sindphi15over2 + P122*P131*P152*cosdphi13over2*cosdphi15over2*sindphi12over2 + P122*P132*P151*cosdphi12over2*cosdphi15over2*sindphi13over2 - P122*P132*P151*cosdphi13over2*cosdphi15over2*sindphi12over2 + P131*P152*P121raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2 - P132*P151*P121raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2 + P131*P152*P122raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2 - P132*P151*P122raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2 - P121*P152*P131raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2 + P122*P151*P131raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2 - P121*P152*P132raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2 + P122*P151*P132raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2 + P121*P132*P151raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2 - P122*P131*P151raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2 + P121*P132*P152raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2 - P122*P131*P152raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2 - P121*P131*P152*cosdphi12over2*sindphi13over2*sindphi15over2 + P121*P131*P152*cosdphi13over2*sindphi12over2*sindphi15over2 + P121*P132*P151*cosdphi12over2*sindphi13over2*sindphi15over2 - P121*P132*P151*cosdphi15over2*sindphi12over2*sindphi13over2 - P122*P131*P151*cosdphi13over2*sindphi12over2*sindphi15over2 + P122*P131*P151*cosdphi15over2*sindphi12over2*sindphi13over2 - P131*P151*P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 + P131*P151*P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 - P132*P152*P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 + P132*P152*P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 - P131*P151*P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 + P131*P151*P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 - P132*P152*P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 + P132*P152*P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 + P121*P151*P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 - P121*P151*P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 + P122*P152*P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 - P122*P152*P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 + P121*P151*P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 - P121*P151*P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 + P122*P152*P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 - P122*P152*P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2 - P121*P131*P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 + P121*P131*P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 - P122*P132*P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 + P122*P132*P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 - P121*P131*P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 + P121*P131*P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 - P122*P132*P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2 + P122*P132*P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2 - P121*P132*cosdphi12over2*cosdphi13over2*cosdphi15over2*y + P122*P131*cosdphi12over2*cosdphi13over2*cosdphi15over2*y + P121*P152*cosdphi12over2*cosdphi13over2*cosdphi15over2*y - P122*P151*cosdphi12over2*cosdphi13over2*cosdphi15over2*y - P131*P152*cosdphi12over2*cosdphi13over2*cosdphi15over2*y + P132*P151*cosdphi12over2*cosdphi13over2*cosdphi15over2*y + P131*P152*P121raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 - P132*P151*P121raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 + P131*P152*P122raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 - P132*P151*P122raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 - P121*P152*P131raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 + P122*P151*P131raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 - P121*P152*P132raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 + P122*P151*P132raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 + P121*P132*P151raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 - P122*P131*P151raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 + P121*P132*P152raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 - P122*P131*P152raised_to2*sindphi12over2*sindphi13over2*sindphi15over2 + P121*P132*cosdphi12over2*cosdphi13over2*sindphi15over2*x - P121*P132*cosdphi12over2*cosdphi15over2*sindphi13over2*x - P122*P131*cosdphi12over2*cosdphi13over2*sindphi15over2*x + P122*P131*cosdphi13over2*cosdphi15over2*sindphi12over2*x + P121*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x - P121*P152*cosdphi12over2*cosdphi15over2*sindphi13over2*x + P122*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*x - P122*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*x - P131*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x + P131*P152*cosdphi13over2*cosdphi15over2*sindphi12over2*x + P132*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*x - P132*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*x + P131*P121raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*x + P131*P122raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*x - P151*P121raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*x - P151*P122raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*x - P121*P131raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*x - P121*P132raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*x + P151*P131raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*x + P151*P132raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*x + P121*P151raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*x + P121*P152raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*x - P131*P151raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*x - P131*P152raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*x + P121*P131*cosdphi12over2*cosdphi15over2*sindphi13over2*y - P121*P131*cosdphi13over2*cosdphi15over2*sindphi12over2*y - P121*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*y + P121*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*y + P131*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*y - P131*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*y + P132*P121raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*y + P132*P122raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*y - P152*P121raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*y - P152*P122raised_to2*cosdphi13over2*cosdphi15over2*sindphi12over2*y - P122*P131raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*y - P122*P132raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*y + P152*P131raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*y + P152*P132raised_to2*cosdphi12over2*cosdphi15over2*sindphi13over2*y + P122*P151raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*y + P122*P152raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*y - P132*P151raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*y - P132*P152raised_to2*cosdphi12over2*cosdphi13over2*sindphi15over2*y - P121*P131*cosdphi12over2*sindphi13over2*sindphi15over2*x + P121*P131*cosdphi13over2*sindphi12over2*sindphi15over2*x + P121*P151*cosdphi12over2*sindphi13over2*sindphi15over2*x - P121*P151*cosdphi15over2*sindphi12over2*sindphi13over2*x - P131*P151*cosdphi13over2*sindphi12over2*sindphi15over2*x + P131*P151*cosdphi15over2*sindphi12over2*sindphi13over2*x - P132*P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x + P132*P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x - P132*P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x + P132*P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x - P152*P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x + P152*P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x - P152*P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x + P152*P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x + P122*P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x - P122*P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x + P122*P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x - P122*P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x + P152*P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x - P152*P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x + P152*P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x - P152*P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*x - P122*P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x + P122*P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x - P122*P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x + P122*P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x - P132*P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x + P132*P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x - P132*P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*x + P132*P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*x - P121*P132*cosdphi12over2*sindphi13over2*sindphi15over2*y + P122*P131*cosdphi13over2*sindphi12over2*sindphi15over2*y + P121*P152*cosdphi12over2*sindphi13over2*sindphi15over2*y - P122*P151*cosdphi15over2*sindphi12over2*sindphi13over2*y - P131*P152*cosdphi13over2*sindphi12over2*sindphi15over2*y + P132*P151*cosdphi15over2*sindphi12over2*sindphi13over2*y + P131*P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y - P131*P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y + P131*P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y - P131*P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y + P151*P121raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y - P151*P121raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y + P151*P122raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y - P151*P122raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y - P121*P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y + P121*P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y - P121*P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y + P121*P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y - P151*P131raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y + P151*P131raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y - P151*P132raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y + P151*P132raised_to2*cosdphi15over2*sindphi12over2*sindphi13over2*y + P121*P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y - P121*P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y + P121*P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y - P121*P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y + P131*P151raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y - P131*P151raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y + P131*P152raised_to2*cosdphi12over2*sindphi13over2*sindphi15over2*y - P131*P152raised_to2*cosdphi13over2*sindphi12over2*sindphi15over2*y + P131*P121raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x + P131*P122raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x - P151*P121raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x - P151*P122raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x - P121*P131raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x - P121*P132raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x + P151*P131raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x + P151*P132raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x + P121*P151raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x + P121*P152raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x - P131*P151raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x - P131*P152raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*x + P132*P121raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y + P132*P122raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y - P152*P121raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y - P152*P122raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y - P122*P131raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y - P122*P132raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y + P152*P131raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y + P152*P132raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y + P122*P151raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y + P122*P152raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y - P132*P151raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y - P132*P152raised_to2*sindphi12over2*sindphi13over2*sindphi15over2*y + P121*P132*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x - P121*P132*P152*cosdphi12over2*cosdphi15over2*sindphi13over2*x - P122*P131*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x + P122*P131*P152*cosdphi13over2*cosdphi15over2*sindphi12over2*x + P122*P132*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*x - P122*P132*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*x + 2*P121*P131*P152*cosdphi12over2*cosdphi15over2*sindphi13over2*y - 2*P121*P131*P152*cosdphi13over2*cosdphi15over2*sindphi12over2*y - 2*P121*P132*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*y + 2*P121*P132*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*y + 2*P122*P131*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*y - 2*P122*P131*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*y - P121*P131*P152*cosdphi12over2*sindphi13over2*sindphi15over2*x + P121*P131*P152*cosdphi13over2*sindphi12over2*sindphi15over2*x + P121*P132*P151*cosdphi12over2*sindphi13over2*sindphi15over2*x - P121*P132*P151*cosdphi15over2*sindphi12over2*sindphi13over2*x - P122*P131*P151*cosdphi13over2*sindphi12over2*sindphi15over2*x + P122*P131*P151*cosdphi15over2*sindphi12over2*sindphi13over2*x + 2*P121*P132*P152*cosdphi13over2*sindphi12over2*sindphi15over2*y - 2*P121*P132*P152*cosdphi15over2*sindphi12over2*sindphi13over2*y - 2*P122*P131*P152*cosdphi12over2*sindphi13over2*sindphi15over2*y + 2*P122*P131*P152*cosdphi15over2*sindphi12over2*sindphi13over2*y + 2*P122*P132*P151*cosdphi12over2*sindphi13over2*sindphi15over2*y - 2*P122*P132*P151*cosdphi13over2*sindphi12over2*sindphi15over2*y + P121*P132*cosdphi12over2*cosdphi13over2*cosdphi15over2*x*y - P122*P131*cosdphi12over2*cosdphi13over2*cosdphi15over2*x*y - P121*P152*cosdphi12over2*cosdphi13over2*cosdphi15over2*x*y + P122*P151*cosdphi12over2*cosdphi13over2*cosdphi15over2*x*y + P131*P152*cosdphi12over2*cosdphi13over2*cosdphi15over2*x*y - P132*P151*cosdphi12over2*cosdphi13over2*cosdphi15over2*x*y + P121*P131*cosdphi12over2*cosdphi15over2*sindphi13over2*x*y - P121*P131*cosdphi13over2*cosdphi15over2*sindphi12over2*x*y - 2*P122*P132*cosdphi12over2*cosdphi15over2*sindphi13over2*x*y + 2*P122*P132*cosdphi13over2*cosdphi15over2*sindphi12over2*x*y - P121*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*x*y + P121*P151*cosdphi13over2*cosdphi15over2*sindphi12over2*x*y + 2*P122*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x*y - 2*P122*P152*cosdphi13over2*cosdphi15over2*sindphi12over2*x*y + P131*P151*cosdphi12over2*cosdphi13over2*sindphi15over2*x*y - P131*P151*cosdphi12over2*cosdphi15over2*sindphi13over2*x*y - 2*P132*P152*cosdphi12over2*cosdphi13over2*sindphi15over2*x*y + 2*P132*P152*cosdphi12over2*cosdphi15over2*sindphi13over2*x*y - P121*P132*cosdphi12over2*sindphi13over2*sindphi15over2*x*y + 2*P121*P132*cosdphi13over2*sindphi12over2*sindphi15over2*x*y - 2*P122*P131*cosdphi12over2*sindphi13over2*sindphi15over2*x*y + P122*P131*cosdphi13over2*sindphi12over2*sindphi15over2*x*y + P121*P152*cosdphi12over2*sindphi13over2*sindphi15over2*x*y - 2*P121*P152*cosdphi15over2*sindphi12over2*sindphi13over2*x*y + 2*P122*P151*cosdphi12over2*sindphi13over2*sindphi15over2*x*y - P122*P151*cosdphi15over2*sindphi12over2*sindphi13over2*x*y - P131*P152*cosdphi13over2*sindphi12over2*sindphi15over2*x*y + 2*P131*P152*cosdphi15over2*sindphi12over2*sindphi13over2*x*y - 2*P132*P151*cosdphi13over2*sindphi12over2*sindphi15over2*x*y + P132*P151*cosdphi15over2*sindphi12over2*sindphi13over2*x*y
 
coeffs(ans, x^3)

I have a long symbolic expression for the determinant of a symbolic matrix. I need the coefficients of x^3 x^2 x and constants. Anything other than x's y's and their powers is known numericals. When I want to see the coefficients of x^3 MATLAB returns 'Error using mupadengine/evalin2sym. Invalid indeterminate.'

Elements of the matrix are actually sines cosines and divisions and all butt MATLAB doesn't accept command expressions for symbolic variables, that's why I declared them that way.

[Walter Roberson]

Which MATLAB release are you using?

[Ali Kiral]

I've run it online

Answer 1

[Sam Chak]

Hi @Ali Kiral

The expression of the determinant is very long. Perhaps you can try this approach.

syms P121 P131 P151
syms P122 P132 P152
syms c12 c13 c15        % cosdphi13over2
syms s12 s13 s15        % sindphi13over2
syms Q121 Q122 Q131     % P121raised_to2
syms Q132 Q151 Q152
syms x y 

M4  = [P121*c12-y*c12+P122*s12+s12*x P122*c12+x*c12-P121*s12+y*s12 Q121*s12+Q122*s12-P121*c12-P122*c12*y+s12*P122*x-s12*P121*y;
       P131*c13-y*c13+P132*s13+s13*x P132*c13+x*c13-P131*s13+y*s13 Q131*s13+Q132*s13-P131*c13-P132*c13*y+s13*P132*x-s13*P131*y;
       P151*c15-y*c15+P152*s15+s15*x P152*c15+x*c15-P151*s15+y*s15 Q151*s15+Q152*s15-P151*c15-P152*c15*y+s15*P152*x-s15*P151*y]

M4 = 

D   = det(M4)

D = 

C   = collect(D, [x, y])

C = 

●

Answer 2

[Walter Roberson]

syms P121 P131 P151 P122 P132 P152 cosd sind cosdphi12over2 cosdphi13over2 cosdphi15over2 sindphi12over2 sindphi13over2 sindphi15over2 P121raised_to2  P122raised_to2  P131raised_to2 P132raised_to2 P151raised_to2 P152raised_to2 x y 
M4=[P121*cosdphi12over2-y*cosdphi12over2+P122*sindphi12over2+sindphi12over2*x P122*cosdphi12over2+x*cosdphi12over2-P121*sindphi12over2+y*sindphi12over2 P121raised_to2*sindphi12over2+P122raised_to2*sindphi12over2-P121*cosdphi12over2-P122*cosdphi12over2*y+sindphi12over2*P122*x-sindphi12over2*P121*y;
P131*cosdphi13over2-y*cosdphi13over2+P132*sindphi13over2+sindphi13over2*x P132*cosdphi13over2+x*cosdphi13over2-P131*sindphi13over2+y*sindphi13over2 P131raised_to2*sindphi13over2+P132raised_to2*sindphi13over2-P131*cosdphi13over2-P132*cosdphi13over2*y+sindphi13over2*P132*x-sindphi13over2*P131*y;
P151*cosdphi15over2-y*cosdphi15over2+P152*sindphi15over2+sindphi15over2*x P152*cosdphi15over2+x*cosdphi15over2-P151*sindphi15over2+y*sindphi15over2 P151raised_to2*sindphi15over2+P152raised_to2*sindphi15over2-P151*cosdphi15over2-P152*cosdphi15over2*y+sindphi15over2*P152*x-sindphi15over2*P151*y]

M4 = 

D = det(M4);
[C, X] = coeffs(D, x);
sympref('AbbreviateOutput', 0)

ans = logical
   1

X(:) == C(:)

ans = 

Answer 3

[Torsten]

syms P121 P131 P151 P122 P132 P152 cosdphi12over2 cosdphi13over2 cosdphi15over2 sindphi12over2 sindphi13over2 sindphi15over2 P121raised_to2  P122raised_to2  P131raised_to2 P132raised_to2 P151raised_to2 P152raised_to2 x y 
M4=[P121*cosdphi12over2-y*cosdphi12over2+P122*sindphi12over2+sindphi12over2*x P122*cosdphi12over2+x*cosdphi12over2-P121*sindphi12over2+y*sindphi12over2 P121raised_to2*sindphi12over2+P122raised_to2*sindphi12over2-P121*cosdphi12over2-P122*cosdphi12over2*y+sindphi12over2*P122*x-sindphi12over2*P121*y;
P131*cosdphi13over2-y*cosdphi13over2+P132*sindphi13over2+sindphi13over2*x P132*cosdphi13over2+x*cosdphi13over2-P131*sindphi13over2+y*sindphi13over2 P131raised_to2*sindphi13over2+P132raised_to2*sindphi13over2-P131*cosdphi13over2-P132*cosdphi13over2*y+sindphi13over2*P132*x-sindphi13over2*P131*y;
P151*cosdphi15over2-y*cosdphi15over2+P152*sindphi15over2+sindphi15over2*x P152*cosdphi15over2+x*cosdphi15over2-P151*sindphi15over2+y*sindphi15over2 P151raised_to2*sindphi15over2+P152raised_to2*sindphi15over2-P151*cosdphi15over2-P152*cosdphi15over2*y+sindphi15over2*P152*x-sindphi15over2*P151*y]

M4 = 

det(M4)

ans = 

[cfs,trms] = coeffs(ans, x);
Resultx3 = cfs(trms == x^3)

Resultx3 = 

Resultx2 = cfs(trms == x^2)

Resultx2 = 

Resultx = cfs(trms == x)

Resultx = 

●

Result1 = cfs(trms == 1)

Result1 =