MATLAB: ‘Polynomial expression expected.’ showed when i tried to get the coefficents

coeffsrootssymbolicsymbolic polynomial

syms T p1 p2 p3 p4 p5 p6 real
J = T + T*((6*p1)/T^2 - (2*p4)/T)^2 + T*((6*p2)/T^2 - (2*p5)/T)^2 + T*((6*p3)/T^2 - (2*p6)/T)^2 + (T^6*((12*p1)/T^3 - (6*p4)/T^2)^2)/3 + (T^6*((12*p2)/T^3 - (6*p5)/T^2)^2)/3 + (T^6*((12*p3)/T^3 - (6*p6)/T^2)^2)/3 - T^2*((6*p1)/T^2 - (2*p4)/T)*((12*p1)/T^3 - (6*p4)/T^2) - T^2*((6*p2)/T^2 - (2*p5)/T)*((12*p2)/T^3 - (6*p5)/T^2) - T^2*((6*p3)/T^2 - (2*p6)/T)*((12*p3)/T^3 - (6*p6)/T^2);
J1 = diff(J,T);
cT = coeffs(J1,T);

Just got J for another window.

why would it show "Error using symengine Polynomial expression expected." as i ran it?

should i get a normal form of J1 first, when i want the coefficients of it? If so, how?

Appreciate for an answer.

Best Answer

coeffs() can only be used for polynomials with respect to the variable. Your expression has division by your variable, and so is not a polynomial.

simplify() would bring a normal form, but it would still have division by the variable and so is not enough.

What you can do is

[N, D] = numden(J1);
Nc = coeffs(N, T, 'all');
Dc = coeffs(D, T, 'all');

Now Nc are the numerator coefficients and Dc are the denominator coefficients.

Related Solutions

MATLAB: Can’t separate the two variables for which solution needs to be found

Well, you can reduce everything down to an expression in p and L, generating a 15th degree polynomial if solved for p, or a 12th degree polynomial if solved for L. There are, of course, no analytical roots for either of them.

To make the expression clearer, I will show it collected by p within L, and by L within p:

(-p^12 + (4*p^12-24*p^11+72*p^10-152*p^9+252*p^8-336*p^7+368*p^6-336*p^5+252*p^4-152*p^3+72*p^2-24*p+4)*L^11 + (-12*p^13+24*p^12+24*p^11-132*p^10+264*p^9-384*p^8+384*p^7-264*p^6+132*p^5-24*p^4-24*p^3+12*p^2)*L^10 + p^10 + (12*p^14+60*p^13-216*p^12+240*p^11-260*p^10+292*p^9-132*p^8+16*p^7+56*p^6-188*p^5+188*p^4-96*p^3+32*p^2-4*p)*L^9 + (-4*p^15-96*p^14-24*p^13+376*p^12-348*p^11+383*p^10-407*p^9+36*p^8+116*p^7-46*p^6-22*p^5+40*p^4-5*p^2+p)*L^8 + (36*p^15+252*p^14-240*p^13-120*p^12+39*p^11-138*p^10+276*p^9-312*p^8+194*p^7+48*p^6-52*p^5+16*p^4+3*p^3-2*p^2)*L^7 + (-108*p^15-204*p^14+332*p^13-175*p^12-105*p^11+150*p^10+98*p^9+22*p^8-62*p^7+63*p^6-p^5-12*p^4+2*p^3)*L^6 + (108*p^15-72*p^14-119*p^13+364*p^12-82*p^11-63*p^10+119*p^9+23*p^8-10*p^7-28*p^6+32*p^5-22*p^4+6*p^3)*L^5 + (108*p^14-54*p^13-37*p^12+166*p^11-43*p^10-29*p^9+18*p^8+26*p^7-45*p^6+16*p^5+3*p^4-p^3)*L^4 + (45*p^13-29*p^12-16*p^11+47*p^10-21*p^9-23*p^8+17*p^7+9*p^6-6*p^5+p^4)*L^3 + (p^13+17*p^12-20*p^11+3*p^10+11*p^9+5*p^8-9*p^7+3*p^6)*L^2 + (-3*p^13+3*p^12+3*p^11-2*p^10-4*p^9+3*p^8)*L) / ((p-1)*(p^4+(p^4-2*p^3+2*p^2-2*p+1)*L^3+p^3+(-p^5-2*p^4+2*p^3+p^2)*L^2+(3*p^5+p)*L)*(-p^2+(p-1)*L)^2*p^2)

Or alternately,

((-4*L^8+36*L^7-108*L^6+108*L^5)*p^15 + (12*L^9-96*L^8+252*L^7-204*L^6-72*L^5+108*L^4)*p^14 + (-12*L^10+60*L^9-24*L^8-240*L^7+332*L^6-119*L^5-54*L^4+45*L^3+L^2-3*L)*p^13 + (4*L^11+24*L^10-216*L^9+376*L^8-120*L^7-175*L^6+364*L^5-37*L^4-29*L^3+17*L^2+3*L-1)*p^12 + 4*L^11 + (-24*L^11+24*L^10+240*L^9-348*L^8+39*L^7-105*L^6-82*L^5+166*L^4-16*L^3-20*L^2+3*L)*p^11 + (72*L^11-132*L^10-260*L^9+383*L^8-138*L^7+150*L^6-63*L^5-43*L^4+47*L^3+3*L^2-2*L+1)*p^10 + (-152*L^11+264*L^10+292*L^9-407*L^8+276*L^7+98*L^6+119*L^5-29*L^4-21*L^3+11*L^2-4*L)*p^9 + (252*L^11-384*L^10-132*L^9+36*L^8-312*L^7+22*L^6+23*L^5+18*L^4-23*L^3+5*L^2+3*L)*p^8 + (-336*L^11+384*L^10+16*L^9+116*L^8+194*L^7-62*L^6-10*L^5+26*L^4+17*L^3-9*L^2)*p^7 + (368*L^11-264*L^10+56*L^9-46*L^8+48*L^7+63*L^6-28*L^5-45*L^4+9*L^3+3*L^2)*p^6 + (-336*L^11+132*L^10-188*L^9-22*L^8-52*L^7-L^6+32*L^5+16*L^4-6*L^3)*p^5 + (252*L^11-24*L^10+188*L^9+40*L^8+16*L^7-12*L^6-22*L^5+3*L^4+L^3)*p^4 + (-152*L^11-24*L^10-96*L^9+3*L^7+2*L^6+6*L^5-L^4)*p^3 + (72*L^11+12*L^10+32*L^9-5*L^8-2*L^7)*p^2 + (-24*L^11-4*L^9+L^8)*p) / ((p-1)*((-L^2+3*L)*p^5+(L^3-2*L^2+1)*p^4+L^3+(-2*L^3+2*L^2+1)*p^3+(2*L^3+L^2)*p^2+(-2*L^3+L)*p)*(L*p-p^2-L)^2*p^2)

Not so nice, either way you look at it.

If you examine the first variant, collected by L, and look at the denominator, you can see that the expression blows up for several cases -- p = 0, p = 1, p = L/2 +/- sqrt(L^2-4*L)/2, or p^4+(p^4-2*p^3+2*p^2-2*p+1)*L^3+p^3+(-p^5-2*p^4+2*p^3+p^2)*L^2+(3*p^5+p)*L = 0 which has 3 roots when solved for L.

The third of those conditions can be expressed as L = p^2/(p-1) which is real-valued for all p except p = 1, so no matter how the cubic behaves, there will be at least one non-solution for each p. In fact the cubic has a minimum of 1 real L root for each positive p (two real solutions beyond a point), and a minimum of two real L roots for each negative p. I believe that the cubic has three real roots for each negative p, but some fancy algebraic mangling would be necessary to prove that those vanishingly small imaginary components are necessarily zero.

Anyhow, for each p there are thus between 1 and 4 L for which x1 and x2 have no solution.

MATLAB: How to use a “for loop” to generate a matrix

H1 = @(R) floor((R-1)/4)*2 + 1;
H2 = @(R) mod(R-1,4)*2 + 18;
Tfun = @(Q,R) P(Q,H1(R))*P(Q,H2(R));
T(3,:) = arrayfun(@(R) Tfun(3,R), 1:16);

Best Answer

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MATLAB: Can’t separate the two variables for which solution needs to be found

MATLAB: How to use a “for loop” to generate a matrix

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