Simbolic Tbx: how to solve trigonometric equation with polynoms?

Let

>> syms y z
>> syms x y z
>> y=sym('- 9*x^4 + 7*x^3 - 13*x^2 + 3*x');z=sym('(1+x)^3');

Working

>> solve(subs('z*y-1=0'))

Working (although one root)

>> solve(subs('sin(z)=0'))

NOT Working

>> solve(subs('sin(y*z-1)=0'))
ans =
solvelib::Union(RootOf(X458^7 + (20*X458^6)/9 +...

How to solve eq. (within Simbolic Tbx)? Even one root...

Answer 1

[Walter Roberson]

The Union is the result, in symbolic form. A Union is a "set" (in mathematical terms). RootOf() of higher order polynomials are not taken unless specifically requested, partly because usually they can only be numerically approximated.

What I suggest is that you use vpa() or double() on the returned answer.

[Igor]

>> format compact

>> res=solve(subs('sin(y*z-1)=0'))

res =

solvelib::Union(RootOf(X38^7 + (20*X38^6)/9 + ...), X34, Z_)

>> double(res)

??? Error using ==> mupadmex

Error in MuPAD command: DOUBLE cannot convert the input expression into a double array.

If the input expression contains a symbolic variable, use the VPA function instead.

Error in ==> sym.sym>sym.double at 927

Xstr = mupadmex('mllib::double', S.s, 0);

>> vpa(res)

ans =

solvelib::Union(RootOf(X42^7 + (20*X42^6)/9 + ...

[Igor]

you see -- no motion further the answer Rootof()

[Walter Roberson]

Checking the documentation, http://www.mathworks.com/help/toolbox/mupad/solvelib/Union.html it appears to me that there is a family of solutions in a free parameter that is an integer. If you want one particular solution, evaluate res with something (e.g., 0) substituted for Z_ and then double() that to get a numeric value.