MATLAB: Is it wrong: e3=sym(‘sin(x)^2+cos(x)=0’)

MATLABr2018bsymbolicSymbolic Math Toolbox

Why is it wrong: e3=sym('sin(x)^2+cos(x)=0')

Best Answer

sym('') was replaced by str2sym('') in latest versions and you seem to be using 2018b version

e3=str2sym('sin(x)^2+cos(x)=0')
%  ^^^^^^^

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MATLAB: Is the simplify function not simplifying

This is the expected behavior of the SIMPLIFY function in the Symbolic Math Toolbox. By default, the function tries to make as few assumptions about the symbolic variables as possible. Considering a simple example, the expression 'log(exp(x))' cannot always be simplified to the expression 'x'. In particular, consider if x = 2*pi*i (where i is the imaginary unit). Then log(exp(x)) = 0, which is clearly not equal to x.

In order to do simplifications with looser assumptions about the symbolic variables, call the MuPAD SIMPLIFY function in the MuPAD notebook interface or in MATLAB through the FEVAL or EVALIN commands. Using the MuPAD command directly allows the inclusion of the 'IgnoreAnalyticConstraints' option which controls the level of mathematical rigor that the solver uses on the analytical constraints on the solution.

For example:

syms x
feval(symengine,'simplify',log(exp(x)),'IgnoreAnalyticConstraints')

For more information on the MuPAD SIMPLIFY command, the 'IgnoreAnalyticConstraints' option, and other options which can be used with the MuPAD SIMPLIFY command you may refer to:

http://www.mathworks.com/help/releases/R2009b/toolbox/mupad/stdlib/simplify.html and http://www.mathworks.com/help/releases/R2009b/toolbox/mupad/stdlib/newSimplify.html

MATLAB: FSOLVE requires all values returned by functions to be of data type double.

If you want to solve a system of equations symbolically or using symbolic variables, use the solve function instead of fsolve. The fsolve function requires that the output of the function you specify as the first input be double precision numbers, not symbolic expressions.

If you must use fsolve with symbolic variables inside the function, you must convert those symbolic expressions into numbers using double before returning the numbers (not the symbolic expressions) from the function.

As a very simple example, put all this code into a function example373677.m and run it:

function y = example373677
y = fsolve(@mysubfun, 3);
 
function z = mysubfun(q)
x = sym('x');
r = x.^3-2*x-5;
z = double(subs(r, q));

Of course, with solve this is easier.

syms x
y = solve(x.^3-2*x-5)

You may need to use vpa to approximate y numerically.

vpa(y)

One of the solutions returned in y should match the result you received from running the function.

Best Answer

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MATLAB: Is the simplify function not simplifying

MATLAB: FSOLVE requires all values returned by functions to be of data type double.

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