MATLAB: Is there a method for solving inequalities using the Symbolic Math Toolbox 5.6 (R2011a)

inequalitysolvesymbolicSymbolic Math Toolbox

I would like to find a range of "x" that satisfies the following inequality:

x^2 - 4*x + 3 < 0

resulting in, for example,

1 < x < 3

Best Answer

MuPad's SOLVE function can handle inequalities. For example, after typing 'mupad' at the command prompt to bring up the MuPAD window, type

solve(x^2 - 4*x + 3 < 0, x, Real)

The following is returned:

(1, 3)

By including the option "Real", MuPAD limits the solutions to real values of "x". You can exclude the option "Real" if you want to obtain complex solutions.

Related Solutions

MATLAB: Is SIMPLIFY not able to simplify a straightforward expression in Symbolic Math Toolbox 5.3 (R2009b)

This is the expected behavior of the SIMPLIFY function in the Symbolic Math Toolbox 5.3 (R2009b). By default, the function tries to make as few assumptions about the symbolic variables as possible. Considering the above 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

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

MATLAB: MeijerG function using MATLAB’s symbolic toolbox

As of R2017b, the function "meijerG" calculates the Meijer G-Function. This function can return either numerical values or symbolic expressions for the Meijer G-Function depending upon the input.

For 'double' inputs, "meijerG" returns a double, as shown below:

>> meijerG(3, [], [], [], 3)

ans =

6.4488

For 'sym' inputs, "meijerG" will return an exact symbolic answer whenever possible. An example is shown below:

>> meijerG(sym(2/5), [], sym(1/2), [], sym(3))

ans =

(2^(4/5)*3^(1/2)*gamma(1/10))/80

The documentation linked below has more details about "meijerG"'s full functionality:

https://www.mathworks.com/help/symbolic/meijerg.html

For prior releases, the symbolic MeijerG function is only available in MuPAD. From MATLAB, it must be evaluated using "evalin", as shown below:

>> y=evalin(symengine, 'simplify(meijerG([[3],[]], [[],[]],3))');

y =

9*exp(-1/3)

Once this command executes, 'y' will contain symbolic MeijerG function for given arguments.

Note that without the call to "simplify", an expression in terms of the MuPAD function "meijerG" may be returned, which will not be understood by MATLAB in further function calls. You can pass this back to "evalin" by first converting it with the "char" function, but this workflow is not recommended.

Best Answer

Related Solutions

MATLAB: Is SIMPLIFY not able to simplify a straightforward expression in Symbolic Math Toolbox 5.3 (R2009b)

MATLAB: MeijerG function using MATLAB’s symbolic toolbox

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