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“Equation” in the following means the equation expression = 0. Equations are solved for a symbolic variable x by the function solve(expression, x). If expression is a quotient, then nominator = 0 is solved. It uses the following strategy to solve equations:

- Unordered List ItemFirst, all occurrences of the variable x in expression
- are counted, both as free variable and embedded inside functions. Example:
- In $x^3\cdot\sin(x)+2x^2-\sqrt{x-1}$ x occurs three times: as free
- variable, in $\sin(x)$ and in $\sqrt{x-1}$.

- Unordered List ItemIf this count is one, then we are dealing with a
- polynomic equation, which is solved for the polynomial's main variable,
- e.g. z. This works always, if the polynomial's degree is 2 or of it is
- biquadratic, otherwise only, if the coefficients are constant. In the next
- step the solution is solved for the desired variable x. As an example:
- One can solve $\sin^2(x)-2\sin(x)+1=0$ for $x$. It first solves
- $z^2-2z+1=0$ for $z$ and then $\sin(x)=z$ for $x$. Examples with free
- variables:

An example with function variable ($exp(j\cdot x)$):

- Unordered List ItemIf count is 2, only one case is further considered: The
- variable occurs free and inside squareroot. This squareroot is then
- isolated, the equation squared and solved. This case leads to additional
- false solutions, which have to be sorted out manually.

- Unordered List ItemIn all other cases Jasymca gives up.