# TransSolvePackage R¶

This package tries to find solutions of equations of type Expression(R). This means expressions involving transcendental, exponential, logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules, it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression sin(x)*cos(x)-2 will be transformed to -2 tan(x/2)^4 -2 tan(x/2)^3 -4 tan(x/2)^2 +2 tan(x/2) -2 by using the function normalize and then to -2 tan(x)^2 + tan(x) -2 with help of subsTan. This function tries to express the given function in terms of tan(x/2) to express in terms of tan(x) . Other examples are the expressions sqrt(x+1)+sqrt(x+7)+1 or sqrt(sin(x))+1 .

solve: (Equation Expression R, Symbol) -> List Equation Expression R
solve(eq, x) finds the solutions of the equation eq where eq is an equation of functions of type Expression(R) with respect to the symbol x.
solve: (Expression R, Symbol) -> List Equation Expression R
solve(expr, x) finds the solutions of the equation expr = 0 with respect to the symbol x where expr is a function of type Expression(R).
solve: (List Equation Expression R, List Expression R) -> List List Equation Expression R
solve(leqs, lexpr) returns a list of solutions to the list of equations leqs with respect to the list of expressions lexpr. Each expression in lexpr is treated as a variable and must be a single kernel.
solve: (List Equation Expression R, List Kernel Expression R) -> List List Equation Expression R
solve(leqs, lker) returns a list of solutions to the list of equations leqs with respect to the list of kernels lker.
solve: (List Equation Expression R, List Symbol) -> List List Equation Expression R
solve(leqs, lvar) returns a list of solutions to the list of equations leqs with respect to the list of symbols lvar.
solve: Equation Expression R -> List Equation Expression R
solve(eq) finds the solutions of the equation eq where eq is an equation of functions of type Expression(R) with respect to the unique symbol x appearing in eq.
solve: Expression R -> List Equation Expression R
solve(expr) finds the solutions of the equation expr = 0 where expr is a function of type Expression(R) with respect to the unique symbol x appearing in eq.