# RadicalSolvePackage RΒΆ

- R: Join(EuclideanDomain, Comparable, CharacteristicZero)

This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain `R`

.

- contractSolve: (Equation Fraction Polynomial R, Symbol) -> SuchThat(List Expression R, List Equation Expression R)
`contractSolve(eq, x)`

finds the solutions expressed in terms of radicals of the equation of rational functions`eq`

with respect to the symbol`x`

. The result contains new symbols for common subexpressions in order to reduce the size of the output.

- contractSolve: (Fraction Polynomial R, Symbol) -> SuchThat(List Expression R, List Equation Expression R)
`contractSolve(rf, x)`

finds the solutions expressed in terms of radicals of the equation`rf`

= 0 with respect to the symbol`x`

, where`rf`

is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.

- radicalRoots: (Fraction Polynomial R, Symbol) -> List Expression R
`radicalRoots(rf, x)`

finds the roots expressed in terms of radicals of the rational function`rf`

with respect to the symbol`x`

.

- radicalRoots: (List Fraction Polynomial R, List Symbol) -> List List Expression R
`radicalRoots(lrf, lvar)`

finds the roots expressed in terms of radicals of the list of rational functions`lrf`

with respect to the list of symbols lvar.

- radicalSolve: (Equation Fraction Polynomial R, Symbol) -> List Equation Expression R
`radicalSolve(eq, x)`

finds the solutions expressed in terms of radicals of the equation of rational functions`eq`

with respect to the symbol`x`

.

- radicalSolve: (Fraction Polynomial R, Symbol) -> List Equation Expression R
`radicalSolve(rf, x)`

finds the solutions expressed in terms of radicals of the equation`rf`

= 0 with respect to the symbol`x`

, where`rf`

is a rational function.

- radicalSolve: (List Equation Fraction Polynomial R, List Symbol) -> List List Equation Expression R
`radicalSolve(leq, lvar)`

finds the solutions expressed in terms of radicals of the system of equations of rational functions`leq`

with respect to the list of symbols lvar.

- radicalSolve: (List Fraction Polynomial R, List Symbol) -> List List Equation Expression R
`radicalSolve(lrf, lvar)`

finds the solutions expressed in terms of radicals of the system of equations`lrf`

= 0 with respect to the list of symbols lvar, where`lrf`

is a list of rational functions.

- radicalSolve: Equation Fraction Polynomial R -> List Equation Expression R
`radicalSolve(eq)`

finds the solutions expressed in terms of radicals of the equation of rational functions`eq`

with respect to the unique symbol`x`

appearing in`eq`

.

- radicalSolve: Fraction Polynomial R -> List Equation Expression R
`radicalSolve(rf)`

finds the solutions expressed in terms of radicals of the equation`rf`

= 0, where`rf`

is a univariate rational function.

- radicalSolve: List Equation Fraction Polynomial R -> List List Equation Expression R
`radicalSolve(leq)`

finds the solutions expressed in terms of radicals of the system of equations of rational functions`leq`

with respect to all symbols appearing in`leq`

.

- radicalSolve: List Fraction Polynomial R -> List List Equation Expression R
`radicalSolve(lrf)`

finds the solutions expressed in terms of radicals of the system of equations`lrf`

= 0, where`lrf`

is a list of rational functions.