RadicalSolvePackage R¶

R: Join(PolynomialFactorizationExplicit, 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.

cyclotomic_case?: SparseUnivariatePolynomial Polynomial R -> Union(Integer, failed): cyclotomic_case?(u) should be local but conditional

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.