RadicalSolvePackage(R)

solverad.spad line 325 [edit on github]

• 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))) -> 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 : (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)) -> 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 : (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(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(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(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.

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.

radical_solve : SparseUnivariatePolynomial(Polynomial(R)) -> Union(List(Expression(R)), "failed")

radical_solve(p) should be local but conditional