RationalLODE(F, UP)

oderf.spad line 302 [edit on github]

• F : Join(Field, CharacteristicZero, RetractableTo(Integer), RetractableTo(Fraction(Integer)))
• UP : UnivariatePolynomialCategory(F)

RationalLODE provides functions for in-field solutions of linear ordinary differential equations, in the rational case.

indicialEquationAtInfinity : LinearOrdinaryDifferentialOperator1(Fraction(UP)) -> UP

indicialEquationAtInfinity op returns the indicial equation of op at infinity.

indicialEquationAtInfinity : LinearOrdinaryDifferentialOperator2(UP, Fraction(UP)) -> UP

indicialEquationAtInfinity op returns the indicial equation of op at infinity.

integrate_sols : LinearOrdinaryDifferentialOperator1(Fraction(UP)) -> Record(ltilde : LinearOrdinaryDifferentialOperator1(Fraction(UP)), r : Union(LinearOrdinaryDifferentialOperator1(Fraction(UP)), "failed"))

integrate_sols(l) integrates the solutions of an operator l.

ratDsolve : (LinearOrdinaryDifferentialOperator1(Fraction(UP)), List(Fraction(UP))) -> Record(basis : List(Fraction(UP)), mat : Matrix(F))

ratDsolve(op, [g1, ..., gm]) returns [[h1, ..., hq], M] such that any rational solution of op y = c1 g1 + ... + cm gm is of the form c1 h1 + ... + cq hq where M [c1, ..., cq] = 0 and q >= m.

ratDsolve : (LinearOrdinaryDifferentialOperator2(UP, Fraction(UP)), List(Fraction(UP))) -> Record(basis : List(Fraction(UP)), mat : Matrix(F))

ratDsolve(op, [g1, ..., gm]) returns [[h1, ..., hq], M] such that any rational solution of op y = c1 g1 + ... + cm gm is of the form c1 h1 + ... + cq hq where M [c1, ..., cq] = 0 and q >= m.

ratDsolve : (LinearOrdinaryDifferentialOperator1(Fraction(UP)), Fraction(UP)) -> Record(particular : Union(Fraction(UP), "failed"), basis : List(Fraction(UP)))

ratDsolve(op, g) returns ["failed", []] if the equation op y = g has no rational solution. Otherwise, it returns [f, [y1, ..., ym]] where f is a particular rational solution and the yi's form a basis for the rational solutions of the homogeneous equation.

ratDsolve : (LinearOrdinaryDifferentialOperator2(UP, Fraction(UP)), Fraction(UP)) -> Record(particular : Union(Fraction(UP), "failed"), basis : List(Fraction(UP)))

ratDsolve(op, g) returns ["failed", []] if the equation op y = g has no rational solution. Otherwise, it returns [f, [y1, ..., ym]] where f is a particular rational solution and the yi's form a basis for the rational solutions of the homogeneous equation.