PrimitiveRatDE(F, UP, L, LQ)

oderf.spad line 73 [edit on github]

PrimitiveRatDE provides functions for in-field solutions of linear ordinary differential equations, in the transcendental case. The derivation to use is given by the parameter L.

denomLODE : (L, List(Fraction(UP))) -> UP

denomLODE(op, [g1, ..., gm]) returns a polynomial d such that any rational solution of op y = c1 g1 + ... + cm gm is of the form p/d for some polynomial p.

denomLODE : (L, Fraction(UP)) -> Union(UP, "failed")

denomLODE(op, g) returns a polynomial d such that any rational solution of op y = g is of the form p/d for some polynomial p, and "failed", if the equation has no rational solution.

indicialEquation : (L, F) -> UP

indicialEquation(op, a) returns the indicial equation of op at a.

indicialEquation : (LQ, F) -> UP

indicialEquation(op, a) returns the indicial equation of op at a.

indicialEquations : L -> List(Record(center : UP, equation : UP))

indicialEquations op returns [[d1, e1], ..., [dq, eq]] where the d_i's are the affine singularities of op, and the e_i's are the indicial equations at each d_i.

indicialEquations : (L, UP) -> List(Record(center : UP, equation : UP))

indicialEquations(op, p) returns [[d1, e1], ..., [dq, eq]] where the d_i's are the affine singularities of op above the roots of p, and the e_i's are the indicial equations at each d_i.

indicialEquations : LQ -> List(Record(center : UP, equation : UP))

indicialEquations op returns [[d1, e1], ..., [dq, eq]] where the d_i's are the affine singularities of op, and the e_i's are the indicial equations at each d_i.

indicialEquations : (LQ, UP) -> List(Record(center : UP, equation : UP))

indicialEquations(op, p) returns [[d1, e1], ..., [dq, eq]] where the d_i's are the affine singularities of op above the roots of p, and the e_i's are the indicial equations at each d_i.

splitDenominator : (LQ, List(Fraction(UP))) -> Record(eq : L, rh : List(Fraction(UP)))

splitDenominator(op, [g1, ..., gm]) returns op0, [h1, ..., hm] such that the equations op y = c1 g1 + ... + cm gm and op0 y = c1 h1 + ... + cm hm have the same solutions.