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