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.