PureAlgebraicLODE(F, UP, UPUP, R)

odeef.spad line 252 [edit on github]

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

In-field solution of an linear ordinary differential equation, pure algebraic case.

algDsolve : (LinearOrdinaryDifferentialOperator1(R), List(R)) -> Record(particular : List(Record(ratpart : R, coeffs : Vector(F))), basis : List(R))

algDsolve(op, lg) is a parametric version of algDsolve(op, g)

algDsolve : (LinearOrdinaryDifferentialOperator1(R), R) -> Record(particular : Union(R, "failed"), basis : List(R))

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