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.