PureAlgebraicLODE(F, UP, UPUP, R)¶
- 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(
- algDsolve: (LinearOrdinaryDifferentialOperator1 R, R) -> Record(particular: Union(R, failed), basis: List R)
["failed", ]if the equation
op y = ghas no solution in
R. Otherwise, it returns
[f, [y1, ..., ym]]where
fis a particular rational solution and the
y_i'sform a basis for the solutions in
Rof the homogeneous equation.