AssociatedEquations(R, L)

lodof.spad line 236 [edit on github]

• R : IntegralDomain
• L : LinearOrdinaryDifferentialOperatorCategory(R)

AssociatedEquations provides functions to compute the associated equations needed for factoring operators

associatedEquations : (L, PositiveInteger) -> Record(minor : List(PositiveInteger), eq : L, minors : List(List(PositiveInteger)), ops : List(L)) if R has Field

associatedEquations(op, m) returns [w, eq, lw, lop] such that eq(w) = 0 where w is the given minor, and lw_i = lop_i(w) for all the other minors.

associatedSystem : (L, PositiveInteger) -> Record(mat : Matrix(R), vec : Vector(List(PositiveInteger)))

associatedSystem(op, m) returns [M, w] such that the m-th associated equation system to L is w' = M w.

uncouplingMatrices : Matrix(R) -> Vector(Matrix(R))

uncouplingMatrices(M) returns [A_1, ..., A_n] such that if y = [y_1, ..., y_n] is a solution of y' = M y, then [$y_j', y_j'', ..., y_j^(n)$] = $A_j y$ for all j's.