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.