MAGMA Computational Algebra System

Wronskian Matrix

Let R be a differential ring and let y₁, y₂, ..., y_n be elements of R. The wronskian matrix of y₁, y₂, ..., y_n is defined as the n x n matrix

The wronskian determinant, or simply the wronskian, of y₁, y₂, ..., y_n is the determinant of the wronskian matrix W(y₁, y₂, ..., y_n).

WronskianMatrix(L) : [RngDiffElt] -> AlgMatElt

Given a sequence of differential ring elements L, return the Wronskian matrix of L whose entries are elements of the universe of L.

WronskianDeterminant(L) : [RngDiffElt] -> RngDiffElt, AlgMatElt

Given a sequence of differential ring elements L, return the determinant of the Wronskian matrix of L as well as the matrix itself.

Example RngDiff_wronskian-mat-det (H97E23)

> F<z> := RationalDifferentialField(Rationals());
> WronskianMatrix([1,z,z^2]);
[1 z z^2]
[0 1 2*z]
[0 0 2]
> WronskianDeterminant([1,z^2,1/z]);
6/z 
[z z^2 1/z]
[1 2*z -1/z^2]
[0 2 2/z^3]