By abuse of language, this terminology will be applied both to the original system and the ideal of differential polynomials generated by the left hand sides.
2.
Given a system of linear differential polynomials S \ equiv \ { e _ 1, e _ 2, \ ldots \ }, the Janet basis corresponding to S is returned.
3.
The left hand sides of such systems of equations may be considered as differential polynomials of a ring, and Janet's normal form as a special basis of the ideal that they generate.
4.
An extension " F " ?" " K " of differential fields is called a Picard Vessiot extension if all constants are in " F " and " K " can be generated by adjoining the solutions of a homogeneous linear ordinary differential polynomial.
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