Abstract
Different first order representations of high order linear PDEs, depending on which notion of the degree of a polynomial is chosen, are possible. Two notions of degree, namely, the total degree and multi-degree, are standard and the most natural. In our recent article, a straightforward way was provided to convert a system of high order constant coefficient linear PDEs into a system of first order PDEs based on the notion of total degree. In the present article, an analogous development is carried out in the multi-degree setting.
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