e/Symbol of a differential operator

Information
has gloss	eng: In mathematics, the symbol of a linear differential operator associates to a differential operator a polynomial by, roughly speaking, replacing each partial derivative by a new variable. The symbol of a differential operator has broad applications to Fourier analysis. In particular, in this connection it leads to the notion of a pseudo-differential operator. The highest-order terms of the symbol, known as the principal symbol, almost completely controls the qualitative behavior of solutions of a partial differential equation. Linear elliptic partial differential equations can be characterized as those whose principal symbol is nowhere zero. In the study of hyperbolic and parabolic partial differential equations, zeros of the principal symbol correspond to the characteristics. Consequently, the symbol is often fundamental for the solution of such equations, and are one of the main computational devices used to study their singularities.
lexicalization	eng: Symbol of a differential operator
instance of	e/Differential operator