1. Notation for monomials is constantly required in fields like partial differential equations. 2. For the case of Geometric Moments, X would be the monomials . 3. We may define the set of all " monomials " M recursively as follows: 4. Often one may think of the space as spanned by all suitable field monomials . 5. Order the monomials in the variables multi-index notation for monomials in the variables. 6. Order the monomials in the variables multi-index notation for monomials in the variables. 7. A prominent example of this circle of ideas is given by the theory of standard monomials . 8. The choice of a total order on the monomials allows sorting the terms of a polynomial. 9. The exponents of the monomials of a critical Lagrangian define a hyperplane in an exponent space. 10. It is enough to check this for monomials in the " e "'s.
