For a map f between a compact manifold M and connected manifold N, this quantity modulo two is defined as the order of the preimage of a regular value modulo two.
For a map f between a compact manifold M and connected manifold N, this quantity modulo two is defined as the order of the preimage of a regular value modulo two. For a homogeneous function f, Euler showed that the sum, over i, of x-sub-i times the partial of f with respect to x-sub-i, is equal to this quantity times f. This word is used to denote the dimension of a field extension as a vector space over its base field. Abel, Ruffini, and Galois (gal-WAH) independently showed that there is no general algebraic formula for the roots of certain functions that have a value of this quantity that is larger than five. Depending on convention, this value is either equal to negative infinity or zero for the zero polynomial. For 10 points, what word describes the largest exponent of a polynomial's terms?
For a map f between a compact manifold M and connected manifold N, this quantity modulo two is defined as the order of the preimage of a regular value modulo two.
degree [or deg; or order]