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For example, itself is a separating set for the pair, as is ′. If a pair of disjoint sets A {\displaystyle A} and B {\displaystyle B} has no computable separating set, then the two sets are computably inseparable .
Purely inseparable extensions do occur naturally; for example, they occur in algebraic geometry over fields of prime characteristic. If K is a field of characteristic p , and if V is an algebraic variety over K of dimension greater than zero, the function field K ( V ) is a purely inseparable extension over the subfield K ( V ) p of p th powers ...
In field theory, a branch of algebra, an algebraic field extension / is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). [1]
Inseparable extensions (that is, extensions which are not separable) may occur only in positive characteristic. The criterion above leads to the quick conclusion that if P is irreducible and not separable, then D P(X) = 0. Thus we must have P(X) = Q(X p) for some polynomial Q over K, where the prime number p is the characteristic.
Examples of such separated services include freight transportation, dry cleaning, and routine maintenance on a wide array of equipment and facilities. Lovelock and Gummesson (2004) conclude that only one category of services — physical acts to customers' bodies, such as a haircut or medical examination — is inseparate. In the other three ...
Inseparable differential equation, an ordinary differential equation that cannot be solved by using separation of variables; Inseparable extension, a field extension by elements that do not all satisfy a separable polynomial; Inseparable polynomial, a polynomial that does not have distinct roots in a splitting field
Hamilton is an example of that—it’s historical, but that was completely original. ... There is a level to which theater kids are never going to be inseparable from that insufferability, the ...
For some equations involving mixed derivatives, the equation does not separate as easily as the heat equation did in the first example above, but nonetheless separation of variables may still be applied. Consider the two-dimensional biharmonic equation