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An irreducible fraction is a fraction p/q for which GCD(p,q)=1, i.e., p and q are relatively prime. For example, in the complex plane, (4+7i)/(2+i)=3+2i is reducible, while ...

If X is any compact space, let A be a subalgebra of the algebra C(X) over the reals R with binary operations + and ×. Then, if A contains the constant functions and separates ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

A tetraview is a visualization technique for bivariate complex functions. In the simplest case, the graph of a complex-valued function w=w(z) can be considered as a ...

A Tschirnhausen transformation can be used to take a general quintic equation to the form x^5-x-a=0, where a may be complex.

The ordered pair (s,t), where s is the number of real embeddings of the number field and t is the number of complex-conjugate pairs of embeddings. The degree of the number ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

Any complex measure lambda decomposes into an absolutely continuous measure lambda_a and a singular measure lambda_c, with respect to some positive measure mu. This is the ...

The vector field N_f(z)=-(f(z))/(f^'(z)) arising in the definition of the Newtonian graph of a complex univariate polynomial f (Smale 1985, Shub et al. 1988, Kozen and ...

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.