Greatest Common Divisor of Two Polynomials - GCD Over A Ring and Over Its Field of Fractions

GCD Over A Ring and Over Its Field of Fractions

In this section, we consider polynomials over a unique factorization domain R, typically the ring of the integers, and over its field of fractions F, typically the field of the rational numbers, and we denote R and F the rings of polynomials in a set of variables over these rings.

Read more about this topic:  Greatest Common Divisor Of Two Polynomials

Famous quotes containing the words ring and/or field:

    He will not idly dance at his work who has wood to cut and cord before nightfall in the short days of winter; but every stroke will be husbanded, and ring soberly through the wood; and so will the strokes of that scholar’s pen, which at evening record the story of the day, ring soberly, yet cheerily, on the ear of the reader, long after the echoes of his axe have died away.
    Henry David Thoreau (1817–1862)

    And they wonder, as waiting the long years through
    In the dust of that little chair,
    What has become of our Little Boy Blue,
    Since he kissed them and put them there.
    —Eugene Field (1850–1895)