Content

There are several meanings of the word content in mathematics.

The content of a polytope or other -dimensional object is its generalized volume (i.e., its "hypervolume"). Just as a three-dimensional object has volume, surface area, and generalized diameter, an -dimensional object has "measures" of order 1, 2, ..., . The content of a region can be computed in the Wolfram Language using RegionMeasure[reg].

The content of an integer polynomial , denoted , is the largest integer  such that  also has integer coefficients. Gauss's lemma for contents states that if  and  are two polynomials with integer coefficients, then  (Séroul 2000, p. 287).

For a general univariate polynomial , the Wolfram Language command FactorTermsList[poly, x] returns a list of three elements, the first being the integer content , the second being the polynomial content, i.e., a primitive (with respect to all variables) polynomial that does not depend on  and which divides all coefficients of , and the third element being the primitive part of . The original polynomial  is then the product of these three parts. For example, FactorTermsList[9E x^3+3E, x] returns 3, E, 1+3x^2.

REFERENCES:

Séroul, R. Programming for Mathematicians. Berlin: Springer-Verlag, p. 287, 2000.