content - Maple Programming Help

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content

content of a multivariate polynomial

primpart

primpart of a multivariate polynomial

 Calling Sequence content(a, x, 'pp') primpart(a, x, 'co')

Parameters

 a - multivariate polynomial in x x - (optional) name or set or list of names pp - (optional) unevaluated name co - (optional) unevaluated name

Description

 • If a is a multivariate polynomial with integer coefficients, content returns the content of a with respect to x, thus returning the greatest common divisor of the coefficients of a with respect to the indeterminate(s) x.  The indeterminate(s) x can be a name, list, or set of names.
 • The third argument pp, if present, will be assigned the primitive part of a, namely a divided by the content of a.
 • If the coefficients of a in x are rational functions then the content computed will be such that the primitive part is a multivariate polynomial over the integers whose content is 1.
 • Similarly, primpart returns a/content(a, x). The third argument co, if present, will be assigned the content. Note:  Whereas the sign is removed from the content, it is not removed from the primitive part.

Examples

 > $\mathrm{content}\left(3-3x,x\right)$
 ${3}$ (1)
 > $\mathrm{content}\left(3xy+6{y}^{2},x\right)$
 ${3}{}{y}$ (2)
 > $\mathrm{content}\left(3xy+6{y}^{2},\left[x,y\right]\right)$
 ${3}$ (3)
 > $\mathrm{content}\left(-4xy+6{y}^{2},x,'\mathrm{pp}'\right)$
 ${2}{}{y}$ (4)
 > $\mathrm{pp}$
 ${3}{}{y}{-}{2}{}{x}$ (5)
 > $\mathrm{content}\left(\frac{x}{a}-\frac{1}{2},x,'\mathrm{pp}'\right)$
 $\frac{{1}}{{2}{}{a}}$ (6)
 > $\mathrm{pp}$
 ${2}{}{x}{-}{a}$ (7)
 > $\mathrm{primpart}\left(-4xy+6{y}^{2},x\right)$
 ${3}{}{y}{-}{2}{}{x}$ (8)
 > $\mathrm{primpart}\left(\frac{x}{a}-\frac{1}{2},x\right)$
 ${2}{}{x}{-}{a}$ (9)

 See Also

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