polynom - Maple Help

RandomTools Flavor: polynom

describe a flavor of a random polynomial

 Calling Sequence polynom(coeffs, x, opt)

Parameters

 coeffs - flavor of the coefficients x - name or a set or list of names opt - (optional) equation of the form $\mathrm{degree}=n$ where $n$ is a non-negative integer; specify options for the random polynomial

Description

 • The flavor polynom(coeffs, x) describes a random polynomial in a given number of variables x with coefficients coeffs of a given random flavor.
 To describe a flavor of a random polynomial, use either polynom(coeffs, x) or polynom(coeffs, x, opt) (where opt is described following) as the argument to RandomTools[Generate] or as part of a structured flavor.
 • By default, the flavor polynom(coeffs, x) describes a random polynomial in the given variable(s) of degree $5$.
 • You can modify the properties of the random polynomial by specifying opt as the equation $\mathrm{degree}=n$, where n is a non-negative integer that indicates the degree of the polynomial. By default, the degree of the polynomial is set to $5$.

Examples

 > $\mathrm{with}\left(\mathrm{RandomTools}\right):$
 > $\mathrm{Generate}\left(\mathrm{polynom}\left(\mathrm{rational},x\right)\right)$
 ${-}\frac{{104281139459}}{{499999999994}}{-}\frac{{153430091789}}{{249999999997}}{}{x}{-}\frac{{238787914764}}{{249999999997}}{}{{x}}^{{2}}{+}\frac{{150093742233}}{{249999999997}}{}{{x}}^{{3}}{-}\frac{{36223971562}}{{249999999997}}{}{{x}}^{{4}}{+}\frac{{342622684449}}{{499999999994}}{}{{x}}^{{5}}$ (1)
 > $\mathrm{Generate}\left(\mathrm{polynom}\left(\mathrm{positive}\left(\mathrm{denominator}=12\right),x,\mathrm{degree}=10\right)\right)$
 $\frac{{1}}{{12}}{+}\frac{{2}}{{3}}{}{x}{+}\frac{{5}}{{12}}{}{{x}}^{{2}}{+}\frac{{5}}{{6}}{}{{x}}^{{3}}{+}\frac{{11}}{{12}}{}{{x}}^{{4}}{+}\frac{{1}}{{6}}{}{{x}}^{{5}}{+}\frac{{1}}{{6}}{}{{x}}^{{6}}{+}\frac{{1}}{{3}}{}{{x}}^{{7}}{+}\frac{{2}}{{3}}{}{{x}}^{{8}}{+}\frac{{11}}{{12}}{}{{x}}^{{9}}{+}\frac{{1}}{{4}}{}{{x}}^{{10}}$ (2)
 > $\mathrm{Generate}\left(\mathrm{polynom}\left(\mathrm{nonnegint}\left(\mathrm{range}=2\right),\left\{x,y\right\}\right)\right)$
 ${y}{}{{x}}^{{4}}{+}{2}{}{{y}}^{{2}}{}{{x}}^{{3}}{+}{2}{}{{x}}^{{2}}{}{{y}}^{{3}}{+}{2}{}{x}{}{{y}}^{{4}}{+}{2}{}{{y}}^{{5}}{+}{y}{}{{x}}^{{3}}{+}{2}{}{{x}}^{{2}}{}{{y}}^{{2}}{+}{{y}}^{{4}}{+}{{x}}^{{3}}{+}{y}{}{{x}}^{{2}}{+}{2}{}{x}{}{{y}}^{{2}}{+}{{x}}^{{2}}{+}{x}{}{y}{+}{2}{}{{y}}^{{2}}{+}{x}$ (3)