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Content

inert content function

Primpart

inert primitive part function

 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

 • Content and Primpart are placeholders for a content and primitive part of a polynomial over a coefficient domain. They are used in conjunction with mod and evala as described below.
 • The calls Content(a, x) mod p and Primpart(a, x) mod p compute the content and primitive part of a respectively modulo the prime integer p. The argument a must be a multivariate polynomial over the rationals or over a finite field specified by RootOfs. See content for more information.
 • The calls evala(Content(a,x)) and evala(Primpart(a,x)) compute a content and a primitive part of a respectively over a coefficient domain which may include algebraic numbers and algebraic functions.  The polynomial a must be a multivariate polynomial with algebraic number (or function) coefficients specified by RootOfs or radicals. See evala,Content for more information.
 • The optional arguments 'pp' and 'co' are assigned a/Content(a) and a/Primpart(a) respectively, computed over the appropriate coefficient domain.

Examples

 > $\mathrm{Content}\left(x\left(y+4\right)+{y}^{2}+4,x\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}5$
 ${y}{+}{4}$ (1)
 > $\mathrm{Primpart}\left(x\left(y+4\right)+{y}^{2}+4,x\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}5$
 ${x}{+}{y}{+}{1}$ (2)
 > $a≔5{x}^{3}+3{y}^{2}$
 ${a}{≔}{5}{}{{x}}^{{3}}{+}{3}{}{{y}}^{{2}}$ (3)
 > $\mathrm{Content}\left(a,x\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}11$
 ${1}$ (4)
 > $\mathrm{Primpart}\left(a,x,'\mathrm{c1}'\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}11$
 ${{x}}^{{3}}{+}{5}{}{{y}}^{{2}}$ (5)
 > $\mathrm{c1}$
 ${5}$ (6)
 > $p≔\mathrm{expand}\left(t\left(\sqrt{2}x+1\right)\left(y-\frac{1}{\sqrt{2}}\right)\right)$
 ${p}{≔}{t}{}\sqrt{{2}}{}{x}{}{y}{-}{t}{}{x}{+}{t}{}{y}{-}\frac{{t}{}\sqrt{{2}}}{{2}}$ (7)
 > $\mathrm{evala}\left(\mathrm{Primpart}\left(p,y\right)\right)$
 ${-}{1}{+}\sqrt{{2}}{}{y}$ (8)
 > $r≔\mathrm{RootOf}\left({x}^{3}+x+1\right)$
 ${r}{≔}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{+}{\mathrm{_Z}}{+}{1}\right)$ (9)
 > $q≔\mathrm{evala}\left(\mathrm{Expand}\left(\left(y-r\right)\left(x+{r}^{2}+1\right)\right)\right)$
 ${q}{≔}{{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{+}{\mathrm{_Z}}{+}{1}\right)}^{{2}}{}{y}{-}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{+}{\mathrm{_Z}}{+}{1}\right){}{x}{+}{x}{}{y}{+}{y}{+}{1}$ (10)
 > $\mathrm{evala}\left(\mathrm{Content}\left(q,x,'\mathrm{q1}'\right)\right)$
 ${y}{-}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{+}{\mathrm{_Z}}{+}{1}\right)$ (11)
 > $\mathrm{q1}$
 ${{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{+}{\mathrm{_Z}}{+}{1}\right)}^{{2}}{+}{x}{+}{1}$ (12)