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$\mathrm{with}\left(\mathrm{Groebner}\right)\:$

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$f\u22545{x}^{3}y\+{x}^{2}{w}^{2}t\+5{x}^{3}yzt2xz{w}^{3}t\+3{y}^{2}{w}^{3}t$

${f}{\u2254}{}{2}{}{t}{}{{w}}^{{3}}{}{x}{}{z}{\+}{3}{}{t}{}{{w}}^{{3}}{}{{y}}^{{2}}{\+}{5}{}{t}{}{{x}}^{{3}}{}{y}{}{z}{\+}{t}{}{{w}}^{{2}}{}{{x}}^{{2}}{\+}{5}{}{{x}}^{{3}}{}{y}$
 (1) 
With respect to the definitions above, we will compute the leading coefficient, leading monomial, and leading term of the polynomial f with respect to lexicographic order with x > y > z > w > t.
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$\mathrm{LeadingCoefficient}\left(f\,\mathrm{plex}\left(x\,y\,z\,w\,t\right)\right)$

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$\mathrm{LeadingMonomial}\left(f\,\mathrm{plex}\left(x\,y\,z\,w\,t\right)\right)$

${{x}}^{{3}}{}{y}{}{z}{}{t}$
 (3) 
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$\mathrm{`*`}\left(\mathrm{LeadingTerm}\left(f\,\mathrm{plex}\left(x\,y\,z\,w\,t\right)\right)\right)$

${5}{}{{x}}^{{3}}{}{y}{}{z}{}{t}$
 (4) 
In releases of Maple prior to Maple 10, Groebner[leadmon] computed what is now returned by LeadingTerm and Groebner[leadterm] computed what is now returned by LeadingMonomial.
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$\mathrm{leadcoeff}\left(f\,\mathrm{plex}\left(x\,y\,z\,w\,t\right)\right)$

Warning, Groebner[leadcoeff] is deprecated. Please, use Groebner[LeadingCoefficient].
 
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$\mathrm{leadterm}\left(f\,\mathrm{plex}\left(x\,y\,z\,w\,t\right)\right)$

Warning, Groebner[leadterm] is deprecated. Please, use Groebner[LeadingMonomial]. See ?Groebner,terminology for details.
 
${{x}}^{{3}}{}{y}{}{z}{}{t}$
 (6) 
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$\mathrm{`*`}\left(\mathrm{leadmon}\left(f\,\mathrm{plex}\left(x\,y\,z\,w\,t\right)\right)\right)$

Warning, Groebner[leadmon] is deprecated. Please, use Groebner[LeadingTerm]. See ?Groebner,terminology for details.
 
${5}{}{{x}}^{{3}}{}{y}{}{z}{}{t}$
 (7) 