leading coefficient of a multivariate polynomial
trailing coefficient of a multivariate polynomial
lcoeff(p) or tcoeff(p)
lcoeff(p, x) or tcoeff(p, x)
lcoeff(p, order=o) or tcoeff(p, order=o)
lcoeff(p, x, 't') or tcoeff(p, x, 't')
lcoeff(p, order=o, 't') or tcoeff(p, order=o, 't')
(optional) indeterminate, list or set of indeterminates
(optional) monomial order
(optional) unevaluated name
The functions lcoeff and tcoeff return the leading (trailing) coefficient of p with respect to the indeterminate(s) x or the monomial order o.
If neither x nor o is specified, then lcoeff (tcoeff) computes the leading (trailing) coefficient with respect to all the indeterminates of p.
If a the third argument t is specified ("call by name"), it is assigned the leading (trailing) monomial of p.
If x is a single indeterminate, and d is the degree (low degree) of p in x, then lcoeff(p, x) (tcoeff(p, x)) is equivalent to coeff(p, x, d). If x is a list or set of indeterminates, lcoeff (tcoeff) computes the leading (trailing) coefficient of p considered as a multivariate polynomial in the variables x, using lexicographic order. More precisely, lcoeff(p, [x1, ..., xn]) is equivalent to lcoeff(...(lcoeff(p, x1), ...), xn) (and similarly for tcoeff).
Other monomial orders can be specified by using the order=o calling sequence. The supported orders are:
plex(x1, ..., xn) - lexicographic order
grlex(x1, ..., xn) - graded lexicographic order
tdeg(x1, ..., xn) - graded reverse lexicographic order
for indeterminates x1, ..., xn. For a description of these orders, see Monomial orders for multivariate polynomials.
Note that p must be collected with respect to the appropriate indeterminates before calling lcoeff or tcoeff. For details, see collect.
When neither x nor o is specified, the order of the indeterminates is given by indets (more specifically,frontend⁡indets,p,`*`,`+`,`::`,constant,series,SDMPolynom,undefined ). In the multivariate case this ordering may be session dependent.
The lcoeff and tcoeff commands are thread-safe as of Maple 15.
For more information on thread safety, see index/threadsafe.
s ≔ 3⁢v2⁢w3⁢x4+1
p ≔ x+4⁢x⁢y+5⁢y−7⁢x2
f ≔ 4⁢x3+5⁢x2⁢z2+2⁢x⁢y2⁢z+1
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