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lcoeff

leading coefficient of a multivariate polynomial

tcoeff

trailing coefficient of a multivariate polynomial

 

Calling Sequence

Parameters

Description

Thread Safety

Examples

Calling Sequence

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')

Parameters

p

-

multivariate polynomial

x

-

(optional) indeterminate, list or set of indeterminates

o

-

(optional) monomial order

't'

-

(optional) unevaluated name

Description

• 

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,frontendindets,p,`*`,`+`,`::`,constant,series,SDMPolynom,undefined ). In the multivariate case this ordering may be session dependent.

Thread Safety

• 

The lcoeff and tcoeff commands are thread-safe as of Maple 15.

• 

For more information on thread safety, see index/threadsafe.

Examples

s3v2w3x4+1

s:=3v2w3x4+1

(1)

lcoeffs

3

(2)

tcoeffs

1

(3)

lcoeffs,v,w,'t'

3x4

(4)

t

v2w3

(5)

px+4xy+5y7x2

p:=7x2+4xy+x+5y

(6)

lcoeffp

7

(7)

tcoeffp

5

(8)

lcoeffp,x

7

(9)

lcoeffp,y

4x+5

(10)

tcoeffp,x

5y

(11)

tcoeffp,y

7x2+x

(12)

collectp,x

7x2+4y+1x+5y

(13)

collectp,y

4x+5y7x2+x

(14)

coeffp,x,1

4y+1

(15)

f4x3+5x2z2+2xy2z+1

f:=5x2z2+2xy2z+4x3+1

(16)

lcoefff,order=plexx,y,z,'m',m

4,x3

(17)

lcoefff,order=grlexx,y,z,'m',m

5,x2z2

(18)

lcoefff,order=tdegx,y,z,'m',m

2,xy2z

(19)

See Also

coeff

coeffs

collect

degree

Groebner/MonomialOrders

indets

ldegree

 


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