Lcoeff - Maple Help

MatrixPolynomialAlgebra

 Lcoeff
 compute the leading coefficient of a matrix of polynomials
 Tcoeff
 compute the trailing coefficient of a matrix of polynomials

 Calling Sequence Lcoeff(A, x) Lcoeff[row](A, x) Lcoeff[column](A, x) Tcoeff(A, x) Tcoeff[row](A, x) Tcoeff[column](A, x)

Parameters

 A - Matrix x - name; specify the variable in which the entries of A are rational polynomials over Q

Description

 • The Lcoeff(A,x) command computes the leading coefficient of a matrix of polynomials A.
 • The Lcoeff[row](A,x) command computes the leading row coefficient of A.  That is, it computes a matrix with rows that are the leading coefficient of each row of A.
 • The Lcoeff[column](A,x) command computes the leading column coefficient of A.
 • The Tcoeff(A,x), Tcoeff[row](A,x), and Tcoeff[column](A,x) commands compute the trailing coefficient, trailing row coefficient, and trailing column coefficients of A, respectively.

Examples

 > $\mathrm{with}\left(\mathrm{MatrixPolynomialAlgebra}\right):$
 > $A≔⟨⟨3+x,4,{x}^{2}-1⟩|⟨1,x,4⟩|⟨-4{x}^{3},2x,-{x}^{3}⟩⟩$
 ${A}{≔}\left[\begin{array}{ccc}{3}{+}{x}& {1}& {-}{4}{}{{x}}^{{3}}\\ {4}& {x}& {2}{}{x}\\ {{x}}^{{2}}{-}{1}& {4}& {-}{{x}}^{{3}}\end{array}\right]$ (1)
 > $\mathrm{Lcoeff}\left(A,x\right)$
 $\left[\begin{array}{ccc}{0}& {0}& {-4}\\ {0}& {0}& {0}\\ {0}& {0}& {-1}\end{array}\right]$ (2)
 > $\mathrm{Lcoeff}\left[\mathrm{row}\right]\left(A,x\right)$
 $\left[\begin{array}{ccc}{0}& {0}& {-4}\\ {0}& {1}& {2}\\ {0}& {0}& {-1}\end{array}\right]$ (3)
 > $\mathrm{Lcoeff}\left[\mathrm{column}\right]\left(A,x\right)$
 $\left[\begin{array}{ccc}{0}& {0}& {-4}\\ {0}& {1}& {0}\\ {1}& {0}& {-1}\end{array}\right]$ (4)
 > $\mathrm{Tcoeff}\left(A,x\right)$
 $\left[\begin{array}{ccc}{3}& {1}& {0}\\ {4}& {0}& {0}\\ {-1}& {4}& {0}\end{array}\right]$ (5)
 > $\mathrm{Tcoeff}\left[\mathrm{row}\right]\left(A,x\right)$
 $\left[\begin{array}{ccc}{3}& {1}& {0}\\ {4}& {0}& {0}\\ {-1}& {4}& {0}\end{array}\right]$ (6)
 > $\mathrm{Tcoeff}\left[\mathrm{column}\right]\left(A,x\right)$
 $\left[\begin{array}{ccc}{3}& {1}& {0}\\ {4}& {0}& {2}\\ {-1}& {4}& {0}\end{array}\right]$ (7)