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MatrixPolynomialAlgebra

 Coeff
 extract a coefficient of a matrix of polynomials

 Calling Sequence Coeff(A, x, n) Coeff[row](A, x, vn) Coeff[column](A, x, vn)

Parameters

 A - Matrix x - name; specify the variable in which the entries of A are rational polynomials over Q n - integer vn - list of integers

Description

 • The Coeff(A,x,n) command computes the n-th coefficient of a matrix of polynomials A.
 • The Coeff[row](A,x,vn) command computes the vn[i]-th coefficient of A for row i. That is, the number of elements in the list vn must equal the number of rows in A.
 • The Coeff[column](A,x,vn) command computes the vn[i]-th coefficient of A for column i. That is, the number of elements in the list vn must equal the number of columns in A.

Examples

 > $\mathrm{with}\left(\mathrm{MatrixPolynomialAlgebra}\right):$
 > $A≔⟨⟨3+x,4,{x}^{2}-1⟩|⟨1,x,4⟩|⟨-4,2,-1⟩⟩$
 ${A}{≔}\left[\begin{array}{ccc}{3}{+}{x}& {1}& {-}{4}\\ {4}& {x}& {2}\\ {{x}}^{{2}}{-}{1}& {4}& {-}{1}\end{array}\right]$ (1)
 > $\mathrm{seq}\left(\mathrm{Coeff}\left(A,x,i\right),i=0..2\right)$
 $\left[\begin{array}{rrr}{3}& {1}& {-}{4}\\ {4}& {0}& {2}\\ {-}{1}& {4}& {-}{1}\end{array}\right]{,}\left[\begin{array}{rrr}{1}& {0}& {0}\\ {0}& {1}& {0}\\ {0}& {0}& {0}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {0}& {0}& {0}\\ {1}& {0}& {0}\end{array}\right]$ (2)
 > $\mathrm{seq}\left(\mathrm{Coeff}[\mathrm{row}]\left(A,x,\left[i+1,i,i\right]\right),i=0..1\right)$
 $\left[\begin{array}{rrr}{1}& {0}& {0}\\ {4}& {0}& {2}\\ {-}{1}& {4}& {-}{1}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {0}& {1}& {0}\\ {0}& {0}& {0}\end{array}\right]$ (3)
 > $\mathrm{seq}\left(\mathrm{Coeff}[\mathrm{column}]\left(A,x,\left[i+1,i,i\right]\right),i=0..1\right)$
 $\left[\begin{array}{rrr}{1}& {1}& {-}{4}\\ {0}& {0}& {2}\\ {0}& {4}& {-}{1}\end{array}\right]{,}\left[\begin{array}{rrr}{0}& {0}& {0}\\ {0}& {1}& {0}\\ {1}& {0}& {0}\end{array}\right]$ (4)

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