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### Member "pari-2.13.1/src/functions/linear_algebra/matadjoint" (1 Nov 2020, 1134 Bytes) of package /linux/misc/pari-2.13.1.tar.gz:

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    1 Function: matadjoint
2 Section: linear_algebra
4 Prototype: GD0,L,
6  algorithm. If flag is 1, compute the characteristic polynomial independently
7  first.
8 Doc:
9  \idx{adjoint matrix} of $M$, i.e.~a matrix $N$
10  of cofactors of $M$, satisfying $M*N=\det(M)*\Id$. $M$ must be a
11  (not necessarily invertible) square matrix of dimension $n$.
12  If $\fl$ is 0 or omitted, we try to use Leverrier-Faddeev's algorithm,
13  which assumes that $n!$ invertible. If it fails or $\fl = 1$,
14  compute $T = \kbd{charpoly}(M)$ independently first and return
15  $(-1)^{n-1} (T(x)-T(0))/x$ evaluated at $M$.
16  \bprog
17  ? a = [1,2,3;3,4,5;6,7,8] * Mod(1,4);
19  %2 =
20  [Mod(1, 4) Mod(1, 4) Mod(2, 4)]
21
22  [Mod(2, 4) Mod(2, 4) Mod(0, 4)]
23
24  [Mod(1, 4) Mod(1, 4) Mod(2, 4)]
25  @eprog\noindent
26  Both algorithms use $O(n^4)$ operations in the base ring. Over a field,
27  they are usually slower than computing the characteristic polynomial or
28  the inverse of $M$ directly.
29 Variant: Also available are