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<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment">MODULE: mat_zz_pE</span>
<span class="Comment">SUMMARY:</span>
<span class="Comment">Defines the class mat_zz_pE.</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
<span class="PreProc">#include </span><span class="String"><NTL/matrix.h></span>
<span class="PreProc">#include </span><span class="String"><NTL/vec_vec_lzz_pE.h></span>
<span class="Type">typedef</span> Mat<zz_pE> mat_zz_pE; <span class="Comment">// backward compatibility</span>
<span class="Type">void</span> add(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> mat_zz_pE& B);
<span class="Comment">// X = A + B</span>
<span class="Type">void</span> sub(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> mat_zz_pE& B);
<span class="Comment">// X = A - B</span>
<span class="Type">void</span> negate(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A);
<span class="Comment">// X = - A</span>
<span class="Type">void</span> mul(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> mat_zz_pE& B);
<span class="Comment">// X = A * B</span>
<span class="Type">void</span> mul(vec_zz_pE& x, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> vec_zz_pE& b);
<span class="Comment">// x = A * b</span>
<span class="Type">void</span> mul(vec_zz_pE& x, <span class="Type">const</span> vec_zz_pE& a, <span class="Type">const</span> mat_zz_pE& B);
<span class="Comment">// x = a * B</span>
<span class="Type">void</span> mul(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> zz_pE& b);
<span class="Type">void</span> mul(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> zz_p& b);
<span class="Type">void</span> mul(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">long</span> b);
<span class="Comment">// X = A * b</span>
<span class="Type">void</span> mul(mat_zz_pE& X, <span class="Type">const</span> zz_pE& a, <span class="Type">const</span> mat_zz_pE& B);
<span class="Type">void</span> mul(mat_zz_pE& X, <span class="Type">const</span> zz_p& a, <span class="Type">const</span> mat_zz_pE& B);
<span class="Type">void</span> mul(mat_zz_pE& X, <span class="Type">long</span> a, <span class="Type">const</span> mat_zz_pE& B);
<span class="Comment">// X = a * B</span>
<span class="Type">void</span> determinant(zz_pE& d, <span class="Type">const</span> mat_zz_pE& A);
zz_pE determinant(<span class="Type">const</span> mat_zz_pE& a);
<span class="Comment">// d = determinant(A)</span>
<span class="Type">void</span> transpose(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A);
mat_zz_pE transpose(<span class="Type">const</span> mat_zz_pE& A);
<span class="Comment">// X = transpose of A</span>
<span class="Type">void</span> solve(zz_pE& d, vec_zz_pE& X,
<span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> vec_zz_pE& b);
<span class="Comment">// A is an n x n matrix, b is a length n vector. Computes d =</span>
<span class="Comment">// determinant(A). If d != 0, solves x*A = b.</span>
<span class="Type">void</span> inv(zz_pE& d, mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A);
<span class="Comment">// A is an n x n matrix. Computes d = determinant(A). If d != 0,</span>
<span class="Comment">// computes X = A^{-1}.</span>
<span class="Type">void</span> sqr(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A);
mat_zz_pE sqr(<span class="Type">const</span> mat_zz_pE& A);
<span class="Comment">// X = A*A </span>
<span class="Type">void</span> inv(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A);
mat_zz_pE inv(<span class="Type">const</span> mat_zz_pE& A);
<span class="Comment">// X = A^{-1}; error is raised if A is singular</span>
<span class="Type">void</span> power(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> ZZ& e);
mat_zz_pE power(<span class="Type">const</span> mat_zz_pE& A, <span class="Type">const</span> ZZ& e);
<span class="Type">void</span> power(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A, <span class="Type">long</span> e);
mat_zz_pE power(<span class="Type">const</span> mat_zz_pE& A, <span class="Type">long</span> e);
<span class="Comment">// X = A^e; e may be negative (in which case A must be nonsingular).</span>
<span class="Type">void</span> ident(mat_zz_pE& X, <span class="Type">long</span> n);
mat_zz_pE ident_mat_zz_pE(<span class="Type">long</span> n);
<span class="Comment">// X = n x n identity matrix</span>
<span class="Type">long</span> IsIdent(<span class="Type">const</span> mat_zz_pE& A, <span class="Type">long</span> n);
<span class="Comment">// test if A is the n x n identity matrix</span>
<span class="Type">void</span> diag(mat_zz_pE& X, <span class="Type">long</span> n, <span class="Type">const</span> zz_pE& d);
mat_zz_pE diag(<span class="Type">long</span> n, <span class="Type">const</span> zz_pE& d);
<span class="Comment">// X = n x n diagonal matrix with d on diagonal</span>
<span class="Type">long</span> IsDiag(<span class="Type">const</span> mat_zz_pE& A, <span class="Type">long</span> n, <span class="Type">const</span> zz_pE& d);
<span class="Comment">// test if X is an n x n diagonal matrix with d on diagonal</span>
<span class="Type">long</span> gauss(mat_zz_pE& M);
<span class="Type">long</span> gauss(mat_zz_pE& M, <span class="Type">long</span> w);
<span class="Comment">// Performs unitary row operations so as to bring M into row echelon</span>
<span class="Comment">// form. If the optional argument w is supplied, stops when first w</span>
<span class="Comment">// columns are in echelon form. The return value is the rank (or the</span>
<span class="Comment">// rank of the first w columns).</span>
<span class="Type">void</span> image(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A);
<span class="Comment">// The rows of X are computed as basis of A's row space. X is is row</span>
<span class="Comment">// echelon form</span>
<span class="Type">void</span> kernel(mat_zz_pE& X, <span class="Type">const</span> mat_zz_pE& A);
<span class="Comment">// Computes a basis for the kernel of the map x -> x*A. where x is a</span>
<span class="Comment">// row vector.</span>
<span class="Comment">// miscellaneous:</span>
<span class="Type">void</span> clear(mat_zz_pE& a);
<span class="Comment">// x = 0 (dimension unchanged)</span>
<span class="Type">long</span> IsZero(<span class="Type">const</span> mat_zz_pE& a);
<span class="Comment">// test if a is the zero matrix (any dimension)</span>
<span class="Comment">// operator notation:</span>
mat_zz_pE <span class="Statement">operator</span>+(<span class="Type">const</span> mat_zz_pE& a, <span class="Type">const</span> mat_zz_pE& b);
mat_zz_pE <span class="Statement">operator</span>-(<span class="Type">const</span> mat_zz_pE& a, <span class="Type">const</span> mat_zz_pE& b);
mat_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_pE& a, <span class="Type">const</span> mat_zz_pE& b);
mat_zz_pE <span class="Statement">operator</span>-(<span class="Type">const</span> mat_zz_pE& a);
<span class="Comment">// matrix/scalar multiplication:</span>
mat_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_pE& a, <span class="Type">const</span> zz_pE& b);
mat_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_pE& a, <span class="Type">const</span> zz_p& b);
mat_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_pE& a, <span class="Type">long</span> b);
mat_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> zz_pE& a, <span class="Type">const</span> mat_zz_pE& b);
mat_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> zz_p& a, <span class="Type">const</span> mat_zz_pE& b);
mat_zz_pE <span class="Statement">operator</span>*(<span class="Type">long</span> a, <span class="Type">const</span> mat_zz_pE& b);
<span class="Comment">// matrix/vector multiplication:</span>
vec_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_pE& a, <span class="Type">const</span> vec_zz_pE& b);
vec_zz_pE <span class="Statement">operator</span>*(<span class="Type">const</span> vec_zz_pE& a, <span class="Type">const</span> mat_zz_pE& b);
<span class="Comment">// assignment operator notation:</span>
mat_zz_pE& <span class="Statement">operator</span>+=(mat_zz_pE& x, <span class="Type">const</span> mat_zz_pE& a);
mat_zz_pE& <span class="Statement">operator</span>-=(mat_zz_pE& x, <span class="Type">const</span> mat_zz_pE& a);
mat_zz_pE& <span class="Statement">operator</span>*=(mat_zz_pE& x, <span class="Type">const</span> mat_zz_pE& a);
mat_zz_pE& <span class="Statement">operator</span>*=(mat_zz_pE& x, <span class="Type">const</span> zz_pE& a);
mat_zz_pE& <span class="Statement">operator</span>*=(mat_zz_pE& x, <span class="Type">const</span> zz_p& a);
mat_zz_pE& <span class="Statement">operator</span>*=(mat_zz_pE& x, <span class="Type">long</span> a);
vec_zz_pE& <span class="Statement">operator</span>*=(vec_zz_pE& x, <span class="Type">const</span> mat_zz_pE& a);
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