void PlainUpdateMap(vec_zz_p& xx, const vec_zz_p& a,
const zz_pX& b, const zz_pX& f)
{
long n = deg(f);
long i, m;
if (IsZero(b)) {
xx.SetLength(0);
return;
}
m = n-1 - deg(b);
vec_zz_p x(INIT_SIZE, n);
for (i = 0; i <= m; i++)
InnerProduct(x[i], a, b.rep, i);
if (deg(b) != 0) {
zz_pX c(INIT_SIZE, n);
LeftShift(c, b, m);
for (i = m+1; i < n; i++) {
MulByXMod(c, c, f);
InnerProduct(x[i], a, c.rep);
}
}
xx = x;
}
NTL_START_IMPL
static
void HessCharPoly(zz_pX& g, const zz_pX& a, const zz_pX& f)
{
long n = deg(f);
if (n <= 0 || deg(a) >= n)
Error("HessCharPoly: bad args");
mat_zz_p M;
M.SetDims(n, n);
long i, j;
zz_pX t;
t = a;
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++)
M[i][j] = coeff(t, j);
if (i < n-1)
MulByXMod(t, t, f);
}
CharPoly(g, M);
}
static
void MulByXPlusY(vec_ZZ_pEX& h, const ZZ_pEX& f, const ZZ_pEX& g)
// h represents the bivariate polynomial h[0] + h[1]*Y + ... + h[n-1]*Y^k,
// where the h[i]'s are polynomials in X, each of degree < deg(f),
// and k < deg(g).
// h is replaced by the bivariate polynomial h*(X+Y) (mod f(X), g(Y)).
{
long n = deg(g);
long k = h.length()-1;
if (k < 0) return;
if (k < n-1) {
h.SetLength(k+2);
h[k+1] = h[k];
for (long i = k; i >= 1; i--) {
MulByXMod(h[i], h[i], f);
add(h[i], h[i], h[i-1]);
}
MulByXMod(h[0], h[0], f);
}
else {
ZZ_pEX b, t;
b = h[n-1];
for (long i = n-1; i >= 1; i--) {
mul(t, b, g.rep[i]);
MulByXMod(h[i], h[i], f);
add(h[i], h[i], h[i-1]);
sub(h[i], h[i], t);
}
mul(t, b, g.rep[0]);
MulByXMod(h[0], h[0], f);
sub(h[0], h[0], t);
}
// normalize
k = h.length()-1;
while (k >= 0 && IsZero(h[k])) k--;
h.SetLength(k+1);
}
