bool FractionField::initialize_frac(const PolyRingFlat *R)
{
initialize_ring(R->charac(),
R->get_degree_ring(),
R->get_heft_vector());
R_ = R;
_MINUS_ONE = R->from_int(-1);
zeroV = from_int(0);
oneV = from_int(1);
minus_oneV = from_int(-1);
if (R->n_quotients() > 0
|| R->getCoefficients()->cast_to_FractionField() // disallowed in x-relem.cpp
|| R->getMonoid()->getNonTermOrderVariables()->len > 0) // disallowed in x-relem.cpp
use_gcd_simplify = false;
else
use_gcd_simplify = true;
#ifdef DEVELOPMENT
#warning "frac simplify: doesn't handle towers of fracs"
#endif
declare_field();
return true;
}
bool QQ::initialize_QQ()
{
initialize_ring(0);
_elem_size = sizeof(mpq_t);
_zero_elem = new_elem();// this sets the element to 0.
#if 0
// trans_one = globalZZ->from_int(1);
#endif
declare_field();
zeroV = from_int(0);
oneV = from_int(1);
minus_oneV = from_int(-1);
return true;
}
bool Z_mod::initialize_Z_mod(int p)
{
initialize_ring(p);
P = p;
declare_field();
int i,j,q,n;
if (P==2)
_minus_one = 0;
else
_minus_one = (P-1)/2;
if (P==2)
_prim_root = 1;
else
{
j=1;
for (i=2; (i<P && j<P-1); i++)
for (q=i,j=1; (q!=1 && j<P); q=(q*i)%P,j++);
_prim_root = i-1;
}
// cerr << "z_mod_p: creating table for P = " << P << endl;
_log_table = newarray_atomic(int,P);
_exp_table = newarray_atomic(int,P);
for (i=0, n=1; i<P-1; i++, n=(n*_prim_root)%P)
{
_log_table[n] = i; // i = log_(base _prim_root)(n)
_exp_table[i] = n; // n = (_prim_root)^i
}
_ZERO = P-1;
_exp_table[_ZERO] = 0;
_log_table[0] = _ZERO;
_P1 = P-1;
zeroV = from_long(0);
oneV = from_long(1);
minus_oneV = from_long(-1);
coeffR = new CoefficientRingZZp(P,_log_table, _exp_table);
aringZZp = new M2::ARingZZp(P); // WARNING: this uses that the primitive element is the SAME as computed above!!
// Remove this warning once Z_mod is not in existence any longer.
return true;
}
bool GF::initialize_GF(const RingElement *prim)
{
// set the GF ring tables. Returns false if there is an error.
_primitive_element = prim;
_originalR = prim->get_ring()->cast_to_PolynomialRing();
initialize_ring(_originalR->charac(),
PolyRing::get_trivial_poly_ring());
declare_field();
int i,j;
if (_originalR->n_quotients() != 1)
{
ERROR("rawGaloisField expected an element of a quotient ring of the form ZZ/p[x]/(f)");
return false;
}
ring_elem f = _originalR->quotient_element(0);
Nterm *t = f;
int n = _originalR->getMonoid()->primary_degree(t->monom);
Q_ = P;
for (i=1; i<n; i++) Q_ *= P;
Qexp_ = n;
Q1_ = Q_-1;
_ZERO = 0;
_ONE = Q1_;
_MINUS_ONE = (P == 2 ? _ONE : Q1_/2);
// Get ready to create the 'one_table'
array<ring_elem> polys;
polys.append(_originalR->from_int(0));
ring_elem primelem = prim->get_value();
polys.append(_originalR->copy(primelem));
ring_elem oneR = _originalR->one();
_x_exponent = -1;
ring_elem x = _originalR->var(0);
if (_originalR->is_equal(primelem, x))
_x_exponent = 1;
for (i=2; i<Q_; i++)
{
ring_elem g = _originalR->mult(polys[i-1], primelem);
polys.append(g);
if (_originalR->is_equal(g, oneR)) break;
if (_originalR->is_equal(g, x))
_x_exponent = i;
}
if (polys.length() != Q_)
{
ERROR("GF: primitive element expected");
return false;
}
assert(_x_exponent >= 0);
// Set 'one_table'.
_one_table = newarray_atomic(int,Q_);
_one_table[0] = Q_-1;
for (i=1; i<=Q_-1; i++)
{
if (system_interrupted())
return false;
ring_elem f1 = _originalR->add(polys[i], oneR);
for (j=1; j<=Q_-1; j++)
if (_originalR->is_equal(f1, polys[j]))
break;
_one_table[i] = j;
}
// Create the Z/P ---> GF(Q) inclusion map
_from_int_table = newarray_atomic(int,P);
int a = _ONE;
_from_int_table[0] = _ZERO;
for (i=1; i<P; i++)
{
_from_int_table[i] = a;
a = _one_table[a];
}
zeroV = from_int(0);
oneV = from_int(1);
minus_oneV = from_int(-1);
// M2::GaloisFieldTable G(*_originalR, primelem);
// G.display(std::cout);
return true;
}
