void mult(const DMat<RT>& A,
const DMat<RT>& B,
DMat<RT>& result_product)
{
//printf("entering dmat mult\n");
typedef typename RT::ElementType ElementType;
typedef typename DMat<RT>::ConstIterator ConstIterator;
M2_ASSERT(A.numColumns() == B.numRows());
M2_ASSERT(A.numRows() == result_product.numRows());
M2_ASSERT(B.numColumns() == result_product.numColumns());
ElementType* result = result_product.array();
ElementType tmp;
A.ring().init(tmp);
// WARNING: this routine expects the result matrix to be in ROW MAJOR ORDER
for (size_t i = 0; i<A.numRows(); i++)
for (size_t j = 0; j<B.numColumns(); j++)
{
ConstIterator i1 = A.rowBegin(i);
ConstIterator iend = A.rowEnd(i);
ConstIterator j1 = B.columnBegin(j);
while (i1 != iend)
{
A.ring().mult(tmp, *i1, *j1);
A.ring().add(*result, *result, tmp);
++i1;
++j1;
}
result++;
}
A.ring().clear(tmp);
}
bool inverse(const DMatZZpFFPACK& mat,
DMatZZpFFPACK& result_inv)
{
M2_ASSERT(mat.numRows() == mat.numColumns());
result_inv.resize(mat.numRows(), mat.numRows());
M2_ASSERT(result_inv.numRows() == mat.numRows());
M2_ASSERT(result_inv.numColumns() == mat.numRows());
if (mat.numRows() == 0)
{
// 26 April 2014: this branch is needed as FFPACK gives answer of 0 in this case.
return true;
}
DMatZZpFFPACK N(mat);
size_t n = mat.numRows();
int nullspacedim;
FFPACK::Invert2(mat.ring().field(),
n,
N.array(),
n,
result_inv.array(),
n,
nullspacedim);
return (nullspacedim == 0);
}
SchreyerOrder *SchreyerOrder::exterior(int pp) const
// p th exterior power
{
// This routine is only called from FreeModule::exterior.
// Therefore: p is in the range 0 < p <= rk.
SchreyerOrder *result = new SchreyerOrder(M);
int rk = rank();
M2_ASSERT(pp > 0);
M2_ASSERT(pp <= rk);
size_t p = static_cast<size_t>(pp);
Subset a(p, 0);
for (size_t i=0; i<p; i++) a[i] = i;
int *base = M->make_one();
int next = 0;
do
{
M->one(base);
for (size_t r=0; r<p; r++)
M->mult(base, base_monom(a[r]), base);
result->append(next++, base);
}
while (Subsets::increment(rk, a));
M->remove(base);
return result;
}
void subtractMultipleTo(DMat<RT>& C,
const DMat<RT>& A,
const DMat<RT>& B)
// C = C - A*B
{
typedef typename RT::ElementType ElementType;
typedef typename DMat<RT>::ConstIterator ConstIterator;
M2_ASSERT(A.numColumns() == B.numRows());
M2_ASSERT(A.numRows() == C.numRows());
M2_ASSERT(B.numColumns() == C.numColumns());
ElementType* result = C.array();
ElementType tmp;
A.ring().init(tmp);
// WARNING: this routine expects the result matrix to be in ROW MAJOR ORDER
for (size_t i = 0; i<A.numRows(); i++)
for (size_t j = 0; j<B.numColumns(); j++)
{
ConstIterator i1 = A.rowBegin(i);
ConstIterator iend = A.rowEnd(i);
ConstIterator j1 = B.columnBegin(j);
while (i1 != iend)
{
A.ring().mult(tmp, *i1, *j1);
A.ring().subtract(*result, *result, tmp);
++i1;
++j1;
}
result++;
}
A.ring().clear(tmp);
}
void addInPlace(SMat<RT>&A, const SMat<RT>& B)
{
M2_ASSERT(&B.ring() == &A.ring());
M2_ASSERT(B.numRows() == A.numRows());
M2_ASSERT(B.numColumns() == A.numColumns());
A.addInPlace(B);
}
void subtractInPlace(SMat<RT>& A, const SMat<RT>& B)
// A -= B
{
M2_ASSERT(&B.ring() == &A.ring());
M2_ASSERT(B.numRows() == A.numRows());
M2_ASSERT(B.numColumns() == A.numColumns());
A.subtractInPlace(B);
}
void transpose(const SMat<RT>& A, SMat<RT>& result)
{
// result should be the 0 matrix of the correct size.
M2_ASSERT(&A != &result); // these cannot be aliased!
M2_ASSERT(result.numRows() == A.numColumns());
M2_ASSERT(result.numColumns() == A.numRows());
throw exc::engine_error("'transpose' not writtten for sparse mutable matrices");
//TODO: MES: write this!!
}
void subtractInPlace(DMat<RT>& A, const DMat<RT>& B)
// A -= B
{
M2_ASSERT(&B.ring() == &A.ring());
M2_ASSERT(B.numRows() == A.numRows());
M2_ASSERT(B.numColumns() == A.numColumns());
size_t len = A.numRows() * A.numColumns();
for (size_t i=0; i<len; i++)
{
A.ring().subtract(A.array()[i], A.array()[i], B.array()[i]);
}
}
void transpose(const DMat<RT>& A, DMat<RT>& result)
{
M2_ASSERT(&A != &result); // these cannot be aliased!
M2_ASSERT(result.numRows() == A.numColumns());
M2_ASSERT(result.numColumns() == A.numRows());
for (size_t c = 0; c < A.numColumns(); ++c)
{
auto i = A.columnBegin(c);
auto j = result.rowBegin(c);
auto end = A.columnEnd(c);
for ( ; i != end; ++i, ++j)
A.ring().set(*j, *i);
}
}
void binomial_ring::intvector_to_binomial(vec f, binomial &result) const
// result should be a preallocated binomial
{
for (int i=0; i<nslots; i++)
{
result.lead[i] = 0;
result.tail[i] = 0;
}
for ( ; f != NULL; f = f->next)
{
std::pair<bool,long> res = globalZZ->coerceToLongInteger(f->coeff);
M2_ASSERT(res.first);
int e = static_cast<int>(res.second);
if (e > 0)
result.lead[f->comp] = e;
else if (e < 0)
result.tail[f->comp] = -e;
}
set_weights(result.lead);
set_weights(result.tail);
normalize(result);
}
void ARingZZpFFPACK::power(ElementType &result, const ElementType a, STT n) const
{
if (is_zero(a))
{
if (n < 0)
ERROR("division by zero");
set(result, a);
return;
}
ElementType base;
set(base, a);
if (n < 0)
{
invert(base,base);
n = -n;
}
n = n % (mCharac-1);
set_from_int(result, 1);
if (n == 0)
return;
// Now use doubling algorithm
M2_ASSERT(n > 0);
for (;;)
{
if ((n % 2) != 0)
mFfpackField.mulin(result,base); // result *= base
n >>= 1;
if (n == 0)
return;
else
mFfpackField.mulin(base, base); // base = base^2
}
}
void ARingZZGMP::syzygy(const ElementType& a, const ElementType& b,
ElementType& x, ElementType& y) const
{
M2_ASSERT(!is_zero(b));
// First check the special cases a = 0, b = 1, -1. Other cases: use gcd.
if (is_zero(a))
{
set_from_long(x, 1);
set_zero(y);
return;
}
if (mpz_cmp_ui(&b,1) == 0)
{
set_from_long(x, 1);
negate(y, a);
return;
}
if (mpz_cmp_si(&b,-1) == 0)
{
set_from_long(x, 1);
set(y, a);
return;
}
elem g;
init(g);
mpz_gcd(&g,&a,&b);
divide(y,a,g);
divide(x,b,g);
if (mpz_sgn(&x) > 0)
negate(y,y);
else
negate(x,x);
clear(g);
}
ring_elem GF::from_rational(mpq_ptr q) const
{
// a should be an element of ZZ/p
ring_elem a = _originalR->getCoefficients()->from_rational(q);
std::pair<bool,long> b = _originalR->getCoefficients()->coerceToLongInteger(a);
M2_ASSERT(b.first);
return GF::from_long(b.second);
}
ARingZZpFFPACK::ARingZZpFFPACK(UTT charact) :
mFfpackField (FieldType(static_cast<double>(charact))),
mFfpackRandomIterator (mFfpackField),
mCharac (charact),
mDimension (1),
mGeneratorComputed (false)
{
M2_ASSERT( FieldType::getMaxModulus()>=mCharac );
}
void set(DMat<RT>& A, MatrixWindow wA, const DMat<RT>& B, MatrixWindow wB)
{
M2_ASSERT(wA.sameSize(wB));
long rA = wA.begin_row;
long rB = wB.begin_row;
for ( ; rA < wA.end_row; ++rA, ++rB)
{
long cA = wA.begin_column;
long cB = wB.begin_column;
for ( ; cA < wA.end_column; ++cA, ++cB)
A.ring().set(A.entry(rA,cA), B.entry(rB,cB));
}
}
bool isEqual(const DMat<RT>& A, const DMat<RT>& B)
{
M2_ASSERT(&A.ring() == &B.ring());
if (B.numRows() != A.numRows()) return false;
if (B.numColumns() != A.numColumns()) return false;
size_t top = A.numRows() * A.numColumns();
auto elemsA = A.array();
auto elemsB = B.array();
for (size_t i = 0; i < top; i++)
if (!A.ring().is_equal(*elemsA++, *elemsB++))
return false;
return true;
}
void scalarMultInPlace(DMat<RT>& A, MatrixWindow wA, const typename RT::ElementType& c)
{
M2_ASSERT(wA.sameSize(wB));
long rA = wA.begin_row;
for ( ; rA < wA.end_row; ++rA)
{
long cA = wA.begin_column;
for ( ; cA < wA.end_column; ++cA)
{
auto& a = A.entry(rA,cA);
A.ring().mult(a, a, c);
}
}
}
void operator=(SubMatrix<MatType> src)
{
M2_ASSERT(sameSize(src));
long rA = begin_row;
long rB = src.begin_row;
for ( ; rA < end_row; ++rA, ++rB)
{
long cA = begin_column;
long cB = src.begin_column;
for ( ; cA < end_column; ++cA, ++cB)
matrix.ring().set(matrix.entry(rA,cA), src.matrix.entry(rB,cB));
}
}
void addMultipleTo(DMatZZpFFPACK& C,
const DMatZZpFFPACK::ElementType& a,
const DMatZZpFFPACK& A,
const DMatZZpFFPACK& B)
{
// Compute C := C + a*A*B
// Both DMat, and FFPACK store dense matrices in row major order.
// Note that the leading dimension in gemm arguments is #columns,
// as the matrix is in row-major order
FFLAS::FFLAS_TRANSPOSE tA = FFLAS::FflasNoTrans;
FFLAS::FFLAS_TRANSPOSE tB = FFLAS::FflasNoTrans;
size_t m = A.numRows();
size_t k = A.numColumns();
M2_ASSERT(A.numColumns() == B.numRows());
size_t n = B.numColumns();
M2_ASSERT(C.numRows() == m);
M2_ASSERT(C.numColumns() == n);
DMatZZpFFPACK::ElementType b;
C.ring().init(b);
C.ring().set_from_long(b, 1);
FFLAS::fgemm( C.ring().field(),
tB, tA,
m,n,k,
a,
A.array(),
A.numColumns(),
B.array(),
B.numColumns(),
b,
C.array(),
C.numColumns()
);
}
void scalarMult(DMat<RT>& A, MatrixWindow wA, const typename RT::ElementType& c, const DMat<RT>& B, MatrixWindow wB)
{
M2_ASSERT(wA.sameSize(wB));
long rA = wA.begin_row;
long rB = wB.begin_row;
for ( ; rA < wA.end_row; ++rA, ++rB)
{
long cA = wA.begin_column;
long cB = wB.begin_column;
for ( ; cA < wA.end_column; ++cA, ++cB)
{
A.ring().mult(A.entry(rA,cA), c, B.entry(rB,cB));
}
}
}
void addMultipleTo(ElementType& c, SubMatrix<MatType> src)
{
M2_ASSERT(sameSize(src));
long rA = begin_row;
long rB = src.begin_row;
for ( ; rA < end_row; ++rA, ++rB)
{
long cA = begin_column;
long cB = src.begin_column;
for ( ; cA < end_column; ++cA, ++cB)
matrix.ring().addMultipleTo(matrix.entry(rA,cA),
c,
src.matrix.entry(rB,cB));
}
}
void addMultipleTo(DMat<RT>& A, MatrixWindow wA, const typename RT::ElementType& c, const DMat<RT>& B, MatrixWindow wB)
{
M2_ASSERT(wA.sameSize(wB));
typename RT::ElementType tmp;
A.ring().init(tmp);
long rA = wA.begin_row;
long rB = wB.begin_row;
for ( ; rA < wA.end_row; ++rA, ++rB)
{
long cA = wA.begin_column;
long cB = wB.begin_column;
for ( ; cA < wA.end_column; ++cA, ++cB)
{
A.ring().mult(tmp, c, B.entry(rB,cB));
auto& a = A.entry(rA,cA);
A.ring().add(a, a, tmp);
}
}
A.ring().clear(tmp);
}
ARingZZpFFPACK::ElementType ARingZZpFFPACK::computeGenerator() const
{
for (UTT currIntElem=2; currIntElem < mCharac; currIntElem++)
{
ElementType currElem;
set_from_int(currElem, currIntElem);
bool found = true;
ElementType tmpElem = currElem;
for (UTT count=0;count < mCharac-2; count++)
{
mult(tmpElem, tmpElem, currElem);
if (is_equal(currElem, tmpElem))
found = false;
}
if (found)
{
std::cerr << "generator = " << currElem << std::endl;
return currElem;
}
}
M2_ASSERT(false); // we should not get here, if the program logic is OK
return ElementType(1);
}
bool GF::promote(const Ring *Rf, const ring_elem f, ring_elem &result) const
{
// Rf = Z/p[x]/F(x) ---> GF(p,n)
// promotion: need to be able to know the value of 'x'.
// lift: need to compute (primite_element)^e
if (Rf != _originalR) return false;
result = from_long(0);
int exp[1];
for (Nterm *t = f; t != NULL; t = t->next)
{
std::pair<bool,long> b = _originalR->getCoefficients()->coerceToLongInteger(t->coeff);
M2_ASSERT(b.first);
ring_elem coef = from_long(b.second);
_originalR->getMonoid()->to_expvector(t->monom, exp);
// exp[0] is the variable we want. Notice that since the ring is a quotient,
// this degree is < n (where Q_ = P^n).
ring_elem g = power(_x_exponent, exp[0]);
g = mult(g, coef);
internal_add_to(result, g);
}
return true;
}
void power(ElementType& result, const ElementType& a, long n) const {
M2_ASSERT(n >= 0);
return fmpq_pow_si(&result,&a,n);
}
int LLLoperations::doLLL(MutableMatrix *A,
MutableMatrix *Achange,
MutableMatrix *LLLstate,
int nsteps)
{
size_t n = A->n_cols();
if (n == 0) return COMP_DONE;
// Extract the state from LLLstate:
int k, kmax;
ring_elem a, alphaTop, alphaBottom;
buffer o;
if (LLLstate->get_entry(0,n,a))
{
std::pair<bool,long> res = globalZZ->coerceToLongInteger(a);
M2_ASSERT(res.first);
k = static_cast<int>(res.second);
}
else
k = 0;
if (LLLstate->get_entry(0,n+1,a))
{
std::pair<bool,long> res = globalZZ->coerceToLongInteger(a);
M2_ASSERT(res.first);
kmax = static_cast<int>(res.second);
}
else
kmax = 0;
LLLstate->get_entry(0,n+2,alphaTop); // Don't free alphaTop!
LLLstate->get_entry(0,n+3,alphaBottom);
while (k < n && nsteps != 0 && !system_interrupted())
{
if (M2_gbTrace >= 1)
{
o.reset();
o << ".";
if (M2_gbTrace >= 2)
o << k;
if (nsteps % 20 == 0)
o << newline;
emit(o.str());
}
nsteps--;
if (k > kmax)
{
if (M2_gbTrace == 1)
{
o.reset();
o << "." << k;
if (nsteps % 20 == 0)
o << newline;
emit(o.str());
}
kmax = k;
for (int j=0; j<=k; j++)
{
ring_elem u;
A->dot_product(k,j,u);
for (int i=0; i<=j-1; i++)
{
// u = (D#i * u - lambda#(k,i) * lambda#(j,i)) // D#(i-1)
ring_elem Di, mki, mji, Di1;
LLLstate->get_entry(i,i,Di);
globalZZ->mult_to(u, Di);
if (LLLstate->get_entry(i,k,mki) && LLLstate->get_entry(i,j,mji))
{
ring_elem t1 = globalZZ->mult(mki,mji);
globalZZ->subtract_to(u,t1);
}
if (i > 0)
{
LLLstate->get_entry(i-1,i-1,Di1); // Cannot be zero!!
ring_elem t1 = globalZZ->divide(u,Di1);
globalZZ->remove(u);
u = t1;
}
}
// At this point we have our element:
LLLstate->set_entry(j,k,u);
if (j == k && globalZZ->is_zero(u))
{
ERROR("LLL vectors not independent");
return COMP_ERROR;
}
}
} // end of the k>kmax initialization
REDI(k,k-1,A,Achange,LLLstate);
if (Lovasz(LLLstate,k,alphaTop,alphaBottom))
{
SWAPI(k,kmax,A,Achange,LLLstate);
k--;
if (k == 0) k = 1;
}
else
{
for (int ell=k-2; ell>=0; ell--)
REDI(k,ell,A,Achange,LLLstate);
k++;
}
}
// Before returning, reset k,kmax:
LLLstate->set_entry(0,n,globalZZ->from_long(k));
LLLstate->set_entry(0,n+1,globalZZ->from_long(kmax));
if (k >= n) return COMP_DONE;
if (nsteps == 0) return COMP_DONE_STEPS;
return COMP_INTERRUPTED;
}
void ARingZZpFFPACK::unsafeInvert(ElementType &result, const ElementType a) const
{
M2_ASSERT(not is_zero(a));
mFfpackField.inv(result, a);
}
void power(ElementType& result, const ElementType& a, long n) const {
M2_ASSERT(n >= 0);
mpz_pow_ui(mpq_numref(&result),mpq_numref(&a),n);
mpz_pow_ui(mpq_denref(&result),mpq_denref(&a),n);
}
GaloisFieldTable::GaloisFieldTable(const PolynomialRing& R,
const ring_elem prim):
mCharac(static_cast<int>(R.characteristic())),
mOriginalRing(R),
mPrimitiveElement(prim)
{
M2_ASSERT(mOriginalRing.n_quotients() == 1);
mGenerator = RingElement::make_raw(&R, R.copy(prim));
ring_elem f = mOriginalRing.quotient_element(0);
Nterm *t = f;
mDimension = mOriginalRing.getMonoid()->primary_degree(t->monom);
mOrder = mCharac;
for (int i=1; i<mDimension; i++) mOrder *= mCharac;
mOne = mOrder - 1; // representation for the number 1: p^n - 1.
mOrderMinusOne = mOne; // p^n - 1
mMinusOne = (mCharac == 2 ? mOne : mOne/2);
// Get ready to create mOneTable.
std::vector<ring_elem> polys;
polys.push_back(mOriginalRing.from_long(0));
polys.push_back(mOriginalRing.copy(mPrimitiveElement));
ring_elem oneR = mOriginalRing.from_long(1);
mGeneratorExponent = static_cast<GFElement>(-1);
ring_elem x = mOriginalRing.var(0);
if (mOriginalRing.is_equal(mPrimitiveElement, x))
mGeneratorExponent = 1;
for (GFElement i=2; i<=mOne; i++)
{
ring_elem g = mOriginalRing.mult(polys[i-1], mPrimitiveElement);
polys.push_back(g);
if (mOriginalRing.is_equal(g, oneR)) break;
if (mOriginalRing.is_equal(g, x))
mGeneratorExponent = i;
}
#if 0
for (size_t i = 0; i < polys.size(); i++)
{
std::cerr << i << " ";
dringelem(&R, polys[i]);
std::cerr << "\n";
}
#endif
M2_ASSERT(polys.size() == mOrder);
M2_ASSERT(mGeneratorExponent != static_cast<GFElement>(-1));
// Set 'one_table'.
mOneTable = newarray_atomic(GFElement,mOrder);
mOneTable[0] = mOrderMinusOne;
for (GFElement i=1; i<=mOrderMinusOne; i++)
{
if (system_interrupted())
{
// first clean up?
return;
}
ring_elem f1 = mOriginalRing.add(polys[i], oneR);
GFElement j;
for (j=0; j<=mOrderMinusOne; j++)
if (mOriginalRing.is_equal(f1, polys[j]))
break;
if (j > mOrderMinusOne)
{
std::cout << "oops: didn't find element " << i << " !!" << std::endl;
}
mOneTable[i] = j;
}
// Create the ZZ/P ---> GF(Q) inclusion map
mFromIntTable = newarray_atomic(GFElement,mCharac);
GFElement a = mOne;;
mFromIntTable[0] = 0;
for (GFElement i=1; i<mCharac; i++)
{
mFromIntTable[i] = a;
a = mOneTable[a];
}
}
const ElementType& entry(size_t row, size_t column) const {
M2_ASSERT(row < numRows());
M2_ASSERT(column < numColumns());
return * fmpq_mat_entry(mArray, row, column);
}