Ejemplo n.º 1
0
def solve(self, B):  # modified Algorithm 2.3.4 of Cohen's book
    """
    Return solution X for self * X = B (B is a vector).
    This function returns tuple (V, M) below.
      V: one solution as vector
      M: kernel of self as list of basis vectors.
    If you want only one solution, use 'inverseImage'.

    Warning: B should not be a matrix instead of a vector
    """
    M_1 = self.copy()
    M_1.insertColumn(self.column + 1, B.compo)
    M_1._cohensSimplify = types.MethodType(parallel_cohens, M_1)
    V = M_1.kernel()
    ker = []
    flag = False
    if not V:
        raise NoInverseImage("no solution")
    n = V.row
    for j in range(1, V.column + 1):
        if not bool(V[n, j]):  # self's kernel
            ker.append(vector.Vector([V[i, j] for i in range(1, n)]))
        elif not (flag):
            d = -ring.inverse(V[n, j])
            sol = vector.Vector([V[i, j] * d for i in range(1, n)])
            flag = True
    if not (flag):
        raise NoInverseImage("no solution")
    return sol, ker
Ejemplo n.º 2
0
def parallel_cohens(self):
    """
    NS: Add some parallel processing to the cohensSimplify procedure
    _cohensSimplify is a common process used in image() and kernel()

    Return a tuple of modified matrix M, image data c and kernel data d.
    """
    print >>sys.stderr, "Parallel Cohens simplify %dx%d" % (self.row, self.column)
    M = self.copy()
    c = [0] * (M.row + 1)
    d = [-1] * (M.column + 1)
    Mpr = [pack_vector(M.getRow(i)) for i in range1(M.row)]
    for k in range(1, M.column + 1):
        for j in range(1, M.row + 1):
            if not c[j] and Mpr[j - 1][0][k - 1]:
                break
        else:  # not found j such that m(j, k)!=0 and c[j]==0
            d[k] = 0
            continue
        Mj = unpack_vector(Mpr[j - 1])
        top = -ring.inverse(Mj[k])
        Mj[k] = -self.coeff_ring.one
        for s in range(k + 1, M.column + 1):
            Mj[s] = top * Mj[s]
        Mjp = pack_vector(Mj)
        Mpr[j - 1] = Mjp
        work = [(Mpr[i - 1], Mjp, k) for i in range(1, M.row + 1) if i != j]
        result = pool.pool().map(cohens_worker, work)
        i = 1
        for v in result:
            if i != j:
                Mpr[i - 1] = v
            else:
                i += 1
                Mpr[i - 1] = v
            i += 1
        c[j] = k
        d[k] = j
    for i in range(1, M.row + 1):
        M.setRow(i, unpack_vector(Mpr[i - 1]))
    return (M, c, d)
Ejemplo n.º 3
0
def reduce_groebner(gbasis, order):
    """
    Return the reduced Groebner basis constructed from a Groebner
    basis.

    1) lb(f) divides lb(g) => g is not in reduced Groebner basis
    2) monic
    """
    reduced_basis = []
    lb_rel = dict([(order.leading_term(g)[0], g) for g in gbasis])
    lbs = sorted([order.leading_term(g)[0] for g in gbasis])[::-1]
    for i, lbi in enumerate(lbs):
        for lbj in lbs[(len(lbs) - 1) : i : -1]:
            if lbi == lbj.lcm(lbi):
                # divisor found
                break
        else:
            g = lb_rel[lbi]
            if g[lbi] != ring.getRing(g[lbi]).one:
                # make it monic
                g = g.scalar_mul(ring.inverse(g[lbi]))
            reduced_basis.append(g)
    return reduced_basis
Ejemplo n.º 4
0
def reduce_groebner(gbasis, order):
    """
    Return the reduced Groebner basis constructed from a Groebner
    basis.

    1) lb(f) divides lb(g) => g is not in reduced Groebner basis
    2) monic
    """
    reduced_basis = []
    lb_rel = dict([(order.leading_term(g)[0], g) for g in gbasis])
    lbs = sorted([order.leading_term(g)[0] for g in gbasis])[::-1]
    for i, lbi in enumerate(lbs):
        for lbj in lbs[(len(lbs) - 1):i:-1]:
            if lbi == lbj.lcm(lbi):
                # divisor found
                break
        else:
            g = lb_rel[lbi]
            if g[lbi] != ring.getRing(g[lbi]).one:
                # make it monic
                g = g.scalar_mul(ring.inverse(g[lbi]))
            reduced_basis.append(g)
    return reduced_basis
Ejemplo n.º 5
0
 def testRational(self):
     self.assertEqual(rational.Rational(3, 2),
                      ring.inverse(rational.Rational(2, 3)))
Ejemplo n.º 6
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 def testComplex(self):
     self.assertEqual(-1j, ring.inverse(1j))
Ejemplo n.º 7
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 def testFloat(self):
     self.assertEqual(0.5, ring.inverse(2.0))
Ejemplo n.º 8
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 def testInt(self):
     self.assertEqual(rational.Rational(1, 2), ring.inverse(2))