Revision history [back]

Here is a function

def matrice_2d(self, variables=None):
    """
    EXAMPLES::

        sage: x, y = PolynomialRing(QQ,['x', 'y']).gens()
        sage: matrice_2d(x**2+x*y+y**3)
        [1 0 0]
        [0 0 0]
        [0 1 0]
        [0 0 1]

        sage: x, y, z = PolynomialRing(QQ,['x','y','z']).gens()
        sage: matrice_2d(x**2+z*x*y+z*y**3+z*x,[y,z])
        [  x   x   0   1]
        [x^2   0   0   0]
        sage: matrice_2d(x**2+z*x*y+z*y**3+z*x,[x,z])
        [  y^3 y + 1     0]
        [    0     0     1]
    """
    if variables is None:
        ring = self.parent().base_ring()
        x, y = self.parent().gens()
        ix = 0
        iy = 1
    else:
        x, y = variables
        ring = self.parent()
        toutes_vars = x.parent().gens()
        ix = toutes_vars.index(x)
        iy = toutes_vars.index(y)
    support = self.exponents()
    minx = min(u[ix] for u in support)
    maxx = max(u[ix] for u in support)
    miny = min(u[iy] for u in support)
    maxy = max(u[iy] for u in support)
    mat = matrix(ring, maxy - miny + 1, maxx - minx + 1)
    for u in support:
        ex = u[ix]
        ey = u[iy]
        i, j = (maxy - ey, ex - minx)
        mat[i, j] = self.coefficient({x: ex, y: ey})
    return mat