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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/modular/modsym/apply.pyx
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##########################################################################

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#

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#       Copyright (C) 2008 William Stein <[email protected]>

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#

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#  Distributed under the terms of the GNU General Public License (GPL)

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#

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#                  http://www.gnu.org/licenses/

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#

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##########################################################################

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from sage.rings.integer cimport Integer

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## from sage.rings.all import QQ

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## R = QQ['X']

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## def apply_to_monomial_0(int i, int j, int a, int b, int c, int d):

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##     f = R([b,a])

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##     g = R([d,c])

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##     if i < 0 or j-i < 0:

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##         raise ValueError, "i (=%s) and j-i (=%s) must both be nonnegative."%(i,j-i)

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##     h = (f**i)*(g**(j-i))

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##     return [int(z) for z in h.padded_list(j+1)]

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cdef class Apply:

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    def __cinit__(self):

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        """

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        EXAMPLES::

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            sage: import sage.modular.modsym.apply

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            sage: sage.modular.modsym.apply.Apply()

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            <sage.modular.modsym.apply.Apply object at ...>

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        """

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        fmpz_poly_init(self.f)

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        fmpz_poly_init(self.g)

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        fmpz_poly_init(self.ff)

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        fmpz_poly_init(self.gg)

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    def __dealloc__(self):

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        # clear flint polys

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        fmpz_poly_clear(self.f)

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        fmpz_poly_clear(self.g)

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        fmpz_poly_clear(self.ff)

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        fmpz_poly_clear(self.gg)

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    cdef int apply_to_monomial_flint(self, fmpz_poly_t ans, int i, int j,

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                                     int a, int b, int c, int d) except -1:

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        if i < 0 or j-i < 0:

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            raise ValueError, "i (=%s) and j-i (=%s) must both be nonnegative."%(i,j-i)

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        # f = b+a*x, g = d+c*x

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        fmpz_poly_set_coeff_si(self.f, 0, b)

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        fmpz_poly_set_coeff_si(self.f, 1, a)

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        fmpz_poly_set_coeff_si(self.g, 0, d)

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        fmpz_poly_set_coeff_si(self.g, 1, c)

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        # h = (f**i)*(g**(j-i))

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        fmpz_poly_power(self.ff, self.f, i)

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        fmpz_poly_power(self.gg, self.g, j-i)

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        fmpz_poly_mul(ans, self.ff, self.gg)

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        return 0

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cdef Apply A = Apply()        

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def apply_to_monomial(int i, int j, int a, int b, int c, int d):

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    r"""

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    Returns a list of the coefficients of

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    .. math::

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        (aX + bY)^i (cX + dY)^{j-i},

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    where `0 \leq i \leq j`, and `a`, `b`, `c`, `d` are integers.

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    One should think of `j` as being `k-2` for the application to

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    modular symbols.

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    INPUT:

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        i, j, a, b, c, d -- all ints

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    OUTPUT:

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        list of ints, which are the coefficients

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        of `Y^j, Y^{j-1}X, \ldots, X^j`, respectively.

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    EXAMPLE:

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    We compute that `(X+Y)^2(X-Y) = X^3 + X^2Y - XY^2 - Y^3`::

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        sage: from sage.modular.modsym.manin_symbols import apply_to_monomial

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        sage: apply_to_monomial(2, 3, 1,1,1,-1)

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        [-1, -1, 1, 1]

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        sage: apply_to_monomial(5, 8, 1,2,3,4)

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        [2048, 9728, 20096, 23584, 17200, 7984, 2304, 378, 27]

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        sage: apply_to_monomial(6,12, 1,1,1,-1)

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        [1, 0, -6, 0, 15, 0, -20, 0, 15, 0, -6, 0, 1]

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    """

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    cdef fmpz_poly_t pr

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    fmpz_poly_init(pr)

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    A.apply_to_monomial_flint(pr, i,j,a,b,c,d)

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    cdef Integer res

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    v = []

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    for k from 0 <= k <= j:

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        res = <Integer>PY_NEW(Integer)

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        fmpz_poly_get_coeff_mpz(res.value, pr, k)

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        v.append(int(res))

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    fmpz_poly_clear(pr)

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    return v

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