Coverage for local/lib/python2.7/site-packages/sage/modular/modsym/apply.pyx : 81%

""" 

Monomial expansion of `(aX + bY)^i (cX + dY)^{j-i}` 

""" 

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

# 

# Copyright (C) 2008 William Stein <wstein@gmail.com> 

# 

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

# 

# http://www.gnu.org/licenses/ 

# 

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

from sage.ext.stdsage cimport PY_NEW 

from sage.libs.flint.fmpz_poly cimport * 

from sage.rings.integer cimport Integer 

cdef class Apply: 

def __cinit__(self): 

""" 

EXAMPLES:: 

sage: import sage.modular.modsym.apply 

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

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

""" 

fmpz_poly_init(self.f) 

fmpz_poly_init(self.g) 

fmpz_poly_init(self.ff) 

fmpz_poly_init(self.gg) 

def __dealloc__(self): 

# clear flint polys 

fmpz_poly_clear(self.f) 

fmpz_poly_clear(self.g) 

fmpz_poly_clear(self.ff) 

fmpz_poly_clear(self.gg) 

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

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

if i < 0 or j - i < 0: 

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

# f = b+a*x, g = d+c*x 

fmpz_poly_set_coeff_si(self.f, 0, b) 

fmpz_poly_set_coeff_si(self.f, 1, a) 

fmpz_poly_set_coeff_si(self.g, 0, d) 

fmpz_poly_set_coeff_si(self.g, 1, c) 

# h = (f**i)*(g**(j-i)) 

fmpz_poly_pow(self.ff, self.f, i) 

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

fmpz_poly_mul(ans, self.ff, self.gg) 

return 0 

cdef Apply A = Apply() 

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

r""" 

Return a list of the coefficients of 

.. MATH:: 

(aX + bY)^i (cX + dY)^{j-i}, 

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

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

modular symbols. 

INPUT: 

- i, j, a, b, c, d -- all ints 

OUTPUT: 

list of ints, which are the coefficients 

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

EXAMPLES: 

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

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

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

[-1, -1, 1, 1] 

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

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

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

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

""" 

cdef fmpz_poly_t pr 

fmpz_poly_init(pr) 

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

cdef Integer res 

v = [] 

for k from 0 <= k <= j: 

res = <Integer>PY_NEW(Integer) 

fmpz_poly_get_coeff_mpz(res.value, pr, k) 

v.append(int(res)) 

fmpz_poly_clear(pr) 

return v