Tinkering.sagews

var_string = ""
deg = 4
for i in range(deg): 
    var_string += "a"
    var_string += str(i)
    var_string += ", "
var_string += "a"
var_string += str(deg)

a = var(var_string)
RRR.<x,y> = SR['x,y']

f = sum([a[i] * x^(deg-i) * y^i for i in range(deg+1)])

A, B, C = var('A, B, C')
QF = A*x^2 + B*x*y + C*y^2
Lap_f = C*derivative(f,x,2) - B * derivative(f,x,y) + A * derivative(f,y,2)

mat_var = matrix([[Lap_f.coefficients()[j].coefficient(a[i]) for i in range(deg+1)] for j in range(3)])
mat_var


#Choose values for the quadratic form here. N is the discriminant.
AA = 1
BB = 0
CC = 5
N = (BB^2 - 4*AA*CC).abs()


#Redefining values. Before, we computed using symbolic expressions. Now, will work in rational polynomials in x and y.

mat = mat_var.subs(A==AA, B==BB, C==CC)
A = AA
B = BB
C = CC
P.<x, y> = QQ['x,y']
QF = A*x^2 + B*x*y + C*y^2

]

[12*C -3*B 2*A 0 0] [ 0 6*C -4*B 6*A 0] [ 0 0 2*C -3*B 12*A] mat mat

cand_mod
cand_mod_coeffs
len(cand_mod_coeffs)
print"\n"
B[0]
mod_bas_list[0]
len(mod_bas_list[0])

Mprec = ModularForms(Gamma1(N), 1+deg, prec = 2*bound)
Bprec = Mprec.basis()
is_modprec = sum([is_mod_Bcoeffs[i] * Bprec[i] for i in range(len(B))])



cand_modprec = sum([
        sum(
            [
                QQ(f(x=a,y=b)) * q^(A*a^2 + B*a*b + C*b^2) for a in range(-2*lim,2*lim)
            ]
        ) for b in range(-2*lim,2*lim)
    ]
) + O(q^(2*bound))

[is_modprec.padded_list(nbound)[i] - cand_modprec.list()[0:nbound][i] for i in range(nbound)]

Error in lines 4-12 Traceback (most recent call last): File "/projects/sage/sage-7.6/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 7, in <module> File "sage/rings/integer.pyx", line 1594, in sage.rings.integer.Integer.__add__ (/projects/sage/sage-7.6/src/build/cythonized/sage/rings/integer.c:11059) return coercion_model.bin_op(left, right, operator.add) File "sage/structure/coerce.pyx", line 1104, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (/projects/sage/sage-7.6/src/build/cythonized/sage/structure/coerce.c:10499) raise bin_op_exception(op, x, y) TypeError: unsupported operand parent(s) for +: 'Integer Ring' and '<type 'list'>'

a = 1
b = 1
A

bound = 20
F = RealField(10)
A = 1
B = 1

blim = (F(bound*4 * A/N).sqrt()).ceil()
def alims(y):
    ans = []
    ans.append(F(-(bound/A).sqrt() - (B/(2*A))*y).floor())
    ans.append(F((bound/A).sqrt() - (B/(2*A)*y)).floor())
    return ans
def alims2(y):
    ans = []
    ans.append(F(-(bound/A).sqrt() - (B/2*A)*y).floor())
    ans.append(F((bound/A).sqrt() - (B/2*A)*y).floor())
    return ans

alims(5)              

Error in lines 6-10 Traceback (most recent call last): File "/projects/sage/sage-7.6/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "<string>", line 5 return ans ^ SyntaxError: invalid syntax

               






nbound = 150
nlim = nbound
Mprec = ModularForms(Gamma1(N), 1+deg, prec=nbound)
basprec = Mprec.basis()
is_modprec = sum([is_mod_Bcoeffs[i] * basprec[i] for i in range(len(basprec))])


cand_modprec = sum([sum([QQ(f(x=a,y=b)) * q^(A*a^2 + B*a*b + C*b^2) for a in range(-nlim,nlim)]) for b in range(-nlim,nlim)]) + O(q^nbound)

is_modprec
print"\n"
cand_modprec

[is_modprec.padded_list(nbound)[i] - cand_modprec.list()[0:nbound][i] for i in range(nbound)]