mnuk_conditions() Fraction Field Timing Test

mnuk_conditions_fraction_fields.py

# coding: utf-8

# In[1]:

R = QQbar['x,y']
x,y = R.gens()

g1 = x^4 + x^2*y^2 + (-2)*x^2*y - x*y^2 + y^2
g2 = -x^7 + 2*x^3*y + y^3
g = g1

d = g.total_degree()

#
# construct generalized adjoint polynomial
#
cvars = ['c_%d_%d'%(i,j) for i in range(d-2) for j in range(d-2)]
vars = list(R.variable_names()) + cvars
C = PolynomialRing(QQbar, cvars)
S = PolynomialRing(C, [x,y])
T = PolynomialRing(QQbar, vars)
c = S.base_ring().gens()
x,y = S(x),S(y)
P = sum(c[j+(d-2)*i] * x**i * y**j
        for i in range(d-2) for j in range(d-2)
        if i+j <= d-3)

#
# construct intergral basis element
#
b = (x^2*y - x*y + y)/x^2

print(g)
print(P)
print(b)


# In[2]:

generic_adjoint = P

R = g.parent()
S = generic_adjoint.parent()
B = S.base_ring()
c = B.gens()
T = QQbar[R.variable_names() + B.variable_names()]

print(S)
print(B)
print(T)


# In[3]:

B = PolynomialRing(QQbar, [R.variable_names()[0]] + list(B.variable_names()))
print(B)


# In[4]:

def method1():
    Q = B.fraction_field()[R.variable_names()[1]]
    u, v = map(Q, R.gens())
    numer = b.numerator()
    denom = b.denominator()
    expr = numer(u,v) * generic_adjoint(u,v)
    modulus = g(u,v)
    r_reduced_mod_g = expr % modulus
    return r_reduced_mod_g

def method2():
    Q = B[R.variable_names()[1]]
    u, v = map(Q, R.gens())
    numer = b.numerator()
    denom = b.denominator()
    expr = numer(u,v) * generic_adjoint(u,v)
    modulus = g(u,v)
    r_reduced_mod_g = expr.change_ring(B.fraction_field()) % modulus
    return r_reduced_mod_g

timeit('method1()')
timeit('method2()')