3.2 KiB
3.2 KiB
In [13]:
R3.<x, y, z> = PolynomialRing(QQ, order='negdeglex') R2.<u, v> = PolynomialRing(QQ, order='negdeglex') R2.<u, v> = PolynomialRing(QQ, order='negdeglex') f = (v^2 - u^3)^4 + u^2 * v^7 + v^9 + u^13 g = (v^2 - u^3)^6 + u^2 * v^11 + v^13 F = z^3 - 3 * f(u=x, v=y) * z + 2 * g(u=x, v=y)
In [14]:
h = F.discriminant(z)(x=u, y=v) h.jacobian_ideal().vector_space_dimension()
Out[14]:
837
In [10]:
Out[10]:
586
In [4]:
Z0 = ZetaFunctions(h) [p.factor() for p in Z0.get_polyfaces_dictionary(compact=True) if p.number_of_terms() > 1]
Out[4]:
[(216) * (u + v) * v^6 * (u^6 - u^5*v + u^4*v^2 - u^3*v^3 + u^2*v^4 - u*v^5 + v^6), (108) * u^7 * (2*v^6 - u^7)]
In [11]:
F1 = F(x=x + 5 * z, y= y + 7 * z) F1.degree(z)
Out[11]:
13
In [12]:
dis = F1.discriminant(z)(x=u, y=v) dis.jacobian_ideal().vector_space_dimension()
Out[12]:
586
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