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Added examples over number fields, fixed an issue with changing the b…
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…ase ring not specifying the embedding.
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@aodesky
aodesky committed Nov 19, 2019
1 parent 827ae2f commit 39c7482
Showing 1 changed file with 38 additions and 13 deletions.
51 changes: 38 additions & 13 deletions src/sage/dynamics/arithmetic_dynamics/projective_ds.py
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Original file line number Diff line number Diff line change
Expand Up @@ -405,14 +405,14 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
polys = [PR(poly) for poly in polys]
domain = ProjectiveSpace(PR)
else:
# Check if we can coerce the given polynomials over the given domain
# Check if we can coerce the given polynomials over the given domain
PR = domain.ambient_space().coordinate_ring()
try:
polys = [PR(poly) for poly in polys]
except TypeError:
raise TypeError('coefficients of polynomial not in {}'.format(domain.base_ring()))
if len(polys) != domain.ambient_space().coordinate_ring().ngens():
raise ValueError('Number of polys does not match dimension of {}'.format(domain))
raise ValueError('Number of polys does not match dimension of {}'.format(domain))
R = domain.base_ring()
if R is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
Expand Down Expand Up @@ -1570,7 +1570,7 @@ def conjugate(self, M, adjugate=False, normalize=False):
((1/3*i)*x^2 + (1/2*i)*y^2 : (-i)*y^2)
TESTS::
sage: R = ZZ
sage: P.<x,y>=ProjectiveSpace(R,1)
sage: f=DynamicalSystem_projective([x^2 + y^2,y^2])
Expand All @@ -1583,7 +1583,7 @@ def conjugate(self, M, adjugate=False, normalize=False):
Dynamical System of Projective Space of dimension 1 over Integer Ring
Defn: Defined on coordinates by sending (x : y) to
(8*x^2 + 16*x*y + 7*y^2 : -24*x^2 - 40*x*y - 16*y^2)
"""
if not (M.is_square() == 1 and M.determinant() != 0
and M.ncols() == self.domain().ambient_space().dimension_relative() + 1):
Expand Down Expand Up @@ -2594,7 +2594,7 @@ def minimal_model(self, return_transformation=False, prime_list=None, algorithm=
sage: f.minimal_model(prime_list=[3])
Dynamical System of Projective Space of dimension 1 over Rational Field
Defn: Defined on coordinates by sending (x : y) to
(2*x^2 : y^2)
(2*x^2 : y^2)
TESTS::
Expand Down Expand Up @@ -2660,7 +2660,7 @@ def minimal_model(self, return_transformation=False, prime_list=None, algorithm=
R = f.domain().coordinate_ring()
F = R(f[0].numerator())
G = R(f[0].denominator())

if G.degree() == 0 or F.degree() == 0:
#can use BM for polynomial
from .endPN_minimal_model import HS_minimal
Expand Down Expand Up @@ -4063,7 +4063,7 @@ def reduced_form(self, **kwds):
sage: f.reduced_form(smallest_coeffs=False)
(
Dynamical System of Projective Space of dimension 1 over Number Field in w with defining polynomial x^2 - 2 with w = 1.414213562373095?
Defn: Defined on coordinates by sending (x : y) to
Defn: Defined on coordinates by sending (x : y) to
(x^3 : (w)*y^3) ,
<BLANKLINE>
[ 1 -12]
Expand All @@ -4081,7 +4081,7 @@ def reduced_form(self, **kwds):
sage: f.reduced_form(smallest_coeffs=False)
(
Dynamical System of Projective Space of dimension 1 over Number Field in w with defining polynomial x^5 + x - 3 with w = 1.132997565885066?
Defn: Defined on coordinates by sending (x : y) to
Defn: Defined on coordinates by sending (x : y) to
(12*x^3 : (2334*w)*y^3) ,
<BLANKLINE>
[ 0 -1]
Expand Down Expand Up @@ -4347,6 +4347,17 @@ def is_chebyshev(self):
sage: F.is_chebyshev()
True
sage: P.<x,y> = ProjectiveSpace(QQ, 1)
sage: F = DynamicalSystem_projective([2*x^2 - y^2, y^2])
sage: L.<i> = CyclotomicField(4)
sage: M = Matrix([[0,i],[-i,0]])
sage: F.conjugate(M)
Dynamical System of Projective Space of dimension 1 over Cyclotomic Field of order 4 and degree 2
Defn: Defined on coordinates by sending (x : y) to
((-i)*x^2 : (-i)*x^2 + (2*i)*y^2)
sage: F.is_chebyshev()
True
REFERENCES:
Algorithm obtained from Milnor. For more information, see Theorem 4.1 in
Expand All @@ -4367,8 +4378,8 @@ def is_chebyshev(self):

# Get field of definition for critical points
# Change base field
critical_field = self.field_of_definition_critical()
F_crit = self.change_ring(critical_field)
critical_field,phi = self.field_of_definition_critical(return_embedding=True)
F_crit = self.change_ring(phi)

# Get the critical points and post-critical set
crit_set = set(F_crit.critical_points())
Expand Down Expand Up @@ -4477,6 +4488,20 @@ def is_lattes(self):
sage: F.is_lattes()
True
sage: f = P.Lattes_map(EllipticCurve([0,0,0,0,2]),2)
sage: f.is_lattes()
True
sage: f = P.Lattes_map(EllipticCurve([0,0,0,0,2]),2)
sage: L.<i> = CyclotomicField(4)
sage: M = Matrix([[i,0],[0,-i]])
sage: f.conjugate(M)
Dynamical System of Projective Space of dimension 1 over Cyclotomic Field of order 4 and degree 2
Defn: Defined on coordinates by sending (x : y) to
((-1/4*i)*x^4 + (-4*i)*x*y^3 : (-i)*x^3*y + (2*i)*y^4)
sage: f.is_lattes()
True
REFERENCES:
Algorithm obtained from Milnor. For more information, see Theorem 4.1 in
Expand All @@ -4496,8 +4521,8 @@ def is_lattes(self):

# Get field of definition for critical points
# Change base field
critical_field = self.field_of_definition_critical()
F_crit = self.change_ring(critical_field)
critical_field,phi = self.field_of_definition_critical(return_embedding=True)
F_crit = self.change_ring(phi)

# Get the critical points and post-critical set
crit = F_crit.critical_points()
Expand Down Expand Up @@ -5856,7 +5881,7 @@ def normal_form(self, return_conjugation=False):
From: Finite Field of size 3
To: Finite Field in z2 of size 3^2
Defn: 1 |--> 1
"""
#defines the field of fixed points
if self.codomain().dimension_relative() != 1:
Expand Down

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