def __classcall_private__(cls, morphism_or_polys, domain=None):
r"""
Return the appropriate dynamical system on an affine scheme.
TESTS::
sage: A.<x> = AffineSpace(ZZ,1)
sage: A1.<z> = AffineSpace(CC,1)
sage: H = End(A1)
sage: f2 = H([z^2+1])
sage: f = DynamicalSystem_affine(f2, A)
sage: f.domain() is A
False
::
sage: P1.<x,y> = ProjectiveSpace(QQ,1)
sage: DynamicalSystem_affine([y, 2*x], domain=P1)
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
sage: H = End(P1)
sage: DynamicalSystem_affine(H([y, 2*x]))
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
::
sage: R.<x,y,z> = QQ[]
sage: f = DynamicalSystem_affine([x+y+z, y*z])
Traceback (most recent call last):
...
ValueError: Number of polys does not match dimension of Affine Space of dimension 3 over Rational Field
::
sage: A.<x,y> = AffineSpace(QQ,2)
sage: f = DynamicalSystem_affine([CC.0*x^2, y^2], domain=A)
Traceback (most recent call last):
...
TypeError: coefficients of polynomial not in Rational Field
"""
if isinstance(morphism_or_polys, SchemeMorphism_polynomial):
morphism = morphism_or_polys
R = morphism.base_ring()
polys = list(morphism)
domain = morphism.domain()
if not is_AffineSpace(domain) and not isinstance(
domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if domain != morphism_or_polys.codomain():
raise ValueError('domain and codomain do not agree')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)
elif isinstance(morphism_or_polys, (list, tuple)):
polys = list(morphism_or_polys)
else:
polys = [morphism_or_polys]
PR = get_coercion_model().common_parent(*polys)
fraction_field = any(is_FractionField(poly.parent()) for poly in polys)
if fraction_field:
K = PR.base_ring().fraction_field()
# Replace base ring with its fraction field
PR = PR.ring().change_ring(K).fraction_field()
polys = [PR(poly) for poly in polys]
else:
quotient_ring = any(
is_QuotientRing(poly.parent()) for poly in polys)
# If any of the list entries lies in a quotient ring, we try
# to lift all entries to a common polynomial ring.
if quotient_ring:
polys = [PR(poly).lift() for poly in polys]
else:
polys = [PR(poly) for poly in polys]
if domain is None:
if PR is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if fraction_field:
PR = PR.ring()
domain = AffineSpace(PR)
else:
# Check if we can coerce the given polynomials over the given domain
PR = domain.ambient_space().coordinate_ring()
try:
if fraction_field:
PR = PR.fraction_field()
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))
R = domain.base_ring()
if R is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if not is_AffineSpace(domain) and not isinstance(
domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)
def __classcall_private__(cls, morphism_or_polys, domain=None):
r"""
Return the appropriate dynamical system on an affine scheme.
TESTS::
sage: A.<x> = AffineSpace(ZZ,1)
sage: A1.<z> = AffineSpace(CC,1)
sage: H = End(A1)
sage: f2 = H([z^2+1])
sage: f = DynamicalSystem_affine(f2, A)
sage: f.domain() is A
False
::
sage: P1.<x,y> = ProjectiveSpace(QQ,1)
sage: DynamicalSystem_affine([y, 2*x], domain=P1)
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
sage: H = End(P1)
sage: DynamicalSystem_affine(H([y, 2*x]))
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
"""
if isinstance(morphism_or_polys, SchemeMorphism_polynomial):
morphism = morphism_or_polys
R = morphism.base_ring()
polys = list(morphism)
domain = morphism.domain()
if not is_AffineSpace(domain) and not isinstance(
domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if domain != morphism_or_polys.codomain():
raise ValueError('domain and codomain do not agree')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)
elif isinstance(morphism_or_polys, (list, tuple)):
polys = list(morphism_or_polys)
else:
polys = [morphism_or_polys]
# We now arrange for all of our list entries to lie in the same ring
# Fraction field case first
fraction_field = False
for poly in polys:
P = poly.parent()
if is_FractionField(P):
fraction_field = True
break
if fraction_field:
K = P.base_ring().fraction_field()
# Replace base ring with its fraction field
P = P.ring().change_ring(K).fraction_field()
polys = [P(poly) for poly in polys]
else:
# If any of the list entries lies in a quotient ring, we try
# to lift all entries to a common polynomial ring.
quotient_ring = False
for poly in polys:
P = poly.parent()
if is_QuotientRing(P):
quotient_ring = True
break
if quotient_ring:
polys = [P(poly).lift() for poly in polys]
else:
poly_ring = False
for poly in polys:
P = poly.parent()
if is_PolynomialRing(P) or is_MPolynomialRing(P):
poly_ring = True
break
if poly_ring:
polys = [P(poly) for poly in polys]
if domain is None:
f = polys[0]
CR = f.parent()
if CR is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if fraction_field:
CR = CR.ring()
domain = AffineSpace(CR)
R = domain.base_ring()
if R is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if not is_AffineSpace(domain) and not isinstance(
domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)
def __classcall_private__(cls, morphism_or_polys, domain=None):
r"""
Return the appropriate dynamical system on an affine scheme.
TESTS::
sage: A.<x> = AffineSpace(ZZ,1)
sage: A1.<z> = AffineSpace(CC,1)
sage: H = End(A1)
sage: f2 = H([z^2+1])
sage: f = DynamicalSystem_affine(f2, A)
sage: f.domain() is A
False
::
sage: P1.<x,y> = ProjectiveSpace(QQ,1)
sage: DynamicalSystem_affine([y, 2*x], domain=P1)
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
sage: H = End(P1)
sage: DynamicalSystem_affine(H([y, 2*x]))
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
"""
if isinstance(morphism_or_polys, SchemeMorphism_polynomial):
morphism = morphism_or_polys
R = morphism.base_ring()
polys = list(morphism)
domain = morphism.domain()
if not is_AffineSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if domain != morphism_or_polys.codomain():
raise ValueError('domain and codomain do not agree')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)
elif isinstance(morphism_or_polys,(list, tuple)):
polys = list(morphism_or_polys)
else:
polys = [morphism_or_polys]
# We now arrange for all of our list entries to lie in the same ring
# Fraction field case first
fraction_field = False
for poly in polys:
P = poly.parent()
if is_FractionField(P):
fraction_field = True
break
if fraction_field:
K = P.base_ring().fraction_field()
# Replace base ring with its fraction field
P = P.ring().change_ring(K).fraction_field()
polys = [P(poly) for poly in polys]
else:
# If any of the list entries lies in a quotient ring, we try
# to lift all entries to a common polynomial ring.
quotient_ring = False
for poly in polys:
P = poly.parent()
if is_QuotientRing(P):
quotient_ring = True
break
if quotient_ring:
polys = [P(poly).lift() for poly in polys]
else:
poly_ring = False
for poly in polys:
P = poly.parent()
if is_PolynomialRing(P) or is_MPolynomialRing(P):
poly_ring = True
break
if poly_ring:
polys = [P(poly) for poly in polys]
if domain is None:
f = polys[0]
CR = f.parent()
if CR is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if fraction_field:
CR = CR.ring()
domain = AffineSpace(CR)
R = domain.base_ring()
if R is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if not is_AffineSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)
def __classcall_private__(cls, morphism_or_polys, domain=None):
r"""
Return the appropriate dynamical system on an affine scheme.
TESTS::
sage: A.<x> = AffineSpace(ZZ,1)
sage: A1.<z> = AffineSpace(CC,1)
sage: H = End(A1)
sage: f2 = H([z^2+1])
sage: f = DynamicalSystem_affine(f2, A)
sage: f.domain() is A
False
::
sage: P1.<x,y> = ProjectiveSpace(QQ,1)
sage: DynamicalSystem_affine([y, 2*x], domain=P1)
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
sage: H = End(P1)
sage: DynamicalSystem_affine(H([y, 2*x]))
Traceback (most recent call last):
...
ValueError: "domain" must be an affine scheme
::
sage: R.<x,y,z> = QQ[]
sage: f = DynamicalSystem_affine([x+y+z, y*z])
Traceback (most recent call last):
...
ValueError: Number of polys does not match dimension of Affine Space of dimension 3 over Rational Field
::
sage: A.<x,y> = AffineSpace(QQ,2)
sage: f = DynamicalSystem_affine([CC.0*x^2, y^2], domain=A)
Traceback (most recent call last):
...
TypeError: coefficients of polynomial not in Rational Field
"""
if isinstance(morphism_or_polys, SchemeMorphism_polynomial):
morphism = morphism_or_polys
R = morphism.base_ring()
polys = list(morphism)
domain = morphism.domain()
if not is_AffineSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if domain != morphism_or_polys.codomain():
raise ValueError('domain and codomain do not agree')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)
elif isinstance(morphism_or_polys,(list, tuple)):
polys = list(morphism_or_polys)
else:
polys = [morphism_or_polys]
PR = get_coercion_model().common_parent(*polys)
fraction_field = any(is_FractionField(poly.parent()) for poly in polys)
if fraction_field:
K = PR.base_ring().fraction_field()
# Replace base ring with its fraction field
PR = PR.ring().change_ring(K).fraction_field()
polys = [PR(poly) for poly in polys]
else:
quotient_ring = any(is_QuotientRing(poly.parent()) for poly in polys)
# If any of the list entries lies in a quotient ring, we try
# to lift all entries to a common polynomial ring.
if quotient_ring:
polys = [PR(poly).lift() for poly in polys]
else:
polys = [PR(poly) for poly in polys]
if domain is None:
if PR is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if fraction_field:
PR = PR.ring()
domain = AffineSpace(PR)
else:
# Check if we can coerce the given polynomials over the given domain
PR = domain.ambient_space().coordinate_ring()
try:
if fraction_field:
PR = PR.fraction_field()
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))
R = domain.base_ring()
if R is SR:
raise TypeError("Symbolic Ring cannot be the base ring")
if not is_AffineSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
raise ValueError('"domain" must be an affine scheme')
if R not in Fields():
return typecall(cls, polys, domain)
if is_FiniteField(R):
return DynamicalSystem_affine_finite_field(polys, domain)
return DynamicalSystem_affine_field(polys, domain)