def __init__(self, parent, polynomials, check=True):
r"""
See :class:`SchemeMorphism_polynomial_toric_variety` for documentation.
TESTS::
sage: fan = FaceFan(lattice_polytope.octahedron(2))
sage: P1xP1 = ToricVariety(fan)
sage: P1xP1.inject_variables()
Defining z0, z1, z2, z3
sage: P1 = P1xP1.subscheme(z0-z2)
sage: H = P1xP1.Hom(P1)
sage: import sage.schemes.toric.morphism as MOR
sage: MOR.SchemeMorphism_polynomial_toric_variety(H, [z0,z1,z0,z3])
Scheme morphism:
From: 2-d toric variety covered by 4 affine patches
To: Closed subscheme of 2-d toric variety
covered by 4 affine patches defined by:
z0 - z2
Defn: Defined on coordinates by sending
[z0 : z1 : z2 : z3] to [z0 : z1 : z0 : z3]
"""
SchemeMorphism_polynomial.__init__(self, parent, polynomials, check)
if check:
# Check that defining polynomials are homogeneous (degrees can be
# different if the target uses weighted coordinates)
for p in self.defining_polynomials():
if not self.domain().ambient_space().is_homogeneous(p):
raise ValueError("%s is not homogeneous!" % p)
def __init__(self, parent, polynomials, check=True):
r"""
See :class:`SchemeMorphism_polynomial_toric_variety` for documentation.
TESTS::
sage: fan = FaceFan(lattice_polytope.octahedron(2))
sage: P1xP1 = ToricVariety(fan)
sage: P1xP1.inject_variables()
Defining z0, z1, z2, z3
sage: P1 = P1xP1.subscheme(z0-z2)
sage: H = P1xP1.Hom(P1)
sage: import sage.schemes.toric.morphism as MOR
sage: MOR.SchemeMorphism_polynomial_toric_variety(H, [z0,z1,z0,z3])
Scheme morphism:
From: 2-d toric variety covered by 4 affine patches
To: Closed subscheme of 2-d toric variety
covered by 4 affine patches defined by:
z0 - z2
Defn: Defined on coordinates by sending
[z0 : z1 : z2 : z3] to [z0 : z1 : z0 : z3]
"""
SchemeMorphism_polynomial.__init__(self, parent, polynomials, check)
if check:
# Check that defining polynomials are homogeneous (degrees can be
# different if the target uses weighted coordinates)
for p in self.defining_polynomials():
if not self.domain().ambient_space().is_homogeneous(p):
raise ValueError("%s is not homogeneous!" % p)
def __init__(self, parent, polys, check=True):
"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
EXAMPLES::
sage: P1.<x,y> = ProjectiveSpace(QQ,1)
sage: H = P1.Hom(P1)
sage: H([y,2*x])
Scheme endomorphism of Projective Space of dimension 1 over Rational Field
Defn: Defined on coordinates by sending (x : y) to
(y : 2*x)
"""
SchemeMorphism_polynomial.__init__(self, parent, polys, check)
if check:
# morphisms from projective space are always given by
# homogeneous polynomials of the same degree
try:
d = polys[0].degree()
except AttributeError:
polys = [f.lift() for f in polys]
if not all([f.is_homogeneous() for f in polys]):
raise ValueError("polys (=%s) must be homogeneous"%polys)
degs = [f.degree() for f in polys]
if not all([d==degs[0] for d in degs[1:]]):
raise ValueError("polys (=%s) must be of the same degree"%polys)
def __init__(self, parent, polys, check=True):
r"""
The Python constructor.
INPUT:
- ``parent`` -- Homset
- ``polys`` -- anything that defines a point in the class
- ``check`` -- Boolean. Whether or not to perform input checks
(Default:`` True``)
EXAMPLES::
sage: T.<x,y,z,w,u> = ProductProjectiveSpaces([2,1],QQ)
sage: H = T.Hom(T)
sage: H([x^2*u,y^2*w,z^2*u,w^2,u^2])
Scheme endomorphism of Product of projective spaces P^2 x P^1 over Rational Field
Defn: Defined by sending (x : y : z , w : u) to
(x^2*u : y^2*w : z^2*u , w^2 : u^2).
::
sage: T.<x,y,z,w,u> = ProductProjectiveSpaces([2,1],QQ)
sage: H = T.Hom(T)
sage: H([x^2*u,y^2*w,z^2*u,w^2,u*z])
Traceback (most recent call last):
...
TypeError: polys (=[x^2*u, y^2*w, z^2*u, w^2, z*u]) must be
multi-homogeneous of the same degrees (by component)
"""
if check:
#check multi-homogeneous
#if self is a subscheme, we may need the lift of the polynomials
try:
polys[0].exponents()
except AttributeError:
polys = [f.lift() for f in polys]
target = parent.codomain().ambient_space()
from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
if is_ProductProjectiveSpaces(target):
splitpolys = target._factors(polys)
for m in range(len(splitpolys)):
d = target._degree(splitpolys[m][0])
if not all(d == target._degree(f) for f in splitpolys[m]):
raise TypeError(
"polys (=%s) must be multi-homogeneous of the same degrees (by component)"
% polys)
else:
#we are mapping into some other kind of space
target._validate(polys)
SchemeMorphism_polynomial.__init__(self, parent, polys, check)
def __init__(self, parent, polys, check = True):
r"""
The Python constructor.
INPUT:
- ``parent`` -- Homset
- ``polys`` -- anything that defines a point in the class
- ``check`` -- Boolean. Whether or not to perform input checks
(Default:`` True``)
EXAMPLES::
sage: T.<x,y,z,w,u> = ProductProjectiveSpaces([2,1],QQ)
sage: H = T.Hom(T)
sage: H([x^2*u,y^2*w,z^2*u,w^2,u^2])
Scheme endomorphism of Product of projective spaces P^2 x P^1 over Rational Field
Defn: Defined by sending (x : y : z , w : u) to
(x^2*u : y^2*w : z^2*u , w^2 : u^2).
::
sage: T.<x,y,z,w,u> = ProductProjectiveSpaces([2,1],QQ)
sage: H = T.Hom(T)
sage: H([x^2*u,y^2*w,z^2*u,w^2,u*z])
Traceback (most recent call last):
...
TypeError: polys (=[x^2*u, y^2*w, z^2*u, w^2, z*u]) must be
multi-homogeneous of the same degrees (by component)
"""
if check:
#check multi-homogeneous
#if self is a subscheme, we may need the lift of the polynomials
try:
polys[0].exponents()
except AttributeError:
polys = [f.lift() for f in polys]
target = parent.codomain().ambient_space()
from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
if is_ProductProjectiveSpaces(target):
splitpolys = target._factors(polys)
for m in range(len(splitpolys)):
d = target._degree(splitpolys[m][0])
if not all(d == target._degree(f) for f in splitpolys[m]):
raise TypeError("polys (=%s) must be multi-homogeneous of the same degrees (by component)"%polys)
else:
#we are mapping into some other kind of space
target._validate(polys)
SchemeMorphism_polynomial.__init__(self, parent, polys, check)
def __init__(self, polys_or_rat_fncts, domain):
r"""
The Python constructor.
EXAMPLES::
sage: from sage.dynamics.arithmetic_dynamics.generic_ds import DynamicalSystem
sage: P.<x,y> = ProjectiveSpace(QQ,1)
sage: f = DynamicalSystem_projective([x^2+y^2, y^2])
sage: isinstance(f, DynamicalSystem)
True
"""
H = End(domain)
# All consistency checks are done by the public class constructors,
# so we can set check=False here.
SchemeMorphism_polynomial.__init__(self, H, polys_or_rat_fncts, check=False)
def __init__(self, polys_or_rat_fncts, domain):
r"""
The Python constructor.
EXAMPLES::
sage: from sage.dynamics.arithmetic_dynamics.generic_ds import DynamicalSystem
sage: P.<x,y> = ProjectiveSpace(QQ,1)
sage: f = DynamicalSystem_projective([x^2+y^2, y^2])
sage: isinstance(f, DynamicalSystem)
True
"""
H = End(domain)
# All consistency checks are done by the public class constructors,
# so we can set check=False here.
SchemeMorphism_polynomial.__init__(self,
H,
polys_or_rat_fncts,
check=False)
def __init__(self, parent, polys, check=True):
r"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
INPUT:
- ``parent`` -- Hom.
- ``polys`` -- list or tuple of polynomial or rational functions.
- ``check`` -- Boolean.
OUTPUT:
- :class:`SchemeMorphism_polynomial_affine_space`.
EXAMPLES::
sage: A.<x,y> = AffineSpace(ZZ, 2)
sage: H = Hom(A, A)
sage: H([3/5*x^2, y^2/(2*x^2)])
Traceback (most recent call last):
...
TypeError: polys (=[3/5*x^2, y^2/(2*x^2)]) must be rational functions in
Multivariate Polynomial Ring in x, y over Integer Ring
::
sage: A.<x,y> = AffineSpace(ZZ, 2)
sage: H = Hom(A, A)
sage: H([3*x^2/(5*y), y^2/(2*x^2)])
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x, y) to
(3*x^2/(5*y), y^2/(2*x^2))
::
sage: A.<x,y> = AffineSpace(QQ, 2)
sage: H = Hom(A, A)
sage: H([3/2*x^2, y^2])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(3/2*x^2, y^2)
::
sage: A.<x,y> = AffineSpace(QQ, 2)
sage: X = A.subscheme([x-y^2])
sage: H = Hom(X, X)
sage: H([9/4*x^2, 3/2*y])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 2
over Rational Field defined by:
-y^2 + x
Defn: Defined on coordinates by sending (x, y) to
(9/4*x^2, 3/2*y)
sage: P.<x,y,z> = ProjectiveSpace(ZZ, 2)
sage: H = Hom(P, P)
sage: f = H([5*x^3 + 3*x*y^2-y^3, 3*z^3 + y*x^2, x^3-z^3])
sage: f.dehomogenize(2)
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x0, x1) to
((5*x0^3 + 3*x0*x1^2 - x1^3)/(x0^3 - 1), (x0^2*x1 + 3)/(x0^3 - 1))
If you pass in quotient ring elements, they are reduced::
sage: A.<x,y,z> = AffineSpace(QQ, 3)
sage: X = A.subscheme([x-y])
sage: H = Hom(X,X)
sage: u,v,w = X.coordinate_ring().gens()
sage: H([u, v, u+v])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 3
over Rational Field defined by:
x - y
Defn: Defined on coordinates by sending (x, y, z) to
(y, y, 2*y)
You must use the ambient space variables to create rational functions::
sage: A.<x,y,z> = AffineSpace(QQ, 3)
sage: X = A.subscheme([x^2-y^2])
sage: H = Hom(X,X)
sage: u,v,w = X.coordinate_ring().gens()
sage: H([u, v, (u+1)/v])
Traceback (most recent call last):
...
ArithmeticError: Division failed. The numerator is not a multiple of the denominator.
sage: H([x, y, (x+1)/y])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 3
over Rational Field defined by:
x^2 - y^2
Defn: Defined on coordinates by sending (x, y, z) to
(x, y, (x + 1)/y)
::
sage: R.<t> = PolynomialRing(QQ)
sage: A.<x,y,z> = AffineSpace(R, 3)
sage: X = A.subscheme(x^2-y^2)
sage: H = End(X)
sage: H([x^2/(t*y), t*y^2, x*z])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 3
over Univariate Polynomial Ring in t over Rational Field defined by:
x^2 - y^2
Defn: Defined on coordinates by sending (x, y, z) to
(x^2/(t*y), t*y^2, x*z)
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError("polys (=%s) must be a list or tuple" % polys)
source_ring = parent.domain().ambient_space().coordinate_ring()
target = parent.codomain().ambient_space()
if len(polys) != target.ngens():
raise ValueError("there must be %s polynomials" %
target.ngens())
try:
polys = [source_ring(poly) for poly in polys]
except TypeError: #maybe given quotient ring elements
try:
polys = [source_ring(poly.lift()) for poly in polys]
except (TypeError, AttributeError):
#must be a rational function since we cannot have
#rational functions for quotient rings
try:
if not all(p.base_ring() == source_ring.base_ring()
for p in polys):
raise TypeError(
"polys (=%s) must be rational functions in %s"
% (polys, source_ring))
polys = [
source_ring(poly.numerator()) /
source_ring(poly.denominator()) for poly in polys
]
except TypeError: #can't seem to coerce
raise TypeError(
"polys (=%s) must be rational functions in %s" %
(polys, source_ring))
self._is_prime_finite_field = is_PrimeFiniteField(
polys[0].base_ring()) # Needed for _fast_eval and _fastpolys
SchemeMorphism_polynomial.__init__(self, parent, polys, False)
def __init__(self, parent, polys, check=True):
r"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
INPUT:
- ``parent`` -- Hom
- ``polys`` -- list or tuple of polynomial or rational functions
- ``check`` -- Boolean
OUTPUT:
- :class:`SchemeMorphism_polynomial_affine_space`
EXAMPLES::
sage: A.<x,y>=AffineSpace(ZZ,2)
sage: H=Hom(A,A)
sage: H([3/5*x^2,y^2/(2*x^2)])
Traceback (most recent call last):
...
TypeError: polys (=[3/5*x^2, y^2/(2*x^2)]) must be rational functions in
Multivariate Polynomial Ring in x, y over Integer Ring
::
sage: A.<x,y>=AffineSpace(ZZ,2)
sage: H=Hom(A,A)
sage: H([3*x^2/(5*y),y^2/(2*x^2)])
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x, y) to
(3*x^2/(5*y), y^2/(2*x^2))
sage: A.<x,y>=AffineSpace(QQ,2)
sage: H=Hom(A,A)
sage: H([3/2*x^2,y^2])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(3/2*x^2, y^2)
sage: A.<x,y>=AffineSpace(QQ,2)
sage: X=A.subscheme([x-y^2])
sage: H=Hom(X,X)
sage: H([9/4*x^2,3/2*y])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 2
over Rational Field defined by:
-y^2 + x
Defn: Defined on coordinates by sending (x, y) to
(9/4*x^2, 3/2*y)
sage: P.<x,y,z>=ProjectiveSpace(ZZ,2)
sage: H=Hom(P,P)
sage: f=H([5*x^3 + 3*x*y^2-y^3,3*z^3 + y*x^2, x^3-z^3])
sage: f.dehomogenize(2)
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x0, x1) to
((5*x0^3 + 3*x0*x1^2 - x1^3)/(x0^3 - 1), (x0^2*x1 + 3)/(x0^3 - 1))
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError("polys (=%s) must be a list or tuple" % polys)
source_ring = parent.domain().ambient_space().coordinate_ring()
target = parent.codomain().ambient_space()
if len(polys) != target.ngens():
raise ValueError("there must be %s polynomials" %
target.ngens())
try:
polys = [source_ring(poly) for poly in polys]
except TypeError:
if all(p.base_ring() == source_ring.base_ring()
for p in polys) == False:
raise TypeError(
"polys (=%s) must be rational functions in %s" %
(polys, source_ring))
try:
polys = [
source_ring(poly.numerator()) /
source_ring(poly.denominator()) for poly in polys
]
except TypeError:
raise TypeError(
"polys (=%s) must be rational functions in %s" %
(polys, source_ring))
if isinstance(source_ring, QuotientRing_generic):
polys = [f.lift() for f in polys]
self._is_prime_finite_field = is_PrimeFiniteField(
polys[0].base_ring()) # Needed for _fast_eval and _fastpolys
SchemeMorphism_polynomial.__init__(self, parent, polys, False)
def __init__(self, parent, polys, check=True):
r"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
INPUT:
- ``parent`` -- Hom
- ``polys`` -- list or tuple of polynomial or rational functions
- ``check`` -- Boolean
OUTPUT:
- :class:`SchemeMorphism_polynomial_affine_space`
EXAMPLES::
sage: A.<x,y>=AffineSpace(ZZ,2)
sage: H=Hom(A,A)
sage: H([3/5*x^2,y^2/(2*x^2)])
Traceback (most recent call last):
...
TypeError: polys (=[3/5*x^2, y^2/(2*x^2)]) must be rational functions in
Multivariate Polynomial Ring in x, y over Integer Ring
::
sage: A.<x,y>=AffineSpace(ZZ,2)
sage: H=Hom(A,A)
sage: H([3*x^2/(5*y),y^2/(2*x^2)])
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x, y) to
(3*x^2/(5*y), y^2/(2*x^2))
sage: A.<x,y>=AffineSpace(QQ,2)
sage: H=Hom(A,A)
sage: H([3/2*x^2,y^2])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(3/2*x^2, y^2)
sage: A.<x,y>=AffineSpace(QQ,2)
sage: X=A.subscheme([x-y^2])
sage: H=Hom(X,X)
sage: H([9/4*x^2,3/2*y])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 2
over Rational Field defined by:
-y^2 + x
Defn: Defined on coordinates by sending (x, y) to
(9/4*x^2, 3/2*y)
sage: P.<x,y,z>=ProjectiveSpace(ZZ,2)
sage: H=Hom(P,P)
sage: f=H([5*x^3 + 3*x*y^2-y^3,3*z^3 + y*x^2, x^3-z^3])
sage: f.dehomogenize(2)
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x0, x1) to
((5*x0^3 + 3*x0*x1^2 - x1^3)/(x0^3 - 1), (x0^2*x1 + 3)/(x0^3 - 1))
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError("polys (=%s) must be a list or tuple"%polys)
source_ring =parent.domain().ambient_space().coordinate_ring()
target = parent.codomain().ambient_space()
if len(polys) != target.ngens():
raise ValueError("there must be %s polynomials"%target.ngens())
try:
polys = [source_ring(poly) for poly in polys]
except TypeError:
if all(p.base_ring()==source_ring.base_ring() for p in polys)==False:
raise TypeError("polys (=%s) must be rational functions in %s"%(polys,source_ring))
try:
polys = [source_ring(poly.numerator())/source_ring(poly.denominator()) for poly in polys]
except TypeError:
raise TypeError("polys (=%s) must be rational functions in %s"%(polys,source_ring))
if isinstance(source_ring, QuotientRing_generic):
polys = [f.lift() for f in polys]
SchemeMorphism_polynomial.__init__(self, parent,polys, False)
def __init__(self, parent, polys, check=True):
r"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
INPUT:
- ``parent`` -- Hom.
- ``polys`` -- list or tuple of polynomial or rational functions.
- ``check`` -- Boolean.
OUTPUT:
- :class:`SchemeMorphism_polynomial_affine_space`.
EXAMPLES::
sage: A.<x,y> = AffineSpace(ZZ, 2)
sage: H = Hom(A, A)
sage: H([3/5*x^2, y^2/(2*x^2)])
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x, y) to
(3*x^2/5, y^2/(2*x^2))
::
sage: A.<x,y> = AffineSpace(ZZ, 2)
sage: H = Hom(A, A)
sage: H([3*x^2/(5*y), y^2/(2*x^2)])
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x, y) to
(3*x^2/(5*y), y^2/(2*x^2))
::
sage: A.<x,y> = AffineSpace(QQ, 2)
sage: H = Hom(A, A)
sage: H([3/2*x^2, y^2])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(3/2*x^2, y^2)
::
sage: A.<x,y> = AffineSpace(QQ, 2)
sage: X = A.subscheme([x-y^2])
sage: H = Hom(X, X)
sage: H([9/4*x^2, 3/2*y])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 2
over Rational Field defined by:
-y^2 + x
Defn: Defined on coordinates by sending (x, y) to
(9/4*x^2, 3/2*y)
sage: P.<x,y,z> = ProjectiveSpace(ZZ, 2)
sage: H = Hom(P, P)
sage: f = H([5*x^3 + 3*x*y^2-y^3, 3*z^3 + y*x^2, x^3-z^3])
sage: f.dehomogenize(2)
Scheme endomorphism of Affine Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x0, x1) to
((5*x0^3 + 3*x0*x1^2 - x1^3)/(x0^3 - 1), (x0^2*x1 + 3)/(x0^3 - 1))
If you pass in quotient ring elements, they are reduced::
sage: A.<x,y,z> = AffineSpace(QQ, 3)
sage: X = A.subscheme([x-y])
sage: H = Hom(X,X)
sage: u,v,w = X.coordinate_ring().gens()
sage: H([u, v, u+v])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 3
over Rational Field defined by:
x - y
Defn: Defined on coordinates by sending (x, y, z) to
(y, y, 2*y)
You must use the ambient space variables to create rational functions::
sage: A.<x,y,z> = AffineSpace(QQ, 3)
sage: X = A.subscheme([x^2-y^2])
sage: H = Hom(X,X)
sage: u,v,w = X.coordinate_ring().gens()
sage: H([u, v, (u+1)/v])
Traceback (most recent call last):
...
ArithmeticError: Division failed. The numerator is not a multiple of the denominator.
sage: H([x, y, (x+1)/y])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 3
over Rational Field defined by:
x^2 - y^2
Defn: Defined on coordinates by sending (x, y, z) to
(x, y, (x + 1)/y)
::
sage: R.<t> = PolynomialRing(QQ)
sage: A.<x,y,z> = AffineSpace(R, 3)
sage: X = A.subscheme(x^2-y^2)
sage: H = End(X)
sage: H([x^2/(t*y), t*y^2, x*z])
Scheme endomorphism of Closed subscheme of Affine Space of dimension 3
over Univariate Polynomial Ring in t over Rational Field defined by:
x^2 - y^2
Defn: Defined on coordinates by sending (x, y, z) to
(x^2/(t*y), t*y^2, x*z)
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError("polys (=%s) must be a list or tuple"%polys)
source_ring = parent.domain().ambient_space().coordinate_ring()
target = parent.codomain().ambient_space()
if len(polys) != target.ngens():
raise ValueError("there must be %s polynomials"%target.ngens())
try:
polys = [source_ring(poly) for poly in polys]
except TypeError: #maybe given quotient ring elements
try:
polys = [source_ring(poly.lift()) for poly in polys]
except (TypeError, AttributeError):
#must be a rational function since we cannot have
#rational functions for quotient rings
try:
if not all(p.base_ring().fraction_field()==source_ring.base_ring().fraction_field() for p in polys):
raise TypeError("polys (=%s) must be rational functions in %s"%(polys, source_ring))
K = FractionField(source_ring)
polys = [K(p) for p in polys]
#polys = [source_ring(poly.numerator())/source_ring(poly.denominator()) for poly in polys]
except TypeError: #can't seem to coerce
raise TypeError("polys (=%s) must be rational functions in %s"%(polys, source_ring))
self._is_prime_finite_field = is_PrimeFiniteField(polys[0].base_ring()) # Needed for _fast_eval and _fastpolys
SchemeMorphism_polynomial.__init__(self, parent, polys, False)
