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19552: fixes for orbit and nth_iterate
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@bhutz
bhutz committed Nov 25, 2015
1 parent df4701b commit ab4c42d
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Showing 2 changed files with 125 additions and 39 deletions.
16 changes: 8 additions & 8 deletions src/sage/schemes/generic/algebraic_scheme.py
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Expand Up @@ -2254,8 +2254,8 @@ def orbit(self, f, N):
::
sage: PS.<x,y,z> = ProjectiveSpace(QQ, 2)
sage: P1.<u,v> = ProjectiveSpace(QQ,1)
sage: H = Hom(PS,P1)
sage: P1.<u,v> = ProjectiveSpace(QQ, 1)
sage: H = Hom(PS, P1)
sage: f = H([x^2, y^2])
sage: X = PS.subscheme([x-y])
sage: X.orbit(f,2)
Expand Down Expand Up @@ -2334,8 +2334,8 @@ def nth_iterate(self, f, n , **kwds):
::
sage: PS.<x,y,z> = ProjectiveSpace(ZZ, 2)
sage: P2.<u,v,w>=ProjectiveSpace(QQ,2)
sage: H = Hom(PS,P2)
sage: P2.<u,v,w>=ProjectiveSpace(QQ, 2)
sage: H = Hom(PS, P2)
sage: f = H([x^2, y^2, z^2])
sage: X = PS.subscheme([x-y])
sage: X.nth_iterate(f,2)
Expand Down Expand Up @@ -2470,8 +2470,8 @@ def _forward_image(self, f):
::
sage: PS.<x,y,z> = ProjectiveSpace(QQ, 2)
sage: P1.<u,v> = ProjectiveSpace(QQ,1)
sage: Y= P1.subscheme([u-v])
sage: P1.<u,v> = ProjectiveSpace(QQ, 1)
sage: Y = P1.subscheme([u-v])
sage: H = End(PS)
sage: f = H([x^2, y^2, z^2])
sage: Y._forward_image(f)
Expand Down Expand Up @@ -2558,8 +2558,8 @@ def preimage(self, f):
::
sage: PS.<x,y,z> = ProjectiveSpace(ZZ, 2)
sage: P1.<u,v> = ProjectiveSpace(ZZ,1)
sage: Y= P1.subscheme([u^2-v^2])
sage: P1.<u,v> = ProjectiveSpace(ZZ, 1)
sage: Y = P1.subscheme([u^2-v^2])
sage: H = End(PS)
sage: f = H([x^2, y^2, z^2])
sage: Y.preimage(f)
Expand Down
148 changes: 117 additions & 31 deletions src/sage/schemes/projective/projective_point.py
View file
Expand Up @@ -613,7 +613,8 @@ def nth_iterate(self,f, n, **kwds):
r"""
For a map ``self`` and a point `P` in ``self.domain()``
this function returns the nth iterate of `P` by ``self``. If ``normalize==True``,
then the coordinates are automatically normalized.
then the coordinates are automatically normalized. If ``check==True``, then
the initialization checks are performed on the new point.
INPUT:
Expand Down Expand Up @@ -666,31 +667,72 @@ def nth_iterate(self,f, n, **kwds):
sage: X(2,2,3).nth_iterate(f,3)
(256 : 256 : 6561)
::
sage: P.<x,y,z> = ProjectiveSpace(QQ,2)
sage: H = Hom(P,P)
sage: f = H([x^2+3*y^2,2*y^2,z^2])
sage: P(2,7,1).nth_iterate(f,-2)
Traceback (most recent call last):
...
TypeError: must be a forward orbit
::
sage: P.<x,y,z> = ProjectiveSpace(QQ,2)
sage: P2.<u,v,w> = ProjectiveSpace(ZZ,2)
sage: H = Hom(P,P2)
sage: f = H([x^2+3*y^2,2*y^2,z^2])
sage: P2(2,7,1).nth_iterate(f,2)
Traceback (most recent call last):
...
TypeError: point is not defined over domain of function
sage: P(2,7,1).nth_iterate(f,2)
Traceback (most recent call last):
...
TypeError: map must be an endomorphism
::
sage: P.<x,y> = ProjectiveSpace(QQ, 1)
sage: H = End(P)
sage: f = H([x^3, x*y^2])
sage: P(0,1).nth_iterate(f,3, check = False)
(0 : 0)
sage: P(0,1).nth_iterate(f,3)
Traceback (most recent call last):
...
ValueError: [0, 0] does not define a valid point since all entries are 0
::
sage: P.<x,y> = ProjectiveSpace(ZZ, 1)
sage: H = End(P)
sage: f = H([x^3, x*y^2])
sage: P(2,1).nth_iterate(f,3, normalize = False)
(134217728 : 524288)
sage: P(2,1).nth_iterate(f,3, normalize = True)
(256 : 1)
.. TODO:: Is there a more efficient way to do this?
"""
if self.codomain() != f.domain():
raise TypeError("Point is not defined over domain of function")
if f.domain() != f.codomain():
raise TypeError("Domain and Codomain of function not equal")
try:
n = ZZ(n)
except TypeError:
raise TypeError("Iterate number must be an integer")
raise TypeError("point is not defined over domain of function")
if not f.is_endomorphism():
raise TypeError("map must be an endomorphism")
n = ZZ(n)
if n < 0:
raise TypeError("Must be a forward orbit")
if n == 0:
return(self)
else:
normalize = kwds.pop("normalize", False)
check = kwds.pop("check",True)
Q = f(self, check)
if normalize == True:
raise TypeError("must be a forward orbit")
Q = self
normalize = kwds.pop("normalize", False)
check = kwds.pop("check",True)
if normalize:
Q.normalize_coordinates()
for i in range(n):
Q = f(Q, check)
if normalize:
Q.normalize_coordinates()
for i in range(2, n+1):
Q = f(Q)
if normalize == True:
Q.normalize_coordinates()
return(Q)
return(Q)

def orbit(self, f, N, **kwds):
r"""
Expand Down Expand Up @@ -748,35 +790,79 @@ def orbit(self, f, N, **kwds):
sage: f = H([x^2+y^2,y^2])
sage: P.point([1,2],False).orbit(f,4,check = False)
[(1 : 2), (5 : 4), (41 : 16), (1937 : 256), (3817505 : 65536)]
::
sage: P.<x,y> = ProjectiveSpace(QQ,1)
sage: P2.<u,v> = ProjectiveSpace(CC,1)
sage: H = Hom(P,P2)
sage: f = H([x^2,2*y^2])
sage: P(2,1).orbit(f,2)
Traceback (most recent call last):
...
TypeError: map must be an endomorphism for iteration
::
sage: P.<x,y> = ProjectiveSpace(QQ,1)
sage: H = End(P)
sage: f = H([x^2,2*y^2])
sage: P(2,1).orbit(f,[-1,4])
Traceback (most recent call last):
...
TypeError: orbit bounds must be non-negative
sage: P(2,1).orbit(f,0.1)
Traceback (most recent call last):
...
TypeError: Attempt to coerce non-integral RealNumber to Integer
::
sage: P.<x,y> = ProjectiveSpace(QQ,1)
sage: H = End(P)
sage: f = H([x^3,x*y^2])
sage: P(0,1).orbit(f,3)
Traceback (most recent call last):
...
ValueError: [0, 0] does not define a valid point since all entries are 0
sage: P(0,1).orbit(f,3, check = False)
[(0 : 1), (0 : 0), (0 : 0), (0 : 0)]
::
sage: P.<x,y> = ProjectiveSpace(ZZ, 1)
sage: H = End(P)
sage: f = H([x^3, x*y^2])
sage: P(2,1).orbit(f,3, normalize = False)
[(2 : 1), (8 : 2), (512 : 32), (134217728 : 524288)]
sage: P(2,1).orbit(f,3, normalize = True)
[(2 : 1), (4 : 1), (16 : 1), (256 : 1)]
"""
if not f.is_endomorphism():
raise TypeError("Map must be an endomorphism for iteration.")
raise TypeError("map must be an endomorphism for iteration")
if (isinstance(N,(list,tuple))==False):
N = [0,N]
try:
N[0] = ZZ(N[0])
N[1] = ZZ(N[1])
except TypeError:
raise TypeError("Orbit bounds must be integers")
N[0] = ZZ(N[0])
N[1] = ZZ(N[1])
if N[0] < 0 or N[1] < 0:
raise TypeError("Orbit bounds must be non-negative")
raise TypeError("orbit bounds must be non-negative")
if N[0] > N[1]:
return([])

Q = copy(self)
check = kwds.pop("check",True)
normalize = kwds.pop("normalize",False)

if normalize == True:
if normalize:
Q.normalize_coordinates()
for i in range(1, N[0]+1):
Q = f(Q, check)
if normalize == True:
if normalize:
Q.normalize_coordinates()
Orb = [Q]
for i in range(N[0]+1, N[1]+1):
Q = f(Q, check)
if normalize == True:
if normalize:
Q.normalize_coordinates()
Orb.append(Q)
return(Orb)
Expand Down

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