#17282: Implementing Wehler K3 Surfaces
-------------------------------------+-------------------------------------
Reporter: jdefaria | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.7
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers: Ben Hutz, Grayson
Authors: Joao Alberto de | Jorgenson
Faria | Work issues:
Report Upstream: N/A | Commit:
Branch: | 1edfe71b0fda3685fd3edc0bd9b9e1532d549f28
u/jdefaria/ticket/17282 | Stopgaps:
Dependencies: |
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Changes (by bhutz):
* status: needs_review => needs_work
Comment:
Here is what I see in the documentation:
ramification poly
* cite call silverman
* output: polynomial in coordinate ring of ambient space
canonical height
* change '-' to 'minus'
canonical height minus
* change '+' to 'minus'
* 'Use v=0 for the archimedean place' should be deleted
* add (local heights) after 'lambda minus heights'
canonical height plus
* - 'Use v=0 for the archimedean place' should be deleted
* add (local heights) after 'lambda plus heights'
degenerate fibers
* Remove the extra 'in' in 'The output is a list of lists where in the
elements of lists are points in the appropriate projective space.'
degenerate primes
* only over ZZ or QQ
is_symmetric_oribt
* fix 'ps`'
lambda minus
* change '-' to 'minus'
lambda plus
* change '+' to 'plus'
nth_iterate_phi
* write out 'phi'
* quotes for `psi' is fine, but you should be consistent throughout the
documentation. This is thefirst place you've done that.
nth_iterate_phi
* write out 'psi'
orbit_phi
* Function is defined in [!CaSi]
phi
* output: a point on self
psi
* output: a point on self
sigmaX
* !``self!`` - you have single quotes
* change 'while we have two points in the fiber' to 'while we can split
the fiber into pairs of points'
* output: a point on self
sigmaY
* !``self!`` - you have single quotes
* change 'while we have two points in the fiber' to 'while we can split
the fiber into pairs of points'
* output: a point on self
you are inconsistent with the hyphenation of bilinear and biquadratic. I
think it
should not be hyphenated.
----
For functionality
fiber:
* add a component = 0 example
* shouldn't the last 3 cases have an else for component == 1?
PP.<x0,x1,x2,y0,y1,y2> = !ProductProjectiveSpaces([2,2],GF(7))
L = x0*y0 + x1*y1 - 1*x2*y2
Q=(2*x0!^2 + x2*x0 + (2*x1!^2 + x2!^2))*y0!^2 + ((x0!^2 + x1*x0 +(x1!^2 +
2*x2*x1 + x2!^2))*y1 + (2*x1!^2 + x2*x1 + x2!^2)*y2)*y0 + ((2*x0!^2+ (x1 +
2*x2)*x0 + (2*x1!^2 + x2*x1))*y1!^2 + ((2*x1 + 2*x2)*x0 + (x1!^2 +x2*x1 +
2*x2!^2))*y2*y1 + (2*x0!^2 + x1*x0 + (2*x1!^2 + x2!^2))*y2!^2)
W = WehlerK3Surface([L,Q])
W.fiber([4,0,1],0)
Should have 2 points...
----
PP.<x0,x1,x2,y0,y1,y2> = !ProductProjectiveSpaces([2,2],GF(7))
L = x0*y0 + x1*y1 - 1*x2*y2
Q = (2*y0!^2 + y2*y0 + (2*y1!^2 + y2!^2))*x0!^2 + ((y0!^2 + y1*y0 +(y1!^2
+ 2*y2*y1 + y2!^2))*x1 + (2*y1!^2 + y2*y1 + y2!^2)*x2)*x0 + ((2*y0!^2+ (y1
+ 2*y2)*y0 + (2*y1!^2 + y2*y1))*x1!^2 + ((2*y1 + 2*y2)*y0 + (y1!^2 +y2*y1
+ 2*y2!^2))*x2*x1 + (2*y0!^2 + y1*y0 + (2*y1!^2 + y2!^2))*x2!^2)
W = WehlerK3Surface([L,Q])
W.fiber([1,0,0],1)
This is returning a point over base field with a entry in a quadratic
extension. That is 2 issues.
----
nth_iterates
* Unless I'm missing something, the negative seems not to be working
R.<x0,x1,x2,y0,y1,y2>=!PolynomialRing(QQ,6)
L = (-y0 - y1)*x0 + (-y0*x1 - y2*x2)
Q = (-y2*y0 - y1!^2)*x0!^2 + ((-y0!^2 - y2*y0 + (-y2*y1 - y2!^2))*x1 +
(-y0!^2 - y2*y1)*x2)*x0 + ((-y0!^2 - y2*y0 - y2!^2)*x1!^2 + (-y2*y0 -
y1!^2)*x2*x1 + (-y0!^2 + (-y1 - y2)*y0)*x2!^2)
X = WehlerK3Surface([L,Q])
P = X([1,0,-1,1,-1,0])
X.nth_iterate_phi(P,1)==X.nth_iterate_psi(P,-1)
--
Ticket URL: <http://trac.sagemath.org/ticket/17282#comment:20>
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