Differences between revisions 1 and 18 (spanning 17 versions)

Modular Abelian Varieties

Code at http://trac.sagemath.org/sage_trac/ticket/2544

Todo on March 16

DONE (craig) Newforms issue:

   sage: f = CuspForms(37).newforms('a')[0]
   sage: f.coefficients(10)
   ------------------------------------
   <type 'exceptions.TypeError'>             Traceback (most recent call last)
   sage: f.coefficients([2..10])
   ------------------------------------
   <type 'exceptions.AttributeError'>        Traceback (most recent call last)
   ...
   <type 'exceptions.AttributeError'>: 'Newform' object has no attribute '_compute'

DONE (william) This is completely wrong (the modabvar function on modular symbols assumes it's ambient!):

   sage: m = ModularSymbols(37)[1]
   sage: m.modular_abelian_variety()
   Jacobian of the modular curve associated to the congruence subgroup Gamma0(37)

DONE (william) Move functions out of abvar_modsym_factor into abvar and delete that file.
DONE (william) Torsion subgroups:
- (already done) Refactor base class
- (done) Get implementation to work with defining data being (lattice, abvar); compute generators.
- (done) Quotients by finite subgroup
DONE (craig) Implement f.number() for f a newform.
DONE-ish (craig) Compute the Hecke algebra image in End(A) and find a good clean way to represent for Hecke stable. New object that is a subring of End(A). Have methods like R.index_in(S).
DONE (craig) abelian varieties should cache their ambient modular abelian variety

Todo on Monday, March 17

(craig) Compute End(A):
- for simple A_f (DONE)
- in general.
- disc of it.
- ideals and annihilators
- order in a ring of integers (for A simple)
- given a ring R in EndAlg(A) where every element has integral charpoly, find an isogenous abelian variety with End(A) = R.
- explicit isomorphism between HeckeAlgebra sitting in End(A) and a commutative ring
- base extension of End(A)
(craig) Degeneracy maps
(william) Decomposition:
- three types:
  - ungrouped as simple abvars (default)
  - groups abvars
  - over End(A)
  - deprecate hecke_decomposition
- (done) label function
- create from label
(william/craig) Morphisms:
- Kernels
- Cokernels
(william/craig) Isogenies:
- Complementary -- invert matrix, clear denom.
- Dual
(william) Intersection pairing
(?) Poincare Reducibility:
- projection
- quotients by abelian subvariety
(craig/william) Minimal isogeny degree for A, B simple.
(craig/william) Create a small mock database

Todo on Tuesday, March 18

Write doctests, etc., for everything above.
Optimize everything

Todo on Wednesday, March 19

Write up paper

-  ⇤ ← Revision 1 as of 2008-03-16 22:55:00 → 
  Size: 1037
  Editor: was
  Comment:
+   ← Revision 18 as of 2008-03-17 21:42:13 → ⇥
  Size: 2900
  Editor: CraigCitro
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 3:
+Code at http://trac.sagemath.org/sage_trac/ticket/2544
-Line 6:
+Line 7:
- * Move functions out of abvar_modsym_factor into abvar and delete that file.
+ * DONE (craig) Newforms issue:
   {{{
   sage: f = CuspForms(37).newforms('a')[0]
   sage: f.coefficients(10)
   ------------------------------------
   <type 'exceptions.TypeError'>             Traceback (most recent call last)
   sage: f.coefficients([2..10])
   ------------------------------------
   <type 'exceptions.AttributeError'>        Traceback (most recent call last)
   ...
   <type 'exceptions.AttributeError'>: 'Newform' object has no attribute '_compute'
   }}}
-Line 8:
+Line 20:
- * Torsion subgroups:
    * Refactor base class
    * Get implementation to work with defining data being (lattice, abvar); compute generators.
+ * DONE (william) This is completely wrong (the modabvar function on modular symbols assumes it's ambient!):
   {{{
   sage: m = ModularSymbols(37)[1]
   sage: m.modular_abelian_variety()
   Jacobian of the modular curve associated to the congruence subgroup Gamma0(37)
   }}}
-Line 12:
+Line 27:
- * Decomposition:
+ * DONE (william) Move functions out of abvar_modsym_factor into abvar and delete that file. 

 * DONE (william) Torsion subgroups:
    * (already done) Refactor base class
    * (done) Get implementation to work with defining data being (lattice, abvar); compute generators. 
    * (done) Quotients by finite subgroup

 * DONE (craig) Implement {{{f.number()}}} for f a newform. 

 * DONE-ish (craig) Compute the Hecke algebra image in End(A) and find a good clean way to represent for Hecke stable.  New object that is a subring of End(A).   Have methods like {{{R.index_in(S)}}}.

 * DONE (craig) abelian varieties should cache their ambient modular abelian variety

== Todo on Monday, March 17 ==

 * (craig) Compute End(A):
     * for simple $A_f$ (DONE)
     * in general.
     * disc of it.
     * ideals and annihilators
     * order in a ring of integers (for A simple)
     * given a ring R in EndAlg(A) where every element has integral charpoly, find an isogenous abelian variety with End(A) = R.
     * explicit isomorphism between HeckeAlgebra sitting in End(A) and a commutative ring
     * base extension of End(A)

 * (craig) Degeneracy maps

 * (william) Decomposition:
-Line 17:
+Line 59:
+        * deprecate hecke_decomposition
   * (done) label function
   * create from label
-Line 18:
+Line 63:
- * Label function

 * Create from label

 * Create a small mock database

 * Compute the Hecke algebra image in End(A) and find a good clean way to represent for Hecke stable.  New object that is a subring of End(A).   Have methods like {{{R.index_in(S)}}}.

 * Compute End(A) in general.

 * Morphisms:
+ * (william/craig) Morphisms:
-Line 31:
+Line 66:
+ * (william/craig) Isogenies:
    * Complementary -- invert matrix, clear denom. 
    * Dual
-Line 32:
+Line 71:
- * Quotients by finite subgroup
+ * (william) Intersection pairing
-Line 34:
+Line 73:
- * Intersection pairing
+ * (?) Poincare Reducibility:
    * projection
    * quotients by abelian subvariety
-Line 36:
+Line 77:
- * Poincare Reducibility:
    * projection
+ * (craig/william) Minimal isogeny degree for A, B simple.
-Line 39:
+Line 79:
- * Quotients by abelian subvariety

 * Minimal isogeny degree for A, B simple.
+ * (craig/william) Create a small mock database
-Line 45:
+Line 82:
+== Todo on Tuesday, March 18 ==
-Line 46:
+Line 84:
-== Todo on March 17 ==
+ * Write doctests, etc., for everything above.
-Line 48:
+Line 86:
- * Optimize decomposition
+ * Optimize everything

== Todo on Wednesday, March 19 ==

 * Write up paper

Diff for "modabvar"

Modular Abelian Varieties

Todo on March 16

Todo on Monday, March 17

Todo on Tuesday, March 18

Todo on Wednesday, March 19