Coleman-Gross local height pairing on hyperelliptic curves

jbalakrishnan commented 14 years ago

Currently, a work in progress (lots of doctests need to be written and internal print statements removed; the code itself will be cleaned up over the next few weeks), but the main function, which computes the Coleman-Gross local height pairing at p for hyperelliptic curves, does the following:

(This example is computing h_7(D_1, D_2) and h_7(D_2, D_1), for D_1 = (P) - (Q) and D_2 = (Pprime)-(Qprime), in the notation of R. Coleman and B. Gross, p-adic heights on curves, Algebraic Number Theory, 1989, pp-73-81.)

        sage: R.<x> = QQ[]                                                                                
        sage: H = HyperellipticCurve(x*(x-1)*(x+9))                                                       
        sage: K = Qp(7,10)                                                                                
        sage: HK = H.change_ring(K)                                                                       
        sage: P = HK(9,36)                                                                                
        sage: Q = HK.teichmuller(P)                                                                       
        sage: Pprime = HK(-4,10)                                                                          
        sage: Qprime = HK.teichmuller(Pprime)                                                             
        sage: HK.height([(1,P),(-1,Q)],[(1,Pprime),(-1,Qprime)],10)                                       
        2*7^2 + 5*7^3 + 7^4 + 7^5 + 2*7^6 + 3*7^7 + 7^8 + 3*7^9 + O(7^10)                                 
        sage: HK.height([(1,Pprime),(-1,Qprime)],[(1,P),(-1,Q)],10)                                       
        2*7^2 + 5*7^3 + 7^4 + 7^5 + 2*7^6 + 3*7^7 + 7^8 + 3*7^9 + O(7^10)

CC: @kedlaya

Component: number theory

Keywords: heights, Coleman integration, hyperelliptic curves

Author: Jennifer Balakrishnan, Frédéric Chapoton

Branch/Commit: u/jen/8441 @ 1bf4349

Issue created by migration from https://trac.sagemath.org/ticket/8441

jbalakrishnan commented 14 years ago

a first attempt at collecting all of the local heights code

jbalakrishnan commented 14 years ago

comment:1

Attachment: 13544.patch.gz

fchapoton commented 11 years ago

comment:2

here is a tentative of rebasing on 5.12.beta3

the part in hyperelliptic_generic is rather clean and could even go in a separate ticket
the part in hyperelliptic_padic_field needs a lot of work and care

fchapoton commented 11 years ago

comment:3

apply only trac_8441_rebased.patch

fchapoton commented 11 years ago

comment:4

apply only trac_8441_rebased.patch

fchapoton commented 10 years ago

comment:5

Attachment: trac_8441_rebased.patch.gz

apply only trac_8441_rebased.patch

fchapoton commented 10 years ago

Branch: u/chapoton/8441

fchapoton commented 10 years ago

Commit: d716e79

fchapoton commented 10 years ago

New commits:

d716e79 #8441: Coleman-Gross local height pairing on hyperelliptic curves

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

f2f4963 Merge branch 'u/chapoton/8441' of ssh://trac.sagemath.org:22/sage into 8441

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 10 years ago

Changed commit from d716e79 to f2f4963

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from f2f4963 to 53001e0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

`abafc89`	`Merge branch 'u/chapoton/8441' into 6.8.b5`
`53001e0`	`trac #8441 changing monsky module location to hyperelliptic`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

3bae2a7 Merge branch 'u/chapoton/8441' of ssh://trac.sagemath.org:22/sage into 8441

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 53001e0 to 3bae2a7

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 3bae2a7 to fe74a15

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

fe74a15 Merge branch 'u/chapoton/8441' into 7.0.b2

fchapoton commented 8 years ago

Author: Jen Balakrishnan, Frédéric Chapoton

fchapoton commented 8 years ago

Changed author from Jen Balakrishnan, Frédéric Chapoton to Jennifer Balakrishnan, Frédéric Chapoton

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

`7c6bd83`	`Merge branch 'u/chapoton/8441' into 7.1.b5`
`c7465ae`	`trac #8441 some work on the doc`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from fe74a15 to c7465ae

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

be587ef Merge branch 'u/chapoton/8441' into 7.2.b0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from c7465ae to be587ef

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

2adba8d Merge branch 'u/chapoton/8441' in 7.3.rc0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from be587ef to 2adba8d

kedlaya commented 8 years ago

comment:17

So is there any mathematical obstruction to giving this a positive review? (I haven't checked all the doctest formatting, so maybe that is still an issue.)

kedlaya commented 8 years ago

comment:18

To answer my own question: it looks like there are still some missing doctests on intermediate functions, and some comments in the code that suggest points that still need to be addressed (but I didn't look more closely at the code to evaluate the suggestions).

Would it make to separate out the part of this code which is actually done into a ticket that can be reviewed and merged right away (and make that a dependency for this ticket)?

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 2adba8d to cbd1d25

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

`c1d4960`	`Merge branch 'u/chapoton/8441' in 7.4.b0`
`cbd1d25`	`trac 8441 python3 print`

fchapoton commented 8 years ago

comment:20

One could easily split to another ticket the simple (but not so interesting) changes in the file hyperelliptic_generic.

jbalakrishnan commented 8 years ago

Changed commit from cbd1d25 to none

jbalakrishnan commented 8 years ago

Changed branch from u/chapoton/8441 to u/jen/8441

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`3bae2a7`	`Merge branch 'u/chapoton/8441' of ssh://trac.sagemath.org:22/sage into 8441`
`fe74a15`	`Merge branch 'u/chapoton/8441' into 7.0.b2`
`7c6bd83`	`Merge branch 'u/chapoton/8441' into 7.1.b5`
`c7465ae`	`trac #8441 some work on the doc`
`be587ef`	`Merge branch 'u/chapoton/8441' into 7.2.b0`
`2adba8d`	`Merge branch 'u/chapoton/8441' in 7.3.rc0`
`c1d4960`	`Merge branch 'u/chapoton/8441' in 7.4.b0`
`cbd1d25`	`trac 8441 python3 print`
`c968e50`	`added a doctest to hyperelliptic_generic.py`
`1bf4349`	`Added some doctests`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Commit: 1bf4349

sagemath / sage

Coleman-Gross local height pairing on hyperelliptic curves #8441