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Comment: implemented all the new functions for singular cubics from Kate's wishlist
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=== Project Leader === |
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| bI£Ær']D¦Ö¯ÞÌè#àCq Ç£_y;¤¥%Adì]#&ÑBX6.[ 59ÎpI DF#K#åÞ#ªmÜÜÞµmß¿:¬IУßIcÊvH²Ìú6måº!»pI? 'áø\ãÀ}â(#sBÜ7Ye·Þ]üú'4ë,êkѲúÖLýümûÈ¡µH,³¡¦Ý|[múrůG!MùdÝ/ÊÆ,øé·)¦4Ã+Þ×¢ød#ex˺!{¾vôæÑ¢Í+sü$læ.³¬¸²IH¥$¤Xu4×£ Ë*÷¼µ9Pªò¼Å' + -1£î¦zýõ}¼ÛF̦,_LZئrÎiL1Jç¦ t9D¡I'&¹î¶Åºï[E*¹büz8Â1-J¦¬æÅUYB:véX¶ ;ÇYa:\6k®ûÖõÜàd¿êP¥2ÏaXÎÞÚ´tD3×9¥úsá£Á³g öÙ·[Ölr¦Yi¸iíjeÖÊÝ )&/·»L¶ÖäÙR\FVaRÔ1¶ø}´É¸Fv¾}¾[kX[(bª5o(Eð#vtÒúôkvyçyôÐ}Àe$êE IX¥¥ ÅçÈzÏYfÃì%!5£ÆøW%étE)8EÌYE"ù1`¤P¼IjE<«Y)(WƽR²dúBéEóyÞ´²GjrNô÷K¹¤²QYE(|Î!Ûô£>ÃÚ`XGãNd°øÅXX~HºK¢é...¤¸¸º.j>Â5D\þl *%¬ m1 ií ?p°[ü:SN% ¯Ì±±0á`0«1~ió S!¹ÌxFÉÿGí ©·Ó§öÞÕ)B¥%)GYç\ïwòçnÅÑà)©Ð£9$Fdæ0ñ$ø¢ ¼n:r ø»¤Gâ:¸ïN±8Òñî30]T"¦$è?ðå$ýæHx{=>âNI7Õ<`±¸4[©æN¤;Ó¨Ðnmoq U"8fò ÅOÎãFeâYÉȦwáÜýÃxØÝdÐ(½ ä"DzQ|%"ø'r:Ì:²÷H#°råÚ5äàuÁ ! Ê( ÖSªÁÞ¤Üu¦¦6 l !7í=ä2"î=Q :Dörý}=Ý®ª% K% øñ ðvwY8=Â,#ät ù|½§ÄG PFK<yä.)8<û½ãÿO=üøCÇ!?ÉÒ)) ¨ä5CÊjYGÊò¯æ'û"Èؤ yGÒ`É# (q±.o,H`Y C 62E J0±K!tGò;Ñ?£éSè?Óð}ïìÉõ[ÜDÚÙ!?ü]ÉáBBûôzÈ |
Kate === Group Members === Aly, Jenn, Diane, Ekin === Project Description === * [[attachment:KateWishList.sws]] * Wrap E.reduction(prime)(P) so that we can also use P.reduction(prime) [[http://trac.sagemath.org/sage_trac/ticket/11822|#11822]] * Implement E.reduction(p) for E defined over a p-adic fields * This found a bug: [[http://trac.sagemath.org/sage_trac/ticket/11826|#11826]] * See what exactly is going on in E.global_minimal_model(), is it returning the unique restricted model? If so, update documentation * Implement Singular Weierstrass Equations and functionality similar to Elliptic Curves * make E.reduction(bad_prime) able to return this singular cubic object [[http://trac.sagemath.org/sage_trac/ticket/11823|#11823]] * change weierstrass model, addition of points, P.is_singular() to check if point is node/cusp, etc * Compute lots of examples to find guesses for bounds on "C" * p-adic Tate's algorithm * Put Kate's EDS class into sage (document properly)? === Singular Cubics === [[http://trac.sagemath.org/sage_trac/ticket/11823 | Trac ticket 11823 ]] * Functions that seem ok out of the box (so need only documentation adjustment/testing): * a_invariants() etc. (b, c also) * discriminant() * base_ring() * base_field() * is_on_curve() * coordinate_ring() * division_polynomial() * formal_group() * multiplication_by_m()? * Functions that should do something appropriate but don't (need coding): * j_invariant() -- should probably return +infinity? * change_weierstrass_model() -- the new curve needs to pass flag * base_extend() -- the problem may be my patch didn't work * change_ring() -- the problem may be my patch didn't work * cardinality() -- for finite fields * local stuff....?? * addition of points on a curve (seems to work, but needs to avoid singular point) * Functions that we should write (new): * is_singular() (done) -- this is also accessible as an internal flag: self._is_singular * P.is_singular_point() -- for a point on the curve * singularity_type() -- tells you if it's a node or a cusp * singular_point() -- returns the node or cusp |
Project Leader
Kate
Group Members
Aly, Jenn, Diane, Ekin
Project Description
Wrap E.reduction(prime)(P) so that we can also use P.reduction(prime) #11822
- Implement E.reduction(p) for E defined over a p-adic fields
This found a bug: #11826
- See what exactly is going on in E.global_minimal_model(), is it returning the unique restricted model? If so, update documentation
- Implement Singular Weierstrass Equations and functionality similar to Elliptic Curves
make E.reduction(bad_prime) able to return this singular cubic object #11823
- change weierstrass model, addition of points, P.is_singular() to check if point is node/cusp, etc
- Compute lots of examples to find guesses for bounds on "C"
- p-adic Tate's algorithm
* Put Kate's EDS class into sage (document properly)?
Singular Cubics
* Functions that seem ok out of the box (so need only documentation adjustment/testing):
- a_invariants() etc. (b, c also)
- discriminant()
- base_ring()
- base_field()
- is_on_curve()
- coordinate_ring()
- division_polynomial()
- formal_group()
- multiplication_by_m()?
* Functions that should do something appropriate but don't (need coding):
- j_invariant() -- should probably return +infinity?
- change_weierstrass_model() -- the new curve needs to pass flag
- base_extend() -- the problem may be my patch didn't work
- change_ring() -- the problem may be my patch didn't work
- cardinality() -- for finite fields
- local stuff....??
- addition of points on a curve (seems to work, but needs to avoid singular point)
* Functions that we should write (new):
- is_singular() (done) -- this is also accessible as an internal flag: self._is_singular
- P.is_singular_point() -- for a point on the curve
- singularity_type() -- tells you if it's a node or a cusp
- singular_point() -- returns the node or cusp