American Citizen on Sat, 19 Sep 2026 20:01:08 +0200


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Re: ellsaturation command seems to stall 

Bill:

Are you recommending that I first do a

newpts = ellsaturation(E, ellrank(E,,pts)[4],100);

or do a check on the height matrix determinant?

if (matdet(ellheightmatrix(E,pts))>0, newpts=ellsaturation(E,pts,100); )
which will be faster? (we have to be careful of the compare > to 0, of course for the second method) 

On 9/19/26 1:58 AM, Bill Allombert wrote:

On Fri, Sep 18, 2026 at 08:42:42PM -0700, American Citizen wrote:

e = [0,0,0,-72861431597512234542597483241318304999170171524,0]
E = ellinit(e);
pts = [[-159584292563591469352487899476/5640625,604884467535685780976790902516983124195628732/13396484375],[-19875088265207102621947453239589602/613842477361,-23190668479332806276529480584169011271541209949960560/480933918005273641],[2597574587884253539128016089286584424837350/8199050792271543961,2191748221922523054556252054243121981245288930562272743596075160/23477149485843576010193595709],[14913210246611888728570538903421836598324440706412/114289368274834186281241,57591154097437521182647324414747899691570150391720633081079403290022093060/38637475998784887960960692812638211],[4132593969455390759213839253184111699726180870668850/2832658051228154165913437641,261078053305587758544937947266389832189966563682739963130186205405814136491840/150761769696696337805847826168015818578939],[66924537388743778762373298037915478362524152321338350/27707221962388303004643881209,17204780294515010335899832096364537991279543034204545408060633464011035035969760/4612001881305404713815667363558277257645427],[-310911297865959224284346132876850222780649215760857975/10332368394182926947048314214976,-1545437798152720947632517222147155849628432282982722722812452864643601017390152795/33212366628400525342454386598582697723846027776]];

print("e = ",e);
print("pts = ",pts);

ellheight(E,pts[1])
ellheight(E,pts[2])
ellheight(E,pts[3])
ellheight(E,pts[4])
ellheight(E,pts[5])
ellheight(E,pts[6])

ellsaturation(E,pts,100)
----------------

this program hangs up. Any idea why?

Yes, your points are not independant,
? #pts
%3 = 7
and not 6
? R=ellrank(E,,pts)
%6 = [6,6,0,[[-19875088265207102621947453239589602/613842477361,23190668479332806276529480584169011271541209949960560/480933918005273641],[-159584292563591469352487899476/5640625,604884467535685780976790902516983124195628732/13396484375],[2597574587884253539128016089286584424837350/8199050792271543961,2191748221922523054556252054243121981245288930562272743596075160/23477149485843576010193595709],[14913210246611888728570538903421836598324440706412/114289368274834186281241,57591154097437521182647324414747899691570150391720633081079403290022093060/38637475998784887960960692812638211],[4132593969455390759213839253184111699726180870668850/2832658051228154165913437641,261078053305587758544937947266389832189966563682739963130186205405814136491840/150761769696696337805847826168015818578939],[66924537388743778762373298037915478362524152321338350/27707221962388303004643881209,17204780294515010335899832096364537991279543034204545408060633464011035035969760/4612001881305404713815667363558277257645427]]]

? ellsaturation(E,R[4],100)
%10 = [[-159584292563591469352487899476/5640625,604884467535685780976790902516983124195628732/13396484375],[-19875088265207102621947453239589602/613842477361,23190668479332806276529480584169011271541209949960560/480933918005273641],[2597574587884253539128016089286584424837350/8199050792271543961,2191748221922523054556252054243121981245288930562272743596075160/23477149485843576010193595709],[66924537388743778762373298037915478362524152321338350/27707221962388303004643881209,17204780294515010335899832096364537991279543034204545408060633464011035035969760/4612001881305404713815667363558277257645427],[14913210246611888728570538903421836598324440706412/114289368274834186281241,57591154097437521182647324414747899691570150391720633081079403290022093060/38637475998784887960960692812638211],[4132593969455390759213839253184111699726180870668850/2832658051228154165913437641,261078053305587758544937947266389832189966563682739963130186205405814136491840/150761769696696337805847826168015818578939]]
? ellsaturation(E,pts[1..6],100)
%11 = [[-159584292563591469352487899476/5640625,604884467535685780976790902516983124195628732/13396484375],[-19875088265207102621947453239589602/613842477361,-23190668479332806276529480584169011271541209949960560/480933918005273641],[2597574587884253539128016089286584424837350/8199050792271543961,2191748221922523054556252054243121981245288930562272743596075160/23477149485843576010193595709],[66924537388743778762373298037915478362524152321338350/27707221962388303004643881209,17204780294515010335899832096364537991279543034204545408060633464011035035969760/4612001881305404713815667363558277257645427],[14913210246611888728570538903421836598324440706412/114289368274834186281241,57591154097437521182647324414747899691570150391720633081079403290022093060/38637475998784887960960692812638211],[4132593969455390759213839253184111699726180870668850/2832658051228154165913437641,261078053305587758544937947266389832189966563682739963130186205405814136491840/150761769696696337805847826168015818578939]]


Cheers,
Bill.