Re: Questions on plotting hyperellratpoints()

[hermann@stamm-wilbrandt.de]

On 2023-11-27 23:48, Bill Allombert wrote:
> plotinit(1);
> for(i=1,#X,plotmove(1,X[i],Y[i]);plotrbox(1,2,2,1));
> plotrecth(1,x=-2,2,x^2);
> plotdraw(1);
>
> I join the result.
>
> Cheers,
> Bill
Thanks Bill for that example.

I learned from you on "hyperellratpoints()" and wanted to get visual 
insight into  its results.
Especially interested I am into the pairs [z,w] with integer w, those 
are drawn as big dots.
Attached screenshot shows window for executing this:

pi@raspberrypi400:~ $ e="353*z^2 + 188*z + 36" h="40" gp -q < plt.3.gp
[[-5, 89], [-5, -89], [0, 6], [0, -6], [5, 99], [5, -99]]
-5 5 -99 99
pi@raspberrypi400:~ $


Yesterday I had to do drawing on AMD Ubuntu PC, because 7x13 font was 
missing on my Pi400.
Got help on which font package to install, now works on Raspberry Pi400 
as well:
https://forums.raspberrypi.com/viewtopic.php?t=360459


The foreach assert in line 5 verifies all hyperellratpoints property.
And the big dots for integer w are those of interest to me (for Kunerth 
algorithm).


$ cat plt.3.gp
assert(b,s)=if(!(b), error(Str(s)));
h=eval(getenv("h"));
e=eval(getenv("e"));
H=hyperellratpoints(e,h);
foreach(H,R,assert(subst(e,z,R[1])==R[2]^2));

print([R|R<-H,type(R[2])=="t_INT"]);
X=[R[1]|R<-H];
Y=[R[2]|R<-H];
Xi=[R[1]|R<-H,type(R[2])=="t_INT"];
Yi=[R[2]|R<-H,type(R[2])=="t_INT"];

print(vecmin(X)," ",vecmax(X)," ",vecmin(Y)," ",vecmax(Y));
dx=(vecmax(X)-vecmin(X))/400;
dy=(vecmax(Y)-vecmin(Y))/240;

plotinit(1);
plotscale(1,vecmin(X)-2*dx,vecmax(X)+2*dx,vecmin(Y)-2*dy,vecmax(Y)+2*dy);
for(i=1,#X,plotmove(1,X[i]-dx/2,Y[i]-dy/2);plotrbox(1,dx,dy,1));
for(i=1,#Xi,plotmove(1,Xi[i]-3*dx/2,Yi[i]-3*dy/2);plotrbox(1,3*dx,3*dy,1));
plotdraw(1);
$

Regards,

Hermann.

Attachment: hyperellratpoints.jpg
Description: JPEG image