Re: question on setminus(set,element)

* American Citizen [2025-07-10 22:21]:
> Can anyone explain why setminus(Set,element) won't work the first time, but
> works the second time?

The first time, your set S contains [Pol(1), Pol(0)]. So, when you try to
remove [1,0], it doesn't work.

Either use S = setunion(S, simplify([[xt, yt]])) or replace S = simplify(S).

Cheers,

    K.B.
-- 
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/

> {point_on_conic(C,pt)=
> my(a,b,c,d,e,f,r,s);
> if(matsize(C)[2]!=6,return(););
> [a,b,c,d,e,f]=C;
> [r,s]=pt;
> return(a*r^2+b*r*s+c*s^2+d*r+e*s+f);
> }
> 
> {parameterize_conic(conic,pt)=
> my(k,x1,y1,P,R,rsz,S,T);
> if(matsize(conic)[2]!=6,return(););
> x1=pt[1];y1=pt[2];
> k=point_on_conic(conic,pt);
> if(k!=0,print("Point not on conic!");return(););
> y=t*(x-x1)+y1;
> P=point_on_conic(conic,[x,y]);
> print("P=",P);
> R=factor(P);
> print("Factored P =",R);
> rsz=matsize(R)[1];
> S=Set();
> for(i=1,rsz,
>   xt=-polcoef(R[i,1],0)/polcoef(R[i,1],1);
>   yt=t*(xt-x1)+y1;
>   print("at root #",i," xt,yt = ",xt,",",yt);
>   print("type xt  = ",type(xt)," type yt = ",type(yt));
>   S=setunion(S,[[xt,yt]]);
>   \\if(type(xt)!="t_POL",S=setunion(S,[xt,yt]););
> );
> print("S=",S);
> print("Attemting to remove point ",pt," from S");
> print("T=setminus(S,[",pt,"])");
> T=setminus(S,[pt]);
> print("T=",T);
> print("we now define S again");
> S=[[1, 0], [(t^2 - 1)/(t^2 + 1), -2*t/(t^2 + 1)]];
> print("S = ",S);
> print("remove ",pt);
> T=setminus(S,[pt]);
> print("new T = ",T," which is what we want");
> print("why cannot the point be removed the first time?");
> 
> if(matsize(T)[2]==1,T=T[1];);
> return(T);
> }
> c=[1,0,1,0,0,-1]
> pt=[1,0]
> parameterize_conic(c,pt)
> 
>