Singular crashes when I try to calculate the radical of an ideal.

[klooster@…]

(See attachment)

[klooster@…]

Input/output

[Oleksandr]

output of Singularg (recent trunk version)

[gorzel]

1. The essence of the crash is the following bug:

>  ring Ra = (0,a),x,dp;
>  poly f0 = a*(a2+a+1);
>  poly f1 = a*(a2+a+1) +1;
>  ring ra = (0,a),x,dp;
>  minpoly = a2+a+1;
>  imap(Ra,f1);
1
>  imap(Ra,f0);
Singular : signal 11 (v: 3130/ 14215 ):
current line:>> imap(Ra,f0);<<
Segment fault/Bus error occurred at 2b7d5ebff260 because of 10246 (r:1305549581)
please inform the authors
trying to restart...

2.) Altough, I guess, it is not too difficult to fix this bug, it seems that the

proc radical is limited for computations for rings (in char 0 ?) without algebraic extension. (The minpoly is not just "forgotten" but it can not be set in the implementation since some variables are moved to parameters.) Or, will the result always be correct when the coefficients of intemediate results are finally reduced by the minpoly?

3.) @klooster: Despite this unsolved question yet, Singular can easily compute the radical:

(I have simplified the code a little bit.)

> LIB "linalg.lib";
> ring R=(0,a),(x,y,z),dp;
> minpoly = a2+a+1;
> poly f1=x3+y3+z3;
> matrix m[3][3]=1,0,1,1,0,a,1,1,0;
> matrix v[3][1]=x2,y2,z2;
> map phir=R,(-det(m)*inverse(m)*v);
> poly f2=phir(f1);
> option(redSB);
> facstd(jacob(f2));
[1]:
   _[1]=z
   _[2]=x-y
[2]:
   _[1]=z
   _[2]=x+y
[3]:
   _[1]=y
   _[2]=x2+(-a-2)*z2
[4]:
   _[1]=x
   _[2]=y2+(a-1)*z2

[seelisch]

fixed with revision 14234 (fix in longalg.cc)