## Bug #1139

### Radical problems

Status:

Closed

Priority:

Urgent

Assignee:

Category:

enhancing/improving

Target version:

**Description**

There are still problems with radical: sometimes it gives an empty list instead of an ideal.

/**/ I := ideal(x^2, x*y+1); /**/ radical(I); []

**Related issues**

### History

#### #1 Updated by John Abbott 7 months ago

**Related to***Bug #1133: Radical bug*added

#### #2 Updated by John Abbott 7 months ago

The problem seems to be when the ideal contains 1.

/**/ radical(ideal(x/x)); []

#### #3 Updated by John Abbott 7 months ago

Here is another case where things go wrong:

/**/ use QQ[x,y,z,t]; /**/ I := ideal(2*x*y*z +2*y*t, -y^3 -x*y*t +x*t^2, x^2*z +2*x*y*z +y^2*t); /**/ radical(I); --> ERROR: I don't know how to evaluate operator + between IDEAL and LIST --> WHERE: at line 1105 (column 19) of radical.cpkg5

#### #4 Updated by John Abbott 7 months ago

Much like the example above:

I := ideal(-x^3 -x*y^2 -x^2, x^2*z -x^2 +y^2, -x^2*t +x*t^2 -x*t); I := ideal(y*z^3 +y^2*z*t, x^2*z +2*y^2, -x*y*t +y*z);

#### #5 Updated by Anna Maria Bigatti 7 months ago

another

/**/ I := ideal(x*(x^2 -y -x), x^2*z +y, t);

#### #6 Updated by Anna Maria Bigatti 7 months ago

**Status**changed from*New*to*Closed***Assignee**set to*Anna Maria Bigatti***% Done**changed from*0*to*100***Estimated time**set to*1.51 h*

Fixed: all the problem was in ideal(1).

(there is a naughty trick in `ElimRedundant(E)`

)

Now `radical(I)`

exits `I`

immediately if IsOne(I).