Opened 10 years ago

Closed 10 years ago

# example incorrectly decomposed by minAssChar

Reported by: Owned by: kroeker@… somebody minor 4-1-0 and higher dontKnow 4-0-1 minAssChar incorrect decomposition

### Description

The following example is incorrectly decomposed by minAssChar:

```LIB("primdec.lib");
ring rng = (0),(xy,xt,xo,xu,xj,xx,xs,xz),dp;
ideal I = -17*xy*xj^2*xx*xz-26*xt*xs+17*xj,24*xy^2*xt*xo^2+12*xy,-10*xy-7*xt*xu^2*xj*xx*xz-25*xj;
def L1 = minAssGTZ(I);
def L2 = minAssChar(I);
L1;
L2;  // size should be 4, not 5

def L3 = minAssChar(L2[4]);
L3;
isSubModule(L2[5],L3[1]); //=1
isSubModule(L2[3],L3[2]); //=1

```

output:

```> ring rng = (0),(xy,xt,xo,xu,xj,xx,xs,xz),dp;
// ** redefining rng **
> ideal I = -17*xy*xj^2*xx*xz-26*xt*xs+17*xj,24*xy^2*xt*xo^2+12*xy,-10*xy-7*xt*xu^2*xj*xx*xz-25*xj;
> def L1 = minAssGTZ(I);
> def L2 = minAssChar(I);
> L1;
[1]:
_[1]=-14161*xu^4*xj^6*xx^4*xz^4+101150*xo^2*xu^2*xj^5*xx^2*xz^2+61880*xu^2*xj^3*xx^2*xs*xz^2+40460*xo^2*xu^2*xj^3*xx*xz+552500*xo^2*xj^4*xx*xs*xz+221000*xo^2*xj^2*xs-67600*xs^2
_[2]=119*xt*xu^2*xj^3*xx^2*xz^2+425*xj^3*xx*xz-260*xt*xs+170*xj
_[3]=119*xu^2*xj^4*xx^3*xz^3+1300*xt*xo^2*xj^2*xx*xs*xz-850*xo^2*xj^3*xx*xz+520*xt*xo^2*xs-260*xj*xx*xs*xz-340*xo^2*xj
_[4]=14161*xu^4*xj^4*xx^3*xz^3-77350*xu^2*xj^3*xx^2*xs*xz^2-101150*xo^2*xu^2*xj^3*xx*xz+61880*xt*xo^2*xu^2*xs-845000*xt*xo^2*xj*xs^2-30940*xu^2*xj*xx*xs*xz-40460*xo^2*xu^2*xj+169000*xs^2
_[5]=238*xt*xo^2*xu^2*xj^2*xx*xz+119*xu^2*xj^3*xx^2*xz^2+1300*xt*xo^2*xj*xs-260*xs
_[6]=52*xt^2*xo^2*xs-34*xt*xo^2*xj-17*xj^2*xx*xz
_[7]=7*xt^2*xo^2*xu^2*xj*xx*xz+25*xt*xo^2*xj-5
_[8]=7/10*xt*xu^2*xj*xx*xz+xy+5/2*xj
[2]:
_[1]=xs
_[2]=xj
_[3]=7/10*xt*xu^2*xj*xx*xz+xy+5/2*xj
[3]:
_[1]=xj
_[2]=xt
_[3]=7/10*xt*xu^2*xj*xx*xz+xy+5/2*xj
[4]:
_[1]=119*xu^2*xj*xx*xz+650*xs
_[2]=26*xt*xs-17*xj
_[3]=7*xt*xu^2*xx*xz+25
_[4]=7/10*xt*xu^2*xj*xx*xz+xy+5/2*xj
> L2;
[1]:
_[1]=xs
_[2]=xj
_[3]=xy
[2]:
_[1]=xj
_[2]=xt
_[3]=xy
[3]:
_[1]=xy
_[2]=26*xt*xs-17*xj
_[3]=119*xu^2*xj*xx*xz+650*xs
_[4]=7*xt*xu^2*xx*xz+25
[4]:
_[1]=130*xt*xs-34*xy-85*xj
_[2]=119*xu^2-1625*xj*xs
_[3]=5*xj^2*xx*xz+2
_[4]=2*xy^2*xt*xo^2+xy
_[5]=34*xy^3*xo^2+85*xy^2*xo^2*xj+65*xy*xs
[5]:
_[1]=2*xy*xt*xo^2+1
_[2]=17*xy*xj^2*xx*xz+26*xt*xs-17*xj
_[3]=7*xu^2*xj*xx*xz-20*xy^2*xo^2-50*xy*xo^2*xj
_[4]=182*xt^2*xu^2*xs-119*xt*xu^2*xj-170*xy^2*xj-425*xy*xj^2
_[5]=52*xt^2*xo^2*xs-34*xt*xo^2*xj-17*xj^2*xx*xz
_[6]=340*xy^3*xo^2*xj+850*xy^2*xo^2*xj^2+182*xt*xu^2*xs-119*xu^2*xj
_[7]=6800*xy^5*xo^4+106250*xy^2*xo^4*xj^3+1274*xt*xu^4*xx*xs*xz+22750*xt*xo^2*xu^2*xj*xs-2380*xy^2*xo^2*xu^2+5950*xy*xo^2*xu^2*xj-14875*xo^2*xu^2*xj^2+9100*xu^2*xs
>
. def L3 = minAssChar(L2[4]);
> L3;
[1]:
_[1]=130*xt*xs-34*xy-85*xj
_[2]=119*xu^2-1625*xj*xs
_[3]=5*xj^2*xx*xz+2
_[4]=2*xy*xt*xo^2+1
_[5]=34*xy^2*xo^2+85*xy*xo^2*xj+65*xs
[2]:
_[1]=xy
_[2]=26*xt*xs-17*xj
_[3]=119*xu^2-1625*xj*xs
_[4]=5*xj^2*xx*xz+2
> isSubModule(L2[5],L3[1]);
1
> isSubModule(L2[3],L3[2]);
1
>
```

### comment:1 Changed 10 years ago by hannes

Resolution: → fixed new → closed
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