Opened 10 years ago

Closed 10 years ago

## #482 closed bug (fixed)

# bug with factorize in alg ext of deg 6 in char 32003

Reported by: | gorzel | Owned by: | somebody |
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Priority: | major | Milestone: | 3-2-0 and higher |

Component: | factory | Version: | 3-1-6 |

Keywords: | Cc: |

### Description (last modified by )

> ring R3s = (0,s),(x,y),dp; > minpoly = s2-s+1; > poly G3 = x3+y3+(-s-1)*x2+(s-2)*xy+(-s-1)*y2+(s+1)*x+(s+1)*y+(-s); > factorize(G3); [1]: _[1]=1 _[2]=x+y+(-s) _[3]=x+(-s)*y+(s-1) _[4]=x+(s-1)*y+(-s) [2]: 1,1,1,1

Now consider this cubic extension of \sqrt{-3} as defined above:

> ring R6s = (32003,s),(x,y),dp; > minpoly = (s6-11914s5+3952s4-5439s3-15290s2-15431s+15606); > factorize(x2-x+1); [1]: _[1]=1 _[2]=x+(-7372s5+12678s4+6785s3+12049s2+6154s+14657) _[3]=x+(7372s5-12678s4-6785s3-12049s2-6154s-14658) [2]: 1,1,1

The same polynomial from above should again factorize, isn't it? But factorize takes very long and gives a wrong result: The s is entirely missing and not all factors are irreducible:

> poly G3 = x3+y3+(-s-1)*x2+(s-2)*xy+(-s-1)*y2+(s+1)*x+(s+1)*y+(-s); > factorize(G3); [1]: _[1]=1 _[2]=x+y _[3]=x2-xy+y2 [2]: 1,1,1 > factorize(x2-xy+y2); [1]: _[1]=1 _[2]=(-7372s5+12678s4+6785s3+12049s2+6154s+14657)*x+y _[3]=(7372s5-12678s4-6785s3-12049s2-6154s-14658)*x+y [2]: 1,1,1

### Change History (2)

### comment:1 Changed 10 years ago by

Description: | modified (diff) |
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### comment:2 Changed 10 years ago by

Resolution: | → fixed |
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Status: | new → closed |

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Fixed with 15724