> < ^ Date: Wed, 18 Sep 1996 10:48:07 +0200
> < ^ From: Willem de Graaf <degraaf@math.uu.nl >
> ^ Subject: Factors

Dear forum,

Probably the following problem is well known, but maybe it is
worthwhile to state it again.
When given an "ugly" polynomial, the function Factors behaves in a strange way.
It does not seem to recognize that some factors are reducible.
Consider the following example:

gap> y:=Indeterminate(Rationals);; y.name:="y";;

```gap> f:=
y^33 - 398550*y^31 + 66186201873*y^29 - 5971817014857100*y^27 +
319879423075055974416*y^25 - 10453569133068665704152000*y^23 +
207491014558959631527689015040*y^21 -
2448295340120142096293200047744000*y^19 +
16690739160259700445725003902608322560*y^17 -
62701173265160849595209547823580350464000*y^15 +
118869582948995926691687807245961904820322304*y^13 -
95752347343101572852967993673317241915126579200*y^11 +
22338679946180069821565185491251863734781426532352*y^9 -
611471306080989784227382973634662004989868009062400*y^7 +
5410092199316503850833490994152109788519901066952704*y^5 -
16075861728797055597248567344887907079321523585024000*y^3 +
11254997789155806098371908864638669722435410984960000*y;

gap> fac:=Factors(f);
[ y - 2, y - 1, y + 1, y + 2, y + 3, y + 4, y + 18, y + 36, y + 54, y + 72,
y + 90, y + 108, y + 162, y + 216, y + 234, y + 252, y + 270, y + 324,
y^14 - 1843*y^13 + 1499052*y^12 - 709215588*y^11 + 216597983904*y^10 -
44820883529424*y^9 + 6420879462453696*y^8 - 639652453551705024*y^7 +
43898005996819409664*y^6 - 2025953383611993090048*y^5 +
60198152116012529098752*y^4 - 1069493914496483223257088*y^3 +
10001847348623751012089856*y^2 - 39533155087560633624821760*y +
53044787182992369175756800, y ]
```

#A factor of 'f' factorizes:

```gap> g:=fac[19];
y^14 - 1843*y^13 + 1499052*y^12 - 709215588*y^11 + 216597983904*y^10 -
44820883529424*y^9 + 6420879462453696*y^8 - 639652453551705024*y^7 +
43898005996819409664*y^6 - 2025953383611993090048*y^5 +
60198152116012529098752*y^4 - 1069493914496483223257088*y^3 +
10001847348623751012089856*y^2 - 39533155087560633624821760*y +
53044787182992369175756800

gap> Factors(g);
[ y - 324, y - 270, y - 252, y - 234, y - 216, y - 162, y - 108, y - 90,
y - 72, y - 54, y - 36, y - 18, y - 4, y - 3 ]
```

Is this behaviour due to a bug, or to the ugly input? Can anybody tell me
a good way to obtain a list of irreducible factors?

Many thanks,

Willem de Graaf
wdg@win.tue.nl

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