> < ^ Date: Sat, 17 Sep 1994 21:16:00 -0700
> < ^ From: Jacob Hirbawi <hirbawi@commquest.com >
> ^ Subject: a problem with factoring polynomials

I am having this problem with factoring polynomials : the product of the
factors doesn't match the original polynomial. I am using GAP 3.4 and I
am fairly sure this example used to work in the previous release.

```################################################################################
t:=Indeterminate(Rationals);
t.name:="t";

p:=t^35 - 3*t^33 - t^32 + 3*t^31 + 3*t^30 - 2*t^29 - 4*t^28 + 3*t^27 + 5*t^26 -
2*t^25 - 6*t^24 - 2*t^23 + 4*t^22 + 3*t^21 - t^20 - t^19 + t^16 + t^15 -
3*t^14 - 4*t^13 + 2*t^12 + 6*t^11 + 2*t^10 - 5*t^9 - 3*t^8 + 4*t^7 + 2*t^6 -
3*t^5 - 3*t^4 + t^3 + 3*t^2 - 1;

gap> p;
t^35 - 3*t^33 - t^32 + 3*t^31 + 3*t^30 - 2*t^29 - 4*t^28 + 3*t^27 + 5*t^26 -
2*t^25 - 6*t^24 - 2*t^23 + 4*t^22 + 3*t^21 - t^20 - t^19 + t^16 + t^15 - 3*t^
14 - 4*t^13 + 2*t^12 + 6*t^11 + 2*t^10 - 5*t^9 - 3*t^8 + 4*t^7 + 2*t^6 - 3*t^
5 - 3*t^4 + t^3 + 3*t^2 - 1

gap> f:=Factors(p);
[ t - 1, t - 1, t - 1, t - 1, t - 1, t - 1, t - 1, t + 1, t + 1, t + 1,
t + 1, t^2 - t + 1, t^2 + t + 1, t^6 + t^5 + t^4 + t^3 + t^2 + t + 1,
t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1 ]

gap> Product(f);
t^33 - t^32 - 3*t^31 + 3*t^30 + 3*t^29 - 3*t^28 - 2*t^27 + t^26 + 4*t^25 -
6*t^23 + 4*t^21 - t^19 + t^14 - 4*t^12 + 6*t^10 - 4*t^8 - t^7 + 2*t^6 + 3*t^
5 - 3*t^4 - 3*t^3 + 3*t^2 + t - 1

gap> p=Product(f);
false
################################################################################
```

I also have this minor question that is unrelated to the above but isn't
worth a seperate post :

The internal routine "AddCoeffs" behaves differently in the new release;
the trailing zeros are not truncated. I have been using this function in
some code I wrote because of its speed; is it bad practice to use internal
functions?

Jacob Hirbawi <JcbHrb@CERF.net>

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