"Factor" question

Horvath Sandor · Thu Aug 11, 2005 5:33 pm

Hi,

My question is certainly a simple one, however I did not guessed the point.

In the Help Manual "D.7.5.2 Factor" you give the following Example:

LIB "zeroset.lib";
ring R = (0,a), x, lp;
minpoly = a2+1;
poly f = x4 - 1;
list fl = Factor(f);
fl;
==> [1]:
==> _[1]=1
==> _[2]=(40a+60)*x+(40a+60)
==> _[3]=(1/65a-29/130)*x+(-1/65a+29/130)
==> _[4]=(4a)*x+4
==> _[5]=(7/520a+1/130)*x+(1/130a-7/520)
....

- which is just (x-1)*(x+1)*(x-a)*(x+a) where the factors are modified by some invertible elements of Q(a)[x] having their product = 1. (some complex rationals actually)

My question is: what is the property that single out the Singular answer in the above example, out of the many others, which all just differ by invertible factors?

Thanks for the answer,
Horvath Sandor

email: shorvath@ms.sapientia.ro
Posted in old Singular Forum on: 2005-02-01 11:59:03+01

"Factor" question

wienand · Tue Sep 20, 2005 5:05 pm

Dear Sandor Horvath,

the command "Factor" from zeroset.lib is obsolete. Nowadays you should use the function "factorize":

Code:

> ring R = (0,a), x, lp;
> minpoly = a2+1;
> poly f = x4 - 1;
> factorize(f);
[1]:
   _[1]=1
   _[2]=x-1
   _[3]=x+1
   _[4]=x+(a)
   _[5]=x+(-a)
[2]:
   1,1,1,1,1

Sincerely,

The Singular Team