Singular

Hi, I need to know the list of running gcd procedure, someone knows where I can find it? I looked all Singular Liberia, but I can not get it. I would appreciate your help. Thank you.

What does 'the list of running gcd procedure' mean?

5.1.41 gcd and 5.1.28 extgcd are commands from the singular kernel.
These are not encoded in líbraries but part of the source code in (C/C++).

But you can also inspect the code of the library crypto.lib (section D.11.3 Teaching)

There you will find implementations for gcd but acting on numbers (not polynommials) only.



C.Gorzel

thanks for replying, I found in the library zeroset.lib the gcd calculation procedure called proc EGCDMain, which in turn calls the proc RemainderMain, which executes the function proc SimplifyPoly. From there I could check the calculations you need.
All this is because I want to calculate the GCD of two polynomials defined by
quotient ring. I have calculated using "reduce", but the calculation is complicated and ends with computer memory, apparently Cingular is not foreseen this problem.
Do you know why?

Note the following, as indicated in the Overwiev of zeroset.lib:


For some years, factorization over Q(a)[t] is already implemented in the kernel now.
So some commands of this library are somehow outdated/obsolete.

In any case, post your example to see what went wrong.

C.Gorzel

Hi Gorzel:
This is an example: I have programmed my own algorithm to calculate gcd remaining divisions, which is what I need and Singular that would produce the copy below.

//ejemplo_mcd
ring R=(0,s), (a,r,u(1..4)), dp;

//poly pr=r3-2r2+r-1;
//poly pr=48r3-84r2+42r-(36+s);
poly pr=-r^3+r^2-s*r+u(1)*s+u(2);

poly dividendo;
poly mcd;
poly qr=diff(pr,r);
poly divisor=pr;
poly resto=qr;
poly div_poly;
while (resto<>0)
{
dividendo=divisor;
divisor=resto;
div_poly=reduce(dividendo,std(divisor));
resto=div_poly;
}
mcd=divisor;
"Entrega el mcd entre pr y dpr";
mcd;

This is result:
> <"ejemplo_mcd";
out of memory in vector::SetLength()
Singular : signal 6 (v: 3040/2007112211):
Segment fault/Bus error occurred at 83f8da1 because of 0 (r:1274263428)
please inform the authors
trying to restart...
? error occurred in para_singular line 20: `div_poly=reduce(dividendo,std(divisor));`
? last reserved name was `std`
skipping text from `;` error at token `)`
Singular : signal 11 (v: 3040/2007112211):
Segment fault/Bus error occurred at 8361221 because of 0 (r:1274263428)
please inform the authors
trying to restart...

Thank for you help!!

I. Berna

Dear I. Berna,

as your output shows,

you are using an old version Singular 3-0-4 dating from 2007.

So upgrade to Singular-3-1-1; it you are working with LINUX go there:
http://www.mathematik.uni-kl.de/ftp/pub ... ular/UNIX/

The crash, which you report here, does not occur in Singular 3-1-1,
so I will not trace the bug.

But with your code there is the problem that it may run into an infinite loop
if one is calling it with coprime multivariate polynomials.



Press continously RETURN, and finally press CTRL-C in the third example.



For the polynomials pr3,qr3, the rest is again a polynomial in the
variables u(1),u(2). So degree does not drop and the loop does not termiante.

See also



Summary:

Use Singular's gcd, if you want to compute the gcd of multivariate polynomials,
and instead reduce you may call divsion

---
Christian Gorzel