bug in NF? (ring = sum of two quotient rings)

[simon king]

Simon King wrote (Aug 22, 2009):

Ich habe glaube ich gerade einen Bug in NF entdeckt.

Der Anhang "kerneltest.sing" definiert zunaechst Quotientenringe Q1, Q2 mit Matrixordnung.

def Q = Q1+Q2;

In Q wird ein Ideal t definiert, wobei t einfach aus den Variablen von Q1 besteht, d.h. ideal t = a_1_0, b_1_1, b_2_1, b_2_2, b_2_3, b_3_4, b_3_5, c_4_8;

Und dann kommt der Hammer:

NF(b_2_1,std(t));

b_2_1

b_2_1==t[3];

1

Das heisst: Obwohl b_2_1 als Erzeuger in t vorkommt, wird es nicht wegreduziert!

Seltsamerweise klappt dies:

NF(b_2_1,std(ideal(t[3])));

0

NF(b_2_1,std(ideal(t[2..3])));

0

NF(b_2_1,std(ideal(t[1..3])));

0

Aber dies klappt nicht:

NF(b_2_1,std(ideal(t[3..5])));

b_2_1

Was passiert da? Sind Summen von Quotientenringen in Singular ein Problem?

Die Matrizen, welche die Matrixordnung definieren, sind jedenfalls von vollem Rang, das habe ich geprueft.

Viele Gruesse Simon

[Simon King]

(perhaps better switch to English)

I forgot to indicate the Singular version I was using: It is Singular 3-1-0 as it comes with Sage 4.1.

Best regards, Simon

[Oleksandr]

This seems to be a very subtle issue: almost any change to the procedure eliminates the bug :( I'd assume this to be a rear side effect of an interplay between quotient structure, ring sum structure and matrix orderings...

As a workaround i'd suggest to simulate factor algebra e.g. as follows:

def R = R1 + R2; setring R;
ideal I = std(imap(R1, I) + imap(R2, I) );

ideal t = a_1_0, b_1_1, b_2_1, b_2_2, b_2_3, b_3_4, b_3_5, c_4_8; 

NF( t[3], std( I + t ) ); // Zero!!!

qring Q = I; ideal t = imap(R, t); NF( t[3], std(t) ); // BUG :(

Please let us know about your findings related to this issues.

Does this bug appears in any noncommutative setting?

[Oleksandr]

btw: this issue may be connected to #160: ​http://www.singular.uni-kl.de:8002/trac/ticket/160

[Simon King]

Replying to motsak:

btw: this issue may be connected to #160: ​http://www.singular.uni-kl.de:8002/trac/ticket/160

I doubt it, because here all variables are of positive degree. Regards, Simon

[Simon King]

Replying to motsak:

As a workaround i'd suggest to simulate factor algebra e.g. as follows:

def R = R1 + R2; setring R;
ideal I = std(imap(R1, I) + imap(R2, I) );

ideal t = a_1_0, b_1_1, b_2_1, b_2_2, b_2_3, b_3_4, b_3_5, c_4_8; 

NF( t[3], std( I + t ) ); // Zero!!!

qring Q = I; ideal t = imap(R, t); NF( t[3], std(t) ); // BUG :(

This might be a way out. By the way, the solution in my application was as follows:

• I factor simply by an ideal generated by some variables.
• Hence, I can get the same result by applying a map that sends these variables to zero and is the identity on the remaining variables.

Cheers, Simon

[seelisch]

abort ring def when adding two quotient rings; give hint to user that there is a (new) specialized command; create spezialized command and include in manual that this may take a while due to necessary std computation

[hannes]

If Q1 and Q2 does not share variables, SB(ideal(Q1))+SB(ideal(Q2))==SB(ideal(Q)). Fixed for that case. Otherwise, throws an error