Incorrect tensor product of rings in positive char

[levandov]

Daniel Andres (RWTH Aachen) has communicated the following: When tensoring a non-commutative ring over positive characteristic with an arbitrary ring with a parameter over the same characteristic, Singular 3-1-1 is stuck in an infinite loop.

This did not occur in version 3-1-0.

In version 3-1-1 it works for:

• commutative rings,
• rings without parameters over positive char,
• rings with parameters over char 0.

LIB "nctools.lib";
ring @W = 2,(x,Dx),dp;
def W = Weyl();
setring W; W; // Weyl algebra in char p
ring r = (2,a),y,dp;
def B = W + r;

In his computation (3-1-1 official release) it resulted into an infinite loop. On my recent svn build it takes time, terminates, but delivers very incorrect non-comm relation.

setring B;
B;

//   characteristic : 2
//   1 parameter    : a 
//   minpoly        : 0
//   number of vars : 3
//        block   1 : ordering dp
//                  : names    x Dx
//        block   2 : ordering dp
//                  : names    y
//        block   3 : ordering C
//   noncommutative relations:
//    Dxx=-2147483647*x*Dx+-2147483647

I suppose the problem lies in the incorrect initalization of non-commutative part.

[Oleksandr]

Bug was ALWAYS present due to the following block in rSum / rSumInternal:

    nMapFunc nMap1 = nSetMap(R1);
    nMapFunc nMap2 = nSetMap(R2);

since nSetMap can change something global, i.e. not usable after the next nSetMap call :(