I was trying to do some noncommutative Ext-computations and got unexpected results. The following is a minimal example (where everything is actually commutative):
Code:
LIB "nchomolog.lib";
ring base = 0,(x,y),dp;
def A = nc_algebra(1,0); setring A;
ideal i = (x,y);
ncExt_R(0,i);
=> _[1,1]=1
ncExt_R(1,i);
=> _[1]=x*gen(1)
ncExt_R(2,i);
=> _[1]=gen(1)
I'm reading this as Ext^i_{k[x,y]}(k, k[x,y]) = 0 for i != 1 and Ext^1 = k[y]. But this is clearly no the correct result. Am I misunderstanding something? Ext_R from homolog.lib gives me the correct Ext's (i.e. Ext^2 = k, everything else vanishes).
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