Procedure from library homolog.lib (see homolog_lib).
Usage:
isFlat(M); M module
Return:
1 if M'=coker(M) is flat;
0 if this is not the case.
Example:
LIB "homolog.lib";
ring A = 0,(x,y),dp;
matrix M[3][3] = x-1,y,x,x,x+1,y,x2,xy+x+1,x2+y;
print(M);
==> x-1,y, x,
==> x, x+1, y,
==> x2, xy+x+1,x2+y
isFlat(M); // coker(M) is not flat over A=Q[x,y]
==> 0
qring B = std(x2+x-y); // the ring B=Q[x,y]/<x2+x-y>
matrix M = fetch(A,M);
isFlat(M); // coker(M) is flat over B
==> 1
setring A;
qring C = std(x2+x+y); // the ring C=Q[x,y]/<x2+x+y>
matrix M = fetch(A,M);
isFlat(M); // coker(M) is not flat over C
==> 0
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