D.3.1.7 is_complex

Procedure from library matrix.lib (see matrix_lib).

Usage:

is_complex(c); c = list of size-compatible modules or matrices

Return:

1 if c[i]*c[i+1]=0 for all i, 0 if not, hence checking whether the list of matrices forms a complex.

Note:

Ideals are treated internally as 1-line matrices.
If printlevel > 0, the position where c is not a complex is shown.

Example:

LIB "matrix.lib";
ring r  = 32003,(x,y,z),ds;
ideal i = x4+y5+z6,xyz,yx2+xz2+zy7;
list L  = nres(i,0);
is_complex(L);
→ 1
L[4]    = matrix(i);
is_complex(L);
→ 0