I think this is a bug in the facility for taking submatrices in M2:
S = ZZ/101[a,b,c,d]
M = matrix"a,b;c,d"
M_{0,0} -- produces the matrix with two columns equal to the first column of M, as it should
M^{0,0} -- produces a matrix with a row of zeros followed by the first row of M -- wrong!
I came on it (with Jerzy Weyman) when writing a program to compute the sub-pfaffians of a certain size, allowing repetition of the rows and columns ( "permanent(k,M) does it without repetition.)
David
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David Eisenbud
Professor of Mathematics
University of California Berkeley