Integer Valence computation
Theorem : if a prime p divides the last invariant factor of A
- p | valence( charpoly(A) )
- p2 | valence( charpoly(ATA) )
- p | valence( minpoly(A) )
- p | valence( minpoly( ATA) )
valence(P) = trailing non-zero coefficient of the polynomial P
Compute the minimum polynomial of A or ATA over the integers if its degree is small
Homology matrices : degree( minpoly(ATA) ) << m
Remark : minpoly(ATA) and minpoly(AAT) are equal or differ by a factor X