Dear Pari-users,
My name is Will Jagy.
I would like to know whether two commands,
qfgaussred()
qfsign()
work entirely with integers and rational numbers when given a square symmetric matrix of integers, so that no numerical errors are introduced.
The brief documentation I found on qfgaussred() does suggest this. Certainly that is what my own C++/GMP program does. I found what seems the exact method in Gantmacher (1959) The Theory of Matrices, volume 1, pages 299-300. He called it Lagrange's method, while in France it is named after Gauss
https://fr.wikipedia.org/wiki/R%C3%A9duction_de_Gauss .
Similar questions for qfsign(). If all it does is read the diagonal entries of the matrix in qfgaussred() then it can be used as is.
Will Jagy
California, USA