# ModularHermitianRowReduction R¶

Modular hermitian row reduction. Author: Manuel Bronstein Date Created: 22 February 1989 Keywords: matrix, reduction.

normalizedDivide: (R, R) -> Record(quotient: R, remainder: R)

normalizedDivide(n, d) returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen, e.g. positive remainders

rowEch: Matrix R -> Matrix R

rowEch(m) computes a modular row-echelon form of m, finding an appropriate modulus.

rowEchelon: (Matrix R, R) -> Matrix R

rowEchelon(m, d) computes a modular row-echelon form mod d of [d ] [ d ] [ . ] [ d] [ M ] where M = m mod d.

rowEchelonLocal: (Matrix R, R, R) -> Matrix R

rowEchelonLocal(m, d, p) computes the row-echelon form of m concatenated with d times the identity matrix over a local ring where p is the only prime.

rowEchLocal: (Matrix R, R) -> Matrix R

rowEchLocal(m, p) computes a modular row-echelon form of m, finding an appropriate modulus over a local ring where p is the only prime.