# hermiteNormalForm -- Compute the Hermite normal form of a fractional ideal in a number field

## Synopsis

• Usage:
hermiteNormalForm a
hermiteNormalForm {a, a', ...}
• Inputs:
• a, an element of a number field, or a list of them
• Outputs:
• , representing the Hermite normal form of the fractional ideal generated by a

## Description

This method computes the Hermite normal form of a fractional ideal in terms of the integral basis given by integers.

 i1 : F = toField(QQ[q]/(q^2+3)); i2 : hermiteNormalForm 1_F o2 = | 1 0 | | 0 1 | 2 2 o2 : Matrix QQ <--- QQ i3 : hermiteNormalForm(q/3) o3 = | 1 1/3 | | 0 1/3 | 2 2 o3 : Matrix QQ <--- QQ

## Ways to use hermiteNormalForm :

• "hermiteNormalForm(List)"
• "hermiteNormalForm(RingElement)"

## For the programmer

The object hermiteNormalForm is .