Przemysław Koprowski

CQF: Magma package for quadratic forms theory

Work in progress: Anything that comes for free comes with no warranty.

Current version (last update August 9, 2024):
CQF Magma package
CQF manual
CQF is released under standard MIT license
Test suite to benchmark the speed of the command IsotropicVector. It works only with version 0.5.9 of CQF.

Example:
> _ := PolynomialRing(Rationals());
> K := NumberField(x^4 - 5*x^2 + 25);
> time C := SolveSumOfSquares(theta + 1); C;
Time: 0.290
[
    1/2*(theta + 2),
    -1/4*theta,
    1/4*(-theta^2 + 5)
]
> &+ [ c^2 : c in C ];
theta + 1

What is new?

Version 0.5.9:

Version 0.5:

Version 0.4.1:

Fixed a bug in that in some cases returned false positives for (local) isotropy of a form over a number field.

Version 0.4:

Added a new function SolveSumOfSquares that decomposes any totally positive element into a sum of squares of minimal length.

Version 0.3:

Version 0.2.2:

Version 0.2.1:

Version 0.2:

Past versions: