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 November 12, 2021):
CQF Magma package
CQF manual
CQF is released under standard MIT license

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 0.4.1:

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: