getIntegralDiscriminant -- computes the integral discriminant for a rational symmetric bilinear form

Usage:

getIntegralDiscriminant(beta)
Inputs:
- beta, a Grothendieck-Witt Class, denoted by $\beta \in \text{GW}(\mathbb{Q})$
Outputs:
- an integer, an integral square class representative of $\text{disc}(\beta)$

Description

The integral discriminant of a symmetric bilinear form $\beta$ is defined to be the square class of the determinant of the matrix representing $\beta$. This is an invariant of the form, and is used in the classification of forms.

i1 : beta = makeGWClass matrix(QQ, {{1,4,7},{4,3,-1},{7,-1,5}});

i2 : getIntegralDiscriminant beta

o2 = -269

i3 : getDiagonalClass beta

o3 = | 1 0   0    |
     | 0 -13 0    |
     | 0 0   3497 |

o3 : GrothendieckWittClass

Ways to use getIntegralDiscriminant:

getIntegralDiscriminant(GrothendieckWittClass)

For the programmer

The object getIntegralDiscriminant is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2:53:0.

getIntegralDiscriminant -- computes the integral discriminant for a rational symmetric bilinear form

Description

See also

Ways to use getIntegralDiscriminant:

For the programmer