getRank -- calculates the rank of a symmetric bilinear form

Usage:

getRank(beta)
Inputs:
- beta, a Grothendieck-Witt Class, a symmetric bilinear form defined over $\mathbb{Q}$
Outputs:
- an integer, the rank of the symmetric bilinear form $\beta$

Description

The rank of a symmetric bilinear form is the dimension of the vector space spanned by the vectors that are orthogonal to all other vectors in the space. This is equivalent to the number of non-zero entries on the diagonal of a diagonalized form.

i1 : beta = makeDiagonalForm(QQ, (3,5,7,11))

o1 = | 3 0 0 0  |
     | 0 5 0 0  |
     | 0 0 7 0  |
     | 0 0 0 11 |

o1 : GrothendieckWittClass

i2 : getRank beta

o2 = 4

Ways to use getRank:

getRank(GrothendieckWittClass)
getRank(Matrix)

For the programmer

The object getRank is a method function.

The source of this document is in A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2:136:0.

getRank -- calculates the rank of a symmetric bilinear form

Description

See also

Ways to use getRank:

For the programmer