getSignature -- computes the signature of a symmetric bilinear form over the real numbers or rational numbers

Description

Given a symmetric bilinear form, after diagonalizing it, we can consider the number of positive entries minus the number of negative entries appearing along the diagonal. This is the signature of a symmetric bilinear form, and is one of the primary invariants used to classify forms. For more information see isIsomorphicForm.

i1 : M = matrix(RR, {{0,0,1},{0,1,0},{1,0,0}});

                3         3
o1 : Matrix RR    <-- RR
              53        53

i2 : beta = makeGWClass M;

i3 : getSignature beta

o3 = 1

See also

• isIsomorphicForm -- determines whether two Grothendieck-Witt classes over CC, RR, QQ, or a finite field of characteristic not 2 are isomorphic.
• getHilbertSymbolReal -- computes the Hilbert symbol of two rational numbers over the real numbers
• getSumDecomposition -- produces a simplified diagonal representative of a Grothendieck-Witt class
• getSumDecompositionString -- produces a simplified diagonal representative of a Grothendieck-Witt class