Macaulay2 » Documentation
Packages » A1BrouwerDegrees :: getSumDecompositionString
next | previous | forward | backward | up | index | toc

# getSumDecompositionString -- produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class

- Usage:
    `getSumDecompositionString(beta)`
- Inputs:
  - beta, a Grothendieck-Witt Class, over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
  - beta, an Unstable Grothendieck-Witt Class, over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
- Outputs:
  - a string, a string representing a simplified diagonal representative of the class

## Description

Given a Grothendieck-Witt class or unstable Grothendieck-Witt class over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two, this method produces a string representing a simplified diagonal representative of the class.

See getSumDecomposition for more details on the decomposition procedure.

    i1 : M = matrix(CC, {{1,2,3},{2,4,5},{3,5,6}});

                    3         3
    o1 : Matrix CC    <-- CC
                  53        53

    i2 : alpha = makeGWClass M;

    i3 : getSumDecompositionString alpha

    o3 = H + <1>

    i4 : N = matrix(RR, {{2.091,2.728,6.747},{2.728,7.329,6.257},{6.747,6.257,0.294}});

                    3         3
    o4 : Matrix RR    <-- RR
                  53        53

    i5 : beta = makeGWClass N;

    i6 : getSumDecompositionString beta

    o6 = H + <1>

    i7 : P = matrix(QQ, {{1,2,3},{2,4,5},{3,5,6}});

                  3       3
    o7 : Matrix QQ  <-- QQ

    i8 : gamma = makeGWClass P;

    i9 : getSumDecompositionString gamma

    o9 = H + <1>

    i10 : Q = matrix(GF(13), {{9,1,7,4},{1,10,3,2},{7,3,6,7},{4,2,7,5}});

                        4            4
    o10 : Matrix (GF 13)  <-- (GF 13)

    i11 : delta = makeGWClass Q;

    i12 : getSumDecompositionString delta

    o12 = H + <1> + <-5>

## See also

- getSumDecomposition -- produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class
- getAnisotropicPart -- produces the anisotropic part of a Grothendieck-Witt class
- getWittIndex -- returns the Witt index of a symmetric bilinear form

## Ways to use getSumDecompositionString:

- `getSumDecompositionString(GrothendieckWittClass)`
- `getSumDecompositionString(UnstableGrothendieckWittClass)`

## For the programmer

The object getSumDecompositionString is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2:97:0.