addGW -- the direct sum of two Grothendieck-Witt classes

Usage:

addGW(beta1, beta2)
Inputs:
- beta1, a Grothendieck-Witt Class, a Grothendieck-Witt class
- beta2, a Grothendieck-Witt Class, a Grothendieck-Witt class
Outputs:
- gamma, a Grothendieck-Witt Class, a Grothendieck-Witt class representing the direct sum of the two input classes

Description

Given two GrothendieckWittClass objects beta1 and beta2, this method computes the direct sum of the two classes, which is a new GrothendieckWittClass object representing the isomorphism class of the direct sum of the two symmetric bilinear forms represented by the input classes. The resulting class has a Gram matrix which is the direct sum of the Gram matrices of the two input classes.

i1 : R = QQ[x]/(x^2 + 1);

i2 : beta1 = makeGWClass matrix(R, {{1,2},{2,x}});

i3 : beta2 = makeGWClass matrix(R, {{3,4},{4,5}});

i4 : addGW(beta1, beta2)

o4 = | 1 2 0 0 |
     | 2 x 0 0 |
     | 0 0 3 4 |
     | 0 0 4 5 |

o4 : GrothendieckWittClass

Ways to use addGW:

addGW(GrothendieckWittClass,GrothendieckWittClass)

For the programmer

The object addGW is a method function.

The source of this document is in A1BrouwerDegrees/Documentation/GrothendieckWittClassesDoc.m2:117:0.

addGW -- the direct sum of two Grothendieck-Witt classes

Description

See also

Ways to use addGW:

For the programmer