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# transferGW -- the transfer of Grothendieck-Witt from an étale algebras to a base field

- Usage:
    `transferGW(beta)`
- Inputs:
  - beta, a Grothendieck-Witt Class, Grothendieck-Witt class over an étale algebra over field of characteristic not 2
- Outputs:
  - a Grothendieck-Witt Class, the image of the Grothendieck-Witt class beta in $\text{GW}(k)$ under the canonical transfer map.

## Description

Given a finite étale algebra $L/k$ and a Grothendieck-Witt class, $\beta$ in $\text{GW}(L)$, computes the image of $\beta$ under the canonical map $\text{GW}(L)\to\text{GW}(k)$ for a finite étale algebra $L/k$.

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

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

    i3 : transferGW(beta)

    o3 = | 2 0  |
         | 0 -8 |

    o3 : GrothendieckWittClass

## See also

- GrothendieckWittClass -- a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field
- getTrace -- Computes the trace over $k$ for an element in a finite dimensional $k$ -algebra

## Ways to use transferGW:

- `transferGW(GrothendieckWittClass)`

## For the programmer

The object transferGW is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWTransferDoc.m2:25:0.