# New Groups From Others

## `BravaisGroup(G): GrpMat[RngInt] -> GrpMat`

For a finite integral matrix group $G$, compute its Bravais group which is the integral group fixing all symmetric bilinear forms fixed by $G$.

## `IntegralGroup(G): GrpMat -> GrpMat, AlgMatElt`

## `IntegralGroup(G): [Mtrx] -> [Mtrx], AlgMatElt`

Return the action of the finite rational matrix group $G$ on an invariant lattice as an integral matrix group, thus giving an equivalent integral group $H$, together with the transformation matrix $T$ from the standard lattice to the invariant lattice. Thus $H = T\cdot G\cdot T^{-1}$.