DGzip(C, T, "plus") returns the additive linear combination of the objects in T with coefficients taken from the list C.

DGzip(T, "wedge") returns the wedge product of the forms in T.

DGzip(T, "tensor") returns the tensor product of the tensors in the list T.

This command is part of the DifferentialGeometry package, and so can be used in the form DGzip(...) only after executing the command with(DifferentialGeometry).  It can always be used in the long form DifferentialGeometry:-DGzip.

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$

$\mathrm{DGsetup}\left(\left[x\,y\,z\,w\right]\,M\right)\:$

$\mathrm{C1}≔\left[a\,b\,c\,d\right]$

$\mathrm{C1}≔\left[a\,b\,c\,d\right]$

$\mathrm{T1}≔\left[\mathrm{D\_x}\,\mathrm{D\_y}\,\mathrm{D\_z}\,\mathrm{D\_w}\right]$

$\mathrm{T1}≔\left[\mathrm{D\_x}\,\mathrm{D\_y}\,\mathrm{D\_z}\,\mathrm{D\_w}\right]$

$X≔\mathrm{DGzip}\left(\mathrm{C1}\,\mathrm{T1}\,''plus''\right)$

$X≔a\mathrm{D\_x}+b\mathrm{D\_y}+c\mathrm{D\_z}+d\mathrm{D\_w}$

$\mathrm{C2}≔\left[\mathrm{seq}\left(a\Vert i\,i=1..6\right)\right]$

$\mathrm{C2}≔\left[\mathrm{a1}\,\mathrm{a2}\,\mathrm{a3}\,\mathrm{a4}\,\mathrm{a5}\,\mathrm{a6}\right]$

$\mathrm{T2}≔\mathrm{Tools}:-\mathrm{GenerateForms}\left(\left[\mathrm{dx}\,\mathrm{dy}\,\mathrm{dz}\,\mathrm{dw}\right]\,2\right)$

$\mathrm{T2}≔\left[\mathrm{dx}\bigwedge \mathrm{dy}\,\mathrm{dx}\bigwedge \mathrm{dz}\,\mathrm{dx}\bigwedge \mathrm{dw}\,\mathrm{dy}\bigwedge \mathrm{dz}\,\mathrm{dy}\bigwedge \mathrm{dw}\,\mathrm{dz}\bigwedge \mathrm{dw}\right]$

$\mathrm{\omega }≔\mathrm{DGzip}\left(\mathrm{C2}\,\mathrm{T2}\,''plus''\right)$

$\mathrm{\omega }≔\mathrm{a1}\mathrm{dx}\bigwedge \mathrm{dy}+\mathrm{a2}\mathrm{dx}\bigwedge \mathrm{dz}+\mathrm{a3}\mathrm{dx}\bigwedge \mathrm{dw}+\mathrm{a4}\mathrm{dy}\bigwedge \mathrm{dz}+\mathrm{a5}\mathrm{dy}\bigwedge \mathrm{dw}+\mathrm{a6}\mathrm{dz}\bigwedge \mathrm{dw}$

$\mathrm{T3}≔\left[\mathrm{dx}\,\mathrm{dy}\,\mathrm{dz}\,\mathrm{dw}\right]$

$\mathrm{T3}≔\left[\mathrm{dx}\,\mathrm{dy}\,\mathrm{dz}\,\mathrm{dw}\right]$

$\mathrm{\nu }≔\mathrm{DGzip}\left(\mathrm{T3}\,''wedge''\right)$

$\mathrm{\nu }≔\mathrm{dx}\bigwedge \mathrm{dy}\bigwedge \mathrm{dz}\bigwedge \mathrm{dw}$

$\mathrm{T4}≔\mathrm{evalDG}\left(\left[\mathrm{dx}\,\mathrm{D\_x}\,\mathrm{dy}\,\mathrm{D\_y}\,\mathrm{dz}\,\mathrm{D\_z}\,\mathrm{dw}\,\mathrm{D\_w}\right]\right)$

$\mathrm{T4}≔\left[\mathrm{dx}\,\mathrm{D\_x}\,\mathrm{dy}\,\mathrm{D\_y}\,\mathrm{dz}\,\mathrm{D\_z}\,\mathrm{dw}\,\mathrm{D\_w}\right]$

$T≔\mathrm{DGzip}\left(\mathrm{T4}\,''tensor''\right)$

$T≔\mathrm{dx}\mathrm{D\_x}\mathrm{dy}\mathrm{D\_y}\mathrm{dz}\mathrm{D\_z}\mathrm{dw}\mathrm{D\_w}$