The command DGform will create a single term differential form.  Let Theta = [theta_1, theta_2, theta_3, ...] denote the coframe for the current frame or, if the optional argument M is given, the frame M.  The list Theta can be obtained from the command DGinfo with the keyword "frameBaseForms" or "frameJetForms".  Let V = [x_1, x_2, x_3, ...] denote the local coordinates for the current frame or, if the optional argument M is given, the frame M.  The list V can be obtained from the command DGinfo with the keyword "frameIndependentVariables" or "frameJetVariables". If the integer i or coordinate x_i is given, the command returns the corresponding 1-form theta_i.  If a list of p integers [i, j, k, ...] or coordinates [x_i, x_j, x_k, ...] is given, the command returns the p-form  theta_i &w theta_j &w theta_k...

The commands DGbiform, DGtensor, and DGvector work in a similar fashion.

The command DGform is part of the DifferentialGeometry:-Tools package and so can be used in the form DGform(...) only after executing the commands with(DifferentialGeometry) and with(Tools) in that order.  It can always be used in the long form DifferentialGeometry:-Tools:-DGform.  DGbiform, DGtensor, and DGvector work in the same way.

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

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

$\mathrm{DGvector}\left(x\right)$

$\mathrm{D\_x}$

$\mathrm{DGvector}\left(3\right)$

$\mathrm{D\_z}$

$\mathrm{DGform}\left(y\right)$

$\mathrm{dy}$

$\mathrm{DGform}\left(4\right)$

$\mathrm{dw}$

$\mathrm{DGform}\left(\left[x\,y\right]\right)$

$\mathrm{dx}\bigwedge \mathrm{dy}$

$\mathrm{DGform}\left(\left[1\,2\,3\,4\right]\right)$

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

$\mathrm{DGtensor}\left(x\,''con\_bas''\right)$

$\mathrm{D\_x}$

$\mathrm{DGtensor}\left(2\,''cov\_bas''\right)$

$\mathrm{dy}$

$\mathrm{DGtensor}\left(\left[1\,1\,1\right]\,\left[\left[''cov\_bas''\,''con\_bas''\,''cov\_bas''\right]\,\left[\right]\right]\right)$

$\mathrm{dx}\mathrm{D\_x}\mathrm{dx}$

$\mathrm{DGsetup}\left(\left[x\,y\,u\,v\,w\right]\,E\right)$

$\mathrm{frame\; name:\; E}$

$\mathrm{DGtensor}\left(\left[x\,v\,v\right]\,\left[\left[''con\_bas''\,''cov\_bas''\,''con\_bas''\right]\,\left[\right]\right]\right)$

$\mathrm{D\_x}\mathrm{dv}\mathrm{D\_v}$

$\mathrm{DGsetup}\left(\left[x\,y\right]\,\left[u\,v\right]\,J\,2\right)\:$

$\mathrm{\omega }≔\mathrm{DGbiform}\left(u\left[1,1\right]\right)$

$\mathrm{\omega }≔{\mathrm{Cu}}_{1,1}$

$\mathrm{convert}\left(\mathrm{\omega }\,\mathrm{DGform}\right)$

$-u_{1,1,1}\mathrm{dx}-u_{1,1,2}\mathrm{dy}+{\mathrm{du}}_{1,1}$