The function create([1,-1], compts_array) returns a tensor_type with "index_char" field set to [1,-1] and "compts" field set to compts_array (where compts_array is either an array or the name of an array).

The contravariant indices (represented by 1) are those indices that appear as superscripts, whereas the covariant indices (represented by -1) are those that appear as subscripts.

The function create([], a*b/(c+d)) returns a tensor_type representing a scalar (zero-rank tensor) with fields "index_char" and "compts" set to $\left[\right]$ and $\frac{ab}{c+d}$ respectively.

When called, create checks its arguments for correct type and for the consistency between the index character and the components fields using a call to `type/tensor_type`.  Upon passing those checks, the appropriate tensor_type is returned.

Note that this function is not a necessity but is provided as a convenient way of create new tensors.

This function is part of the tensor package, and so can be used in the form create(..) only after performing the command with(tensor), or with(tensor,create).  This function can always be accessed in the long form tensor[create](..).

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

$\mathrm{cmpts}≔\mathrm{array}\left(\left[\left[a\,b\,c\right]\,\left[d\,e\,f\right]\,\left[g\,h\,i\right]\right]\right)$

$\mathrm{cmpts}≔\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$

$\mathrm{create}\left(\left[-1\,1\right]\,\mathrm{cmpts}\right)$

$table\left(\left[\mathrm{index\_char}=\left[\mathrm{-1}\,1\right]\,\mathrm{compts}=\mathrm{cmpts}\right]\right)$

$\mathrm{create}\left(\left[\right]\,\arctan \left(\frac{y}{x}\right)\right)$

$table\left(\left[\mathrm{index\_char}=\left[\right]\,\mathrm{compts}=\arctan \left(\frac{y}{x}\right)\right]\right)$

$\mathrm{create}\left(\left[-1\,1\right]\,\mathrm{array}\left(\left[\left[a\,b\,c\right]\,\left[d\,e\,f\right]\,\left[g\,h\,i\right]\right]\right)\right)$

$table\left(\left[\mathrm{index\_char}=\left[\mathrm{-1}\,1\right]\,\mathrm{compts}=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]\right]\right)$

$A≔\mathrm{create}\left(\left[1\,1\right]\,\mathrm{array}\left(\left[\left[1\,0\,0\right]\,\left[0\,\frac{1}{r^2}\,0\right]\,\left[0\,0\,\frac{1}{r^2{\sin \left(\mathrm{\theta }\right)}^2}\right]\right]\right)\right)$

$A≔table\left(\left[\mathrm{index\_char}=\left[1\,1\right]\,\mathrm{compts}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \frac{1}{r^2}& 0\\ 0& 0& \frac{1}{r^2{\sin \left(\mathrm{\theta }\right)}^2}\end{array}\right]\right]\right)$