The function contract(A, [i1,i2], [i3,i4], ...) computes the contraction of the tensor A over the pairs of indices i1 and i2, i3 and i4, etc.

There must not be any duplicates in the given indices (it is impossible to contract over a single index more than once) and the indices of each pair must be of opposite covariant-contravariant character.

The return value is the resultant tensor_type object of rank equal to rank(A) - 2 * (# of pairs in the call).

Simplification:  This routine uses the `tensor/prod/simp` routine for simplification purposes.  The simplification routine is applied to each component of the result after it is computed.  By default, `tensor/prod/simp` is initialized to the `tensor/simp` routine. It is recommended that the `tensor/prod/simp` routine be customized to suit the needs of the particular problem.

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

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

$T≔\mathrm{create}\left(\left[1\,-1\right]\,\mathrm{array}\left(\left[\left[w\,x\,0\right]\,\left[y\,z\,0\right]\,\left[0\,y^2\,xyw\right]\right]\right)\right)$

$T≔table\left(\left[\mathrm{index\_char}=\left[1\,\mathrm{-1}\right]\,\mathrm{compts}=\left[\begin{array}{ccc}w& x& 0\\ y& z& 0\\ 0& y^2& xyw\end{array}\right]\right]\right)$

$\mathrm{contract}\left(T\,\left[1\,2\right]\right)$

$table\left(\left[\mathrm{index\_char}=\left[\right]\,\mathrm{compts}=xyw+w+z\right]\right)$