This function forms the following linear combination of tensors:

Each * represents a scalar multiplication and each + represents naturally a tensor addition.

There is no limit on how many tensors to be summed; that is, N can be any positive integer.

Any of the algebraic c's can be omitted, in which case it is by default substituted by 1.

Simplification:  This routine uses the `tensor/lin_com/simp` routine for simplification purposes.  The simplification routine is applied to each component of result after it is computed.  By default, `tensor/lin_com/simp` is initialized to the `tensor/simp` routine.  It is recommended that the `tensor/lin_com/simp` routine be customized to suit the needs of the particular problem.  It should be noted that `tensor/lin_com/simp` is used frequently as a simplifier by other routines.  See ?tensor[simp] for a list of simplifiers used by each routine of the package.

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

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

$A≔\mathrm{array}\left(1..3\,1..3\,\left[\left[a\,0\,0\right]\,\left[0\,a\,0\right]\,\left[0\,0\,a\right]\right]\right)\:$

$B≔\mathrm{array}\left(1..3\,1..3\,\left[\left[0\,b\,0\right]\,\left[0\,0\,0\right]\,\left[0\,b\,0\right]\right]\right)\:$

$C≔\mathrm{array}\left(1..3\,1..3\,\left[\left[0\,0\,c\right]\,\left[0\,0\,0\right]\,\left[c\,0\,0\right]\right]\right)\:$

$\mathrm{T1}≔\mathrm{table}\left(\left['\mathrm{index\_char}'=\left[-1\,-1\right]\,'\mathrm{compts}'=\mathrm{op}\left(A\right)\right]\right)\:$

$\mathrm{T2}≔\mathrm{table}\left(\left['\mathrm{index\_char}'=\left[-1\,-1\right]\,'\mathrm{compts}'=\mathrm{op}\left(B\right)\right]\right)\:$

$\mathrm{T3}≔\mathrm{table}\left(\left['\mathrm{index\_char}'=\left[-1\,-1\right]\,'\mathrm{compts}'=\mathrm{op}\left(C\right)\right]\right)\:$

$\mathrm{SUM}≔\mathrm{lin\_com}\left(x\,\mathrm{T1}\,\mathrm{T2}\,z\,\mathrm{T3}\right)$

$\mathrm{SUM}≔table\left(\left[\mathrm{compts}=\left[\begin{array}{ccc}ax& b& cz\\ 0& ax& 0\\ cz& b& ax\end{array}\right]\,\mathrm{index\_char}=\left[\mathrm{-1}\,\mathrm{-1}\right]\right]\right)$

$\mathrm{T4}≔\mathrm{create}\left(\left[\right]\,x\right)\:$$\mathrm{T5}≔\mathrm{create}\left(\left[\right]\,y\right)\:$$\mathrm{T6}≔\mathrm{create}\left(\left[\right]\,z\right)\:$

$\mathrm{SUM}≔\mathrm{lin\_com}\left(\mathrm{T4}\,b+c\,\mathrm{T5}\,ca\,\mathrm{T6}\right)$

$\mathrm{SUM}≔table\left(\left[\mathrm{compts}=caz+yb+yc+x\,\mathrm{index\_char}=\left[\right]\right]\right)$