The TensorArray receives a tensorial expression having n free indices, typically involving sums and products, and returns a corresponding n dimensional Array, which can be indexed as a single object to return the values of the tensorial expression for given values of its free indices.

To check and determine the free and repeated indices of an expression use Check.

The returned Array is constructed taking into account the covariant and contravariant character of each free index in expression. To compute the values of expression you index this array giving values between 1 and the spacetime dimension to the indices.

Pauli, Dirac and Gell-Mann matrices, respectively represented by the Psigma Dgamma and StandardModel:-Glambda commands, are implemented as spacetime and SU(3) vectors, where each component represents a matrix. Thus, when computing tensor arrays of components, one can optionally visualize the matrices behind these tensor representations and rewrite in matrix form, or additionally perform the matrix operations involved if any. For this purpose, pass the optional arguments rewriteinmatrixform or performmatrixoperations.

By default, in the returned result, summation is explicitly performed over all the repeated indices found in expression, taking into account the covariant/contravariant character of each index. To avoid performing this summation and keep repeated indices not summed pass the optional argument performsumoverrepeatedindices = false.

By default, the Array is constructed without simplifying its components; to have them simplified indicate the simplifier on the right-hand-side of the optional argument simplifier = .... A frequently convenient simplification is achieved with simplifier = simplify.

When expression involves sums and products of tensors having free indices, the ordering of the free indices in the returned Array is arbitrary. To indicated a desired ordering of these free indices, use the option freeindices = [...] where the list [...] indicates the desired ordering.

The array of components of a tensorial expression with at most 2 free indices is all visible on the screen as the output TensorArray. Things are not so simple when that number is 3 or larger, when only a slice of the array of components is shown. To visualize the expression's components in these cases you can use the explore option, which launches an applet that allows for giving values to all but two of the free indices, and shows the 2x2 corresponding slice for the other two, with the ordering shown.

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

$\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$

$\left[\mathrm{mathematicalnotation}=\mathrm{true}\right]$

$\mathrm{g\_}\left[\mathrm{sc}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{Systems\; of\; spacetime\; coordinates\; are:}\left\{X=\left(r\,\mathrm{\theta }\,\mathrm{\phi }\,t\right)\right\}$

$\mathrm{Default\; differentiation\; variables\; for\; d\_,\; D\_\; and\; dAlembertian\; are:}\left\{X=\left(r\,\mathrm{\theta }\,\mathrm{\phi }\,t\right)\right\}$

$\mathrm{Setting}\mathrm{lowercaselatin\_is}\mathrm{letters\; to\; represent}\mathrm{space}\mathrm{indices}$

$\mathrm{The\; Schwarzschild\; metric\; in\; coordinates}\left[r\,\mathrm{\theta }\,\mathrm{\phi }\,t\right]$

$\mathrm{Parameters:}\left[m\right]$

$\mathrm{Signature:}\left(\mathrm{-\; -\; -\; +}\right)$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$g_{\mathrm{\mu },\mathrm{\nu }}=\left[\right]$

$\mathrm{Define}\left(A\right)$

$\mathrm{Defined\; objects\; with\; tensor\; properties}$

$\left\{A\,{▿}_{\mathrm{\mu }}\,{\mathrm{\gamma }}_{\mathrm{\mu }}\,{\mathrm{\sigma }}_{\mathrm{\mu }}\,R_{\mathrm{\mu },\mathrm{\nu }}\,R_{\mathrm{\mu },\mathrm{\nu },\mathrm{\alpha },\mathrm{\beta }}\,C_{\mathrm{\mu },\mathrm{\nu },\mathrm{\alpha },\mathrm{\beta }}\,{\partial }_{\mathrm{\mu }}\,g_{\mathrm{\mu },\mathrm{\nu }}\,{\mathrm{\gamma }}_{i,j}\,{\mathrm{\Gamma }}_{\mathrm{\mu },\mathrm{\nu },\mathrm{\alpha }}\,G_{\mathrm{\mu },\mathrm{\nu }}\,{\mathrm{\epsilon }}_{\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }}\,X_{\mathrm{\mu }}\right\}$

$\mathrm{g\_}\left[\mathrm{\mu },\mathrm{\rho }\right]A\left[\mathrm{~rho}\right]A\left[\mathrm{\nu }\right]$

$g_{\mathrm{\mu },\mathrm{\rho }}{A}_{\phantom{}\phantom{\mathrm{\rho }}}^{\phantom{}\mathrm{\rho }}{A}_{\mathrm{\nu }}$

$\mathrm{Check}\left(\,\mathrm{all}\right)$

$\mathrm{The\; repeated\; indices\; per\; term\; are:}\left[\left\{\mathrm{...}\right\}\,\left\{\mathrm{...}\right\}\,\mathrm{...}\right]\mathrm{,\; the\; free\; indices\; are:}\left\{\mathrm{...}\right\}$

$\left[\left\{\mathrm{\rho }\right\}\right],\left\{\mathrm{\mu }\,\mathrm{\nu }\right\}$

$T≔\mathrm{TensorArray}\left(\right)$

$T≔\left[\right]$

$\mathrm{TensorArray}\left(\,\mathrm{performsumoverrepeatedindices}=\mathrm{false}\right)$

$T≔\mathrm{TensorArray}\left(\,\mathrm{freeindices}=\left[\mathrm{\nu }\,\mathrm{\mu }\right]\right)$

$T≔\left[\right]$

$T≔\mathrm{TensorArray}\left(\,\mathrm{freeindices}=\left[\mathrm{\nu }\,\mathrm{\mu }\right]\,\mathrm{output}=\mathrm{setofequations}\right)$

$T≔\left\{\frac{A_1{A}_{\phantom{}\phantom{1}}^{\phantom{}1}r}{2m-r}=0\,\frac{A_1{A}_{\phantom{}\phantom{4}}^{\phantom{}4}\left(r-2m\right)}{r}=0\,\frac{A_2{A}_{\phantom{}\phantom{1}}^{\phantom{}1}r}{2m-r}=0\,\frac{A_2{A}_{\phantom{}\phantom{4}}^{\phantom{}4}\left(r-2m\right)}{r}=0\,\frac{A_3{A}_{\phantom{}\phantom{1}}^{\phantom{}1}r}{2m-r}=0\,\frac{A_3{A}_{\phantom{}\phantom{4}}^{\phantom{}4}\left(r-2m\right)}{r}=0\,\frac{A_4{A}_{\phantom{}\phantom{1}}^{\phantom{}1}r}{2m-r}=0\,\frac{A_4{A}_{\phantom{}\phantom{4}}^{\phantom{}4}\left(r-2m\right)}{r}=0\,-A_1{r}^2{A}_{\phantom{}\phantom{2}}^{\phantom{}2}=0\,-A_2{r}^2{A}_{\phantom{}\phantom{2}}^{\phantom{}2}=0\,-A_3{r}^2{A}_{\phantom{}\phantom{2}}^{\phantom{}2}=0\,-A_4{r}^2{A}_{\phantom{}\phantom{2}}^{\phantom{}2}=0\,-A_1{A}_{\phantom{}\phantom{3}}^{\phantom{}3}{r}^2{\sin \left(\mathrm{\theta }\right)}^2=0\,-A_2{A}_{\phantom{}\phantom{3}}^{\phantom{}3}{r}^2{\sin \left(\mathrm{\theta }\right)}^2=0\,-A_3{A}_{\phantom{}\phantom{3}}^{\phantom{}3}{r}^2{\sin \left(\mathrm{\theta }\right)}^2=0\,-A_4{A}_{\phantom{}\phantom{3}}^{\phantom{}3}{r}^2{\sin \left(\mathrm{\theta }\right)}^2=0\right\}$

$\mathrm{TensorArray}\left(\mathrm{g\_}\left[\mathrm{\mu },\mathrm{\nu }\right]\,\mathrm{output}=\mathrm{lineelement}\right)$

$\frac{r{\mathbf{\ⅆ}\left(r\right)}^2}{2m-r}-r^2{\mathbf{\ⅆ}\left(\mathrm{\theta }\right)}^2-r^2{\sin \left(\mathrm{\theta }\right)}^2{\mathbf{\ⅆ}\left(\mathrm{\phi }\right)}^2+\frac{\left(r-2m\right){\mathbf{\ⅆ}\left(t\right)}^2}{r}$

$\mathrm{Riemann}\left[\mathrm{\mu },\mathrm{\nu },\mathrm{\alpha },\mathrm{\beta }\right]$

$R_{\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }}$

$\mathrm{convert}\left(\,\mathrm{Christoffel}\right)$

$g_{\mathrm{\alpha },\mathrm{\lambda }}\left({\partial }_{\mathrm{\mu }}\left({\mathrm{\Gamma }}_{\phantom{}\phantom{\mathrm{\lambda }}\mathrm{\beta },\mathrm{\nu }}^{\phantom{}\mathrm{\lambda }\phantom{\mathrm{\beta },\mathrm{\nu }}}\right)-{\partial }_{\mathrm{\nu }}\left({\mathrm{\Gamma }}_{\phantom{}\phantom{\mathrm{\lambda }}\mathrm{\beta },\mathrm{\mu }}^{\phantom{}\mathrm{\lambda }\phantom{\mathrm{\beta },\mathrm{\mu }}}\right)+{\mathrm{\Gamma }}_{\phantom{}\phantom{\mathrm{\lambda }}\mathrm{\mu },\mathrm{\upsilon }}^{\phantom{}\mathrm{\lambda }\phantom{\mathrm{\mu },\mathrm{\upsilon }}}{\mathrm{\Gamma }}_{\phantom{}\phantom{\mathrm{\upsilon }}\mathrm{\beta },\mathrm{\nu }}^{\phantom{}\mathrm{\upsilon }\phantom{\mathrm{\beta },\mathrm{\nu }}}-{\mathrm{\Gamma }}_{\phantom{}\phantom{\mathrm{\lambda }}\mathrm{\nu },\mathrm{\upsilon }}^{\phantom{}\mathrm{\lambda }\phantom{\mathrm{\nu },\mathrm{\upsilon }}}{\mathrm{\Gamma }}_{\phantom{}\phantom{\mathrm{\upsilon }}\mathrm{\beta },\mathrm{\mu }}^{\phantom{}\mathrm{\upsilon }\phantom{\mathrm{\beta },\mathrm{\mu }}}\right)$

$R≔\mathrm{TensorArray}\left(\,\mathrm{simplifier}=\mathrm{simplify}@\mathrm{normal}\right)$

$R\left[1,3,1,3\right]$

$-\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}$

$\mathrm{Riemann}\left[1,3,1,3\right]$

$-\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}$

$\mathrm{Riemann}\left[\mathrm{nonzero}\right]$

$R_{\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }}=\left\{\left(1\,2\,1\,2\right)=-\frac{m}{2m-r}\,\left(1\,2\,2\,1\right)=\frac{m}{2m-r}\,\left(1\,3\,1\,3\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(1\,3\,3\,1\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(1\,4\,1\,4\right)=\frac{2m}{r^3}\,\left(1\,4\,4\,1\right)=-\frac{2m}{r^3}\,\left(2\,1\,1\,2\right)=\frac{m}{2m-r}\,\left(2\,1\,2\,1\right)=-\frac{m}{2m-r}\,\left(2\,3\,2\,3\right)=-2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(2\,3\,3\,2\right)=2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(2\,4\,2\,4\right)=\frac{\left(2m-r\right)m}{r^2}\,\left(2\,4\,4\,2\right)=\frac{-2m^2+rm}{r^2}\,\left(3\,1\,1\,3\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(3\,1\,3\,1\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(3\,2\,2\,3\right)=2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(3\,2\,3\,2\right)=-2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(3\,4\,3\,4\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\,\left(3\,4\,4\,3\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\,\left(4\,1\,1\,4\right)=-\frac{2m}{r^3}\,\left(4\,1\,4\,1\right)=\frac{2m}{r^3}\,\left(4\,2\,2\,4\right)=\frac{-2m^2+rm}{r^2}\,\left(4\,2\,4\,2\right)=\frac{\left(2m-r\right)m}{r^2}\,\left(4\,3\,3\,4\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\,\left(4\,3\,4\,3\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\right\}$

$\mathrm{ArrayElems}\left(R\right)$

$\left\{\left(1\,2\,1\,2\right)=-\frac{m}{2m-r}\,\left(1\,2\,2\,1\right)=\frac{m}{2m-r}\,\left(1\,3\,1\,3\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(1\,3\,3\,1\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(1\,4\,1\,4\right)=\frac{2m}{r^3}\,\left(1\,4\,4\,1\right)=-\frac{2m}{r^3}\,\left(2\,1\,1\,2\right)=\frac{m}{2m-r}\,\left(2\,1\,2\,1\right)=-\frac{m}{2m-r}\,\left(2\,3\,2\,3\right)=-2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(2\,3\,3\,2\right)=2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(2\,4\,2\,4\right)=\frac{\left(2m-r\right)m}{r^2}\,\left(2\,4\,4\,2\right)=\frac{-2m^2+rm}{r^2}\,\left(3\,1\,1\,3\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(3\,1\,3\,1\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^{2}m}{2m-r}\,\left(3\,2\,2\,3\right)=2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(3\,2\,3\,2\right)=-2{\sin \left(\mathrm{\theta }\right)}^{2}mr\,\left(3\,4\,3\,4\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\,\left(3\,4\,4\,3\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\,\left(4\,1\,1\,4\right)=-\frac{2m}{r^3}\,\left(4\,1\,4\,1\right)=\frac{2m}{r^3}\,\left(4\,2\,2\,4\right)=\frac{-2m^2+rm}{r^2}\,\left(4\,2\,4\,2\right)=\frac{\left(2m-r\right)m}{r^2}\,\left(4\,3\,3\,4\right)=-\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\,\left(4\,3\,4\,3\right)=\frac{{\sin \left(\mathrm{\theta }\right)}^2\left(2m-r\right)m}{r^2}\right\}$

$\mathrm{evalb}\left(\mathrm{simplify}\left(\mathrm{rhs}\left(\right)=\right)\right)$

$\mathrm{true}$

$\mathrm{Riemann}\left[\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }\right]\mathrm{Riemann}\left[\mathrm{~alpha},\mathrm{~beta},\mathrm{~nu},\mathrm{~sigma}\right]$

$R_{\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }}{R}_{\phantom{}\phantom{\mathrm{\alpha },\mathrm{\beta },\mathrm{\nu },\mathrm{\sigma }}}^{\phantom{}\mathrm{\alpha },\mathrm{\beta },\mathrm{\nu },\mathrm{\sigma }}$

$\mathrm{Check}\left(\,\mathrm{all}\right)$

$\mathrm{The\; repeated\; indices\; per\; term\; are:}\left[\left\{\mathrm{...}\right\}\,\left\{\mathrm{...}\right\}\,\mathrm{...}\right]\mathrm{,\; the\; free\; indices\; are:}\left\{\mathrm{...}\right\}$

$\left[\left\{\mathrm{\alpha }\,\mathrm{\beta }\,\mathrm{\nu }\right\}\right],\left\{\mathrm{\mu }\,\mathrm{~\σ}\right\}$

$\mathrm{TensorArray}\left(\,\mathrm{simplifier}=\mathrm{simplify}\right)$

$\mathrm{TensorArray}\left(\mathrm{Riemann}\left[\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }\right]\right)$

$\mathrm{TensorArray}\left(\mathrm{Riemann}\left[\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }\right]\,\mathrm{explore}\right)$

$R_{\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }}\left(\mathrm{ordering\; of\; free\; indices}=\left[\mathrm{\alpha }\,\mathrm{\beta }\,\mathrm{\mu }\,\mathrm{\nu }\right]\right)$

In the title, the tensorial expression being explored and an indication of its free indices, as well as the ordering used to produce the display. Note that, for a tensorial expression that is not just a tensor, that ordering is not determined by the expression.

Which indices are being explored: Index 1 = alpha and Index 2 = beta, so the 4 x 4 matrix displayed is for the remaining indices $\mathrm{\mu }$ and $\mathrm{\nu }$, in that order (as shown in ordering of free indices = [...] within the title).

You can move the slider of each Value of Index to set the values of alpha or beta without having to recompute anything, and the 4 x 4 matrix for $\mathrm{\mu }$ and $\mathrm{\nu }$ is automatically updated.

You can actually choose which of the 4 indices will be Index 1 or Index 2 by clicking in the corresponding boxes, and in that way also indirectly select the remaining two indices shown in the 4 x 4 matrix of components, always with the ordering you see in ordering of free indices (after removing Index 1 and Index 2).

$\mathrm{Setup}\left(\mathrm{metric}=-{\mathrm{dt}}^2+\frac{{a\left(t\right)}^2{\mathrm{dr}}^2}{-k{r}^2+1}+{a\left(t\right)}^2{r}^2{\mathrm{dtheta}}^2+{a\left(t\right)}^2{r}^2{\sin \left(\mathrm{\theta }\right)}^2{\mathrm{dphi}}^2\right)\:$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{Coordinates:}\left[r\,\mathrm{\theta }\,\mathrm{\phi }\,t\right]\mathrm{.\; Signature:}\left(\mathrm{-\; -\; -\; +}\right)$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$g_{\mathrm{\mu },\mathrm{\nu }}=\left[\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{g\_}\left[\right]$

$g_{\mathrm{\mu },\mathrm{\nu }}=\left[\right]$

$\mathrm{TensorArray}\left(\mathrm{Ricci}\left[\mathrm{\alpha },\mathrm{\rho }\right]\mathrm{Ricci}\left[\mathrm{\beta },\mathrm{\nu }\right]\mathrm{Ricci}\left[\mathrm{\mu },\mathrm{\sigma }\right]\,\mathrm{explore}\right)$

$R_{\mathrm{\alpha },\mathrm{\rho }}{R}_{\mathrm{\beta },\mathrm{\nu }}{R}_{\mathrm{\mu },\mathrm{\sigma }}\left(\mathrm{ordering\; of\; free\; indices}=\left[\mathrm{\alpha }\,\mathrm{\beta }\,\mathrm{\mu }\,\mathrm{\nu }\,\mathrm{\rho }\,\mathrm{\sigma }\right]\right)$

$\mathrm{Setup}\left(\mathrm{su2indices}=\mathrm{lowercaselatin\_ah}\right)$

$\left[\mathrm{su2indices}=\mathrm{lowercaselatin\_ah}\right]$

$\mathrm{Define}\left(\mathrm{redo}\,\mathrm{Psigma}\left[a\right]\right)$

$\mathrm{Defined\; Pauli\; sigma\; matrices\; (Psigma):}{\mathrm{\sigma }}_1,{\mathrm{\sigma }}_2,{\mathrm{\sigma }}_3$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{Defined\; objects\; with\; tensor\; properties}$

$\left\{A_{\phantom{}\phantom{\mathrm{\rho }}}^{\phantom{}\mathrm{\rho }}\,{▿}_{\mathrm{\mu }}\,{\mathrm{\gamma }}_{\mathrm{\mu }}\,{\mathrm{\sigma }}_a\,R_{\mathrm{\mu },\mathrm{\nu }}\,R_{\mathrm{\mu },\mathrm{\nu },\mathrm{\alpha },\mathrm{\beta }}\,C_{\mathrm{\mu },\mathrm{\nu },\mathrm{\alpha },\mathrm{\beta }}\,{\partial }_{\mathrm{\mu }}\,g_{\mathrm{\mu },\mathrm{\nu }}\,{\mathrm{\gamma }}_{i,j}\,{\mathrm{\Gamma }}_{\mathrm{\mu },\mathrm{\nu },\mathrm{\alpha }}\,G_{\mathrm{\mu },\mathrm{\nu }}\,{\mathrm{\epsilon }}_{\mathrm{\alpha },\mathrm{\beta },\mathrm{\mu },\mathrm{\nu }}\,X_{\mathrm{\mu }}\right\}$

$\mathrm{g\_}\left[\right]$

$g_{\mathrm{\mu },\mathrm{\nu }}=\left[\right]$

$\mathrm{Psigma}\left[\mathrm{definition}\right]$

${\left[{\mathrm{\sigma }}_a,{\mathrm{\sigma }}_b\right]}_{-}=2\mathrm{I}{\mathrm{\epsilon }}_{a,b,c}{\mathrm{\sigma }}_c,{\left[{\mathrm{\sigma }}_a,{\mathrm{\sigma }}_b\right]}_{+}=2{\mathrm{\delta }}_{a,b}$

$\mathrm{TensorArray}\left(\left[1\right]\right)$

$\mathrm{TensorArray}\left(\left[1\right]\,\mathrm{rewriteinmatrixform}\right)$

$\mathrm{value}\left(\right)$

$\mathrm{TensorArray}\left(\left[1\right]\,\mathrm{rewriteinmatrixform}\,\mathrm{simplifier}=\mathrm{value}\right)$

$\mathrm{TensorArray}\left(\left[1\right]\,\mathrm{performmatrixoperations}\,\mathrm{simplifier}=\mathrm{value}\right)$

$\mathrm{expand}\left(\right)$

$\mathrm{Library}:-\mathrm{PerformMatrixOperations}\left(\right)$

Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.

The Physics[TensorArray] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.

The Physics[TensorArray] command was updated in Maple 2020.

The explore and output = ... parameters were introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.