Add trace function for squared TinyMatrix

Also add corresponding tests

doc/userdoc.org

@@ -2589,7 +2589,8 @@ The output is
 #+RESULTS: dot-examples
 
 A set of ~det~ functions is defined to get the determinant of matrices
-$\mathbb{R}^{1\times1}$, $\mathbb{R}^{2\times2}$ and $\mathbb{R}^{3\times3}$.
+of $\mathbb{R}^{1\times1}$, $\mathbb{R}^{2\times2}$ and
+$\mathbb{R}^{3\times3}$.
 #+NAME: det-examples
 #+BEGIN_SRC pugs :exports both :results output
    import math;
@@ -2601,20 +2602,47 @@ $\mathbb{R}^{1\times1}$, $\mathbb{R}^{2\times2}$ and $\mathbb{R}^{3\times3}$.
 The output is
 #+RESULTS: det-examples
 
+The ~trace~ functions compute the trace of matrices of
+$\mathbb{R}^{1\times1}$, $\mathbb{R}^{2\times2}$ and $\mathbb{R}^{3\times3}$.
+#+NAME: trace-examples
+#+BEGIN_SRC pugs :exports both :results output
+   import math;
+   cout << "trace([[1.2]]) = " << trace([[1.2]]) << "\n";
+   cout << "trace([[1,2],[3,4]]) = " << trace([[1,2],[3,4]]) << "\n";
+   cout << "trace([[1,2,3],[4,5,6],[7,8,9]]) = "
+        << trace([[1,2,3],[4,5,6],[7,8,9]]) << "\n";
+#+END_SRC
+The output is
+#+RESULTS: trace-examples
+
 Also, one can compute inverses of $\mathbb{R}^{1\times1}$,
 $\mathbb{R}^{2\times2}$ and $\mathbb{R}^{3\times3}$ matrices using the
 ~inverse~ function set.
 #+NAME: inverse-examples
 #+BEGIN_SRC pugs :exports both :results output
    import math;
-   cout << "det([[1.2]]) = " << inverse([[1.2]]) << "\n";
-   cout << "det([[1,2],[3,4]]) = " << inverse([[1,2],[3,4]]) << "\n";
-   cout << "det([[3,2,1],[5,6,4],[7,8,9]]) = "
-        << det([[3,2,1],[5,6,4],[7,8,9]]) << "\n";
+   cout << "inverse([[1.2]]) = " << inverse([[1.2]]) << "\n";
+   cout << "inverse([[1,2],[3,4]]) = " << inverse([[1,2],[3,4]]) << "\n";
+   cout << "inverse([[3,2,1],[5,6,4],[7,8,9]]) = "
+        << inverse([[3,2,1],[5,6,4],[7,8,9]]) << "\n";
 #+END_SRC
 The output is
 #+RESULTS: inverse-examples
 
+Transpose of matrices of $\mathbb{R}^{1\times1}$,
+$\mathbb{R}^{2\times2}$ and $\mathbb{R}^{3\times3}$ are obtained using the
+~transpose~ functions.
+#+NAME: transpose-examples
+#+BEGIN_SRC pugs :exports both :results output
+   import math;
+   cout << "transpose([[1.2]]) = " << transpose([[1.2]]) << "\n";
+   cout << "transpose([[1,2],[3,4]]) = " << transpose([[1,2],[3,4]]) << "\n";
+   cout << "transpose([[3,2,1],[5,6,4],[7,8,9]]) = "
+        << transpose([[3,2,1],[5,6,4],[7,8,9]]) << "\n";
+#+END_SRC
+The output is
+#+RESULTS: transpose-examples
+
 #+BEGIN_note
 Observe that the use of a proper rounding or truncation function is
 the right way to convert a real value to an integer one. Available
@@ -3246,18 +3274,20 @@ Here is the list of these functions
 - ~tan: Vh -> Vh~
 - ~tanh: Vh -> Vh~
 
-The ~det~ functions are defined for $\mathbb{P}_0(\mathbb{R^{}}^{1\times1})$,
+A few functions are defined for $\mathbb{P}_0(\mathbb{R^{}}^{1\times1})$,
 $\mathbb{P}_0(\mathbb{R^{}}^{2\times2})$ and
 $\mathbb{P}_0(\mathbb{R^{}}^{3\times3})$ data and the return value is a
 $\mathbb{P}_0(\mathbb{R})$ function. The value is simply the
 application of the function to the cell values.
 - ~det: Vh -> Vh~
+- ~trace: Vh -> Vh~
 
-The ~inverse~ functions are defined for $\mathbb{P}_0(\mathbb{R}^{d\times d})$
+Also, functions are defined for $\mathbb{P}_0(\mathbb{R}^{d\times d})$
 data and the return value is a $\mathbb{P}_0(\mathbb{R}^{d\times d})$
 function, with $d\in\{1,2,3\}$. The value is simply the application of
 the function to the cell values.
 - ~inverse: Vh -> Vh~
+- ~transpose: Vh -> Vh~
 
 ******  ~Vh*Vh -> Vh~