## 1. Mathematical Expressions

Following tables present tools to declare and manipulate expressions.

 Feel++ Keyword Description `Px()` Variable $x$ `Py()` Variable $y$ `Pz()` Variable $z$ `cst( c )` Constant function equal to $c$

You can of course use all current operators ( + - / * ) and the usual following functions:

 Feel++ Keyword Math Object Description `abs(expr)` $|f(\overrightarrow{x})|$ element wise absolute value of $f$ `cos(expr)` $\cos(f(\overrightarrow{x}))$ element wise cos value of $f$ `sin(expr)` $\sin(f(\overrightarrow{x}))$ element wise sin value of $f$ `tan(expr)` $\tan(f(\overrightarrow{x}))$ element wise tan value of $f$ `acos(expr)` $\mathrm{acos}(f(\overrightarrow{x}))$ element wise acos value of $f$ `asin(expr)` $\mathrm{asin}(f(\overrightarrow{x}))$ element wise asin value of $f$ `atan(expr)` $\mathrm{atan}(f(\overrightarrow{x}))$ element wise atan value of $f$ `cosh(expr)` $\cosh(f(\overrightarrow{x}))$ element wise cosh value of $f$ `sinh(expr)` $\sinh(f(\overrightarrow{x}))$ element wise sinh value of $f$ `tanh(expr)` $\tanh(f(\overrightarrow{x}))$ element wise tanh value of $f$ `exp(expr)` $\exp(f(\overrightarrow{x}))$ element wise exp value of $f$ `log(expr)` $\log(f(\overrightarrow{x}))$ element wise log value of $f$ `sqrt(expr)` $\sqrt{f(\overrightarrow{x})}$ element wise sqrt value of $f$ `ceil(expr)` $\lceil{f(\overrightarrow{x})}\rceil$ element wise ceil of $f$ `floor(expr)` $\lfloor{f(\overrightarrow{x})}\rfloor$ element wise floor of $f$ `sign(expr)` $\begin{cases} 1 & \text{if}\ f(\overrightarrow{x}) \geq 0\\-1 & \text{if}\ f(\overrightarrow{x}) < 0\end{cases}$ element wise sign value of $f$ `chi(expr)` $\chi(f(\overrightarrow{x}))=\begin{cases}0 & \text{if}\ f(\overrightarrow{x}) = 0\\1 & \text{if}\ f(\overrightarrow{x}) \neq 0\\\end{cases}$ element wise boolean test of $f$ `rand()` random number in $[0,1$] regenerated at each call `rand(lo,hi)` random number in $[lo,hi$] regenerated at each call