# Formula (Main window)

## Basic example
Simple calculation can be made by assigning a formula to p (or u and v). Open the two files in the directory “bathymetry”:

1. Primary menu → formulatAndIso, then Secondary menu → p = a - b
2. Primary menu → etopo-37_IBI.nc → topography,  then Secondary menu → a → interp
3. Primary menu → gebco_[...].tif → 1,  then Secondary menu → b → interp

![Menu](../../_static/operation_menu.jpg)

## Native functions and variables
Some functions are already coded, the calculation of the slope can be with the two following methods:

1. Primary menu → formulatAndIso, then Secondary menu 
2. → p = ( gradx(p0)^2 + grady(p0)^2 )^0.5
2. → p = ellipseM( gradx(p0) , grady(p0) )
3. Primary menu → etopo-37_IBI.nc → topography,  then Secondary menu → p0 → interp


### Operators 
 | Name | Description |
 |------|-------------|
 | `+`, `-`, `*`, `/`, `^`, `%` | Addition, difference, product, ratio, power, scalar product |
 | `<`, `<=`, `>`, `>=`, `==`, `!=` | Comparison operator (return 0 or 1) |
 | `or` | Merge the fields of different variables |

### Variables 

 | Name | Description |
 |------|-------------|
 | `d2r` | Degree to radian (π/180) |
 | `e` | Exponential |
 | `nan` | Not a number |
 | `pi` | π |
 | `r2d` | Radian to degree (180/π) |
 | `lat` | Latitude over the view |
 | `lon` | Longitude over the view |
 | `p` | Variable that displays a gridded field |
 | `u` | Variable that displays a gridded zonal velocity (quiver) |
 | `v` | Variable that displays a gridded meridional velocity (quiver) |
 | `pcloud` | Variable that displays a pixel cloud |
 | `landmask` | Landmask |
 | `pmask` | Mask of the plotted variable [ p or (u,v) ] |
 | | If `pmask <= 1` then masked; |
 | | If `pmask >= 0` unmasked; |
 | | Gradient of white mask between 0-1 |
 | `p[4445]` | Value of the variable `p` at index 4445 |
 | `p[4445.3]` | Interpolation of the variable at the location between index 4445 and 4446 |

### Functions 

 | Name | Description |
 |------|-------------|
 | `abs()` | Norm (real or complex) |
 | `arg()` | Phase lag (complex) |
 | `cos()` | Cosine |
 | `exp()` | Exponential |
 | `gradx()` | Zonal gradient |
 | `grady()` | Meridian gradient |
 | `sin()` | Sine |
 | `sinh()` | Hyperbolic sine |
 | `cnes2date()` | Convert Julian days since 1950 to date format (e.g., `yyyy-mm-dd hh:mm:ss`) |
 | `date2cnes()` | Convert date format (e.g., `yyyy-mm-dd hh:mm:ss`) to Julian days since 1950 |
 | `dx()` | Zonal difference to the neighbor pixel |
 | `dy()` | Meridian difference to the neighbor pixel |
 | `fliph()` | Flip along x-axis |
 | `flipv()` | Flip along y-axis |
 | `nearest()` | Interpolate the masked value with the nearest one |
 | `geokm(plg)` | Cumulative distance along a polygon |
 | `ellipseM(X,Y)` | Norm of vector or maximum current of ellipse |