# Reserved Words

Reserved words are considered words that have a specific purpose in the operations performed by OptFerm. This means, that there are variables that can be modified in runtime during OptFerm operations, and sometimes is necessary to know the values of these variables to perform a certain mathematical operation in the established model. Thus, by using the reserved words it is possible to access to the corresponding value, that it is being calculated in the runtime operations of the OptFerm. For instance, a mathematical equation is defined in the model, and needs the current time instant given by the ODE solver, to be calculated. Thus, the @time word must be used in the equation.

## [endstatevars]

Returns the current size of the vector corresponding to the defined State Variables.

## [endrates]

Returns the current size of the vector corresponding to the defined Kinetic Variables.

## @dt

Returns the step-size (dt) used in ODE solver operations (simulation process).

## @feed

Returns the total feeding rate at time instant (t), calculated along the simulation process.

## @time

Returns the time instant (t), along the simulation process.

# Special Functions

Some special functions are implemented in OptFerm to help users in performing basic mathematical operations. All special functions are preceded by "$" followed by function name.

## $max

Calculates the maximum value of the input argument, and accepts an expression or a variable as input argument.

Formulation:

```
$max(expression) or $max(variable) or $max(variable[increment_variable])
```

Examples:

```
$max(x[i]+s[i]);
$max(D);
$max(D*R*F[i]);
```

## $min

Calculates the minimum value of the input argument, and accepts an expression or a variable as input argument.

Formulation:

```
$min(expression) or $min(variable) or $min(variable[increment_variable])
```

Examples:

```
$min(x[i]+s[i]);
$min(D);
$min(D*R*F[i]);
```

## $sum

Calculates the sum of the input argument in a **for** statement, and accepts an expression or a variable as input argument.

Formulation:

```
$sum(expression) or $sum(variable) or $sum(variable[increment_variable])
```

Examples:

```
$sum(x[i]+s[i]);
$sum(D[i]);
$sum(D*R*F[i]);
```

## $productivity

Is a generic equation that calculates the productivity of the process, using the following mathematical equation:

Where, *X* is the biomass or desired product, *W* is the weight or volume, and *ftime* is the final fermentation time.

However, the productivity function is used in the OptFerm using a simple format:

```
$productivity(desired product or biomass variable, weight or volume variable);
```

Suppose that a variable **P** was defined for a desired product in the State Variables field, and the variable VOL in the Volume Variable field of the model. Thus, the productivity function can be set as follow:

```
$productivity(P,VOL);
```