# Built-In Fuctions Supported by EMSO

In the topics below are listed the Built-In Functions Supported by the EMSO process simulator.

Examples of use of the functions were added at the library EML in the folder sample/miscellaneous.

## Element-by-Element Functions

All functions in this category work for scalars, vectors, and matrices.

The returned values of these functions always have the same dimensions of its arguments.

### Hyperbolic

 hyperbolic sine sinh(Z) Returns the hyperbolic sine of Z hyperbolic cosine cosh(Z) Returns the hyperbolic cosine of Z hyperbolic tangent tanh(Z) Returns the hyperbolic tangent of Z hyperbolic cotangent coth(Z) Returns the hyperbolic cotangent of Z

### Trigonometric

 sine sin(Z) Returns the sine of Z cosine cos(Z) Returns the cosine of Z tangent tan(Z) Returns the tangent of Z arc sine asin(Z) Returns the angle whose sine is Z arc cosine acos(Z) Returns the angle whose cosine is Z arc tangent atan(Z) Returns the angle whose tangent is Z

### Mathematic

 exponential exp(Z) Returns the exponential function, e raised to the power Z logarithm log(Z) Returns the base 10 logarithm of Z natural logarithm ln(Z) Returns the natural logarithm (base e) of Z square root sqrt(Z) Returns the square root of Z Time derivative diff(Z) Returns the derivative of a function Z with respect to time

### Discontinuous Functions

 absolute value abs(Z) Returns the magnitude or absolute value of Z maximum value max(Z) Returns the maximum value of Z minimum value min(Z) Returns the minimum value of Z signal sign(Z) Returns the signal of Z (sign(Z):-1 if Z < 0 e 1 if Z > 0) small integer round(Z) Returns the small integer value of Z

## Matrix Transformation Functions

The functions in this category make sense only for vector and matrix arguments. The return value can be a scalar, vector, or matrix depending on the function and the argument.

### Vector and Matrix

 sum sum(VEC) Returns a scalar with the sum of all elements of the vector VEC sum(MAT) Returns a vector with the sum of each column of the matrix MAT sumt(MAT) Returns a vector with the sum of each row of the matrix MAT product prod(VEC) Returns a scalar with the product of all elemtns of the vector VEC prod(MAT) Returns a vector with the product of each column of the matrix MAT prodt(MAT) Returns a vector with the product of each row of the matrix MAT transpose transp(MAT) Returns the transpose of a matrix MAT