### 1.3 Usage and technical Conventions

Most simulations are interactive. The user has several alternatives to intervene, although not necessarily in parallel.

Individual points or elements of the graphical presentation can be “pulled” with the mouse and thus parameters can be changed. In this case, the mouse pointer changes into a hand symbol when it is positioned on the element. However, this change only becomes active, if the Enter key has been pressed and the text field, that turned yellow when entering text, becomes clear again. If the text field turns red a mistake with the input has happened ( quite often comma instead of full stop as decimal point; correct is for example 12.3 instead of 12,3). From a List of options given functions or parameter values can be selected with the mouse.With sliding controls individual parameters can be changed continuously or in steps.

Functions that are displayed in a text field can be changed or rewritten from scratch. Again, the changed function is submitted with ENTER.

When formulas are written in text of printed, we often use because of silent conventions short hand notations

• that are ambiguous and that can be understood as text, like ab for a times b or sin a for sin(a)
• that can be misunderstood by software as formatting characters for text like $Math content$ for $Math content$ or xˆ2,
• those special characters that can not be interpreted by programs like $Math content$ for $Math content$ for derivatives with respect to time.

For the input for numerical programs such as EXCEL/VBA, Java, VBA or Mathematics the notation must be unambiguous.

The fundamental rule is: all parts of the formula must be entered directly via keyboard without the use of special characters. Combined characters must be mapped to an equivalent number of keyboard characters, in order for these to be correctly identified by the program. ( Example: $Math content$ as derivative combined from two keyboard characters; a unique text like “derivative with respect to t” might also interpreted by a program). In particular the following notations have to be noted.

• Addition and subtraction: $Math content$
• Multiplication: $Math content$
• Do not omit brackets: $Math content$
• Division: $Math content$
• Power: $Math content$
• Exponential function:$Math content$
Parser

Many simulations use a parser to translate the formulas entered as text into the Java-format. In this case the following notation is permissible which can also be used recursively

 atanh(x) ceil(x) cos(x) cosh(x) exp(x) frac(x) floor(x) int(x) ln(x) log(x) random(x) round(x) abs(x) acos(x) acosh(x) asin(x) asinh(x) atanh(x) sign(x) sin(x) sinh(x) sqr(x) sqrt(x) step(x) tan(x) tanh(x) atan2(x,y) max(x,y) min(x,y) mod(x,y)

Here we have acos=arc cosine, cosh=hyperbolic cosine.

The important expression atan2(x,y) prevents the ambiguities of the ARCTAN via automatically yielding the correct angle in the second and third quadrant; here $Math content$ and $Math content$ are the sides of the triangle involved and $Math content$ is opposite to the angle.

Step(x) is a very interesting function in practice. It switches at $Math content$ from $Math content$ to $Math content$. If one wants to superimpose the function $Math content$ to the function $Math content$ from $Math content$ onwards, then this can be written as $Math content$. For some simulations the Math package is used together with Java for calculations. In this case the functions are prepended with Math as follows: Math.cos(x). Math

Further details about the functions and terminology used in Java can be found from many sources on the internet, for example via searching for Java & Math.