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# Expression Syntax For Generic Applets

Expression syntax are used to describe mathematical operations, functions and conditions in applets.

# Expression for math functions

In the generic framework, there are predefined expressions for constants of functions that are used to describe the value of a number or function variable. Be aware that you shouldn't use these expressions as names of your variables, as this will cause problems.

Category Syntax Examples Note
Numbers 0-9 42, 2.5, ...
Number Constants pi, e pi/2, e (~2.718...)
Parentheses () (-x+1)*(x+2)
Standard Operations +,-,/,*,^ 1+2, pi/2
Absolute value abs(arg) or |arg| abs(x),
Trigonometric functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, atan2 sin(2*pi), (cos(x))^2, atan2(-1,1) if z is a complex number, atan(z) is the phase of z. It is in the range (-pi, pi], you may use also arcsin, arccos, etc

atan2 takes two real arguments x and y separated by a semicolon: atan2(x;y)
Signum sign(arg) sign(x) = 1, x>0; sign(0)=0; sign(x)=-1,x<0 If the number field is complex or complex-rational, sign(arg) is only defined for im(arg)=0.
Theta/Heaviside theta(arg) theta(x) = 1,x>=0; theta(x)=0, x<0 If the number field is complex or complex-rational, theta(arg) is only defined for im(arg)=0.
Dirac delta function (1 for x = 0, 0 otherwise) dirac(arg) dirac(x) If the number field is complex or complex-rational, dirac(arg) is only defined for im(arg)=0.
Exponential function exp(x) or e^x exp(2*x)
minimum/maximum function min(arg), max(arg) min(myMatrix), min([1;3;-2;5]) arg has to be a matrix or row vector: either an identifier or directly described using the python like syntax. Those two functions are not defined for non-real numbers.

If the number field is chosen to be complex or complex-rational, the imaginary unit is i, and there are the functions re and im for the real and imaginary part, e.g. re(1+2*i) and im (1-i).

# Expression for conditions

This is used to described conditions, such as in \randadjustif or in generic visualization's \IFELSE command
It is basically a relation between the values of two Operations or function from the 1st category

Category Syntax Examples Note
Equal left=right x=0, x=y, |(x)|=1 is true if the value of the left side equals the value of the right side
Not equal left!=right x!=0, x!=y
Greater than left>right x > y
Less than left < right x < y
Greater than or equal left >=right x >= y
Less than or equal left <=right x <= y, abs(x)<3, sin(x)<0.5
Grouping brackets [left>=right] [abs(x)>3] AND [abs(x)<5] use to group a relation
Negation NOT [left > right] NOT [x = y] negate the relation in the brackets, returns true if x != y
AND [cond1] AND [cond2] [x>0] AND [x<3]
OR [cond1] OR [cond2] [x<0] OR [x>3]

# Special syntax in a generic visualization: var()

In a generic visualization, var(arg) can be used in operations or conditions and it will be replaced by the value of
the variable with the name arg. Remember to write var as a function var(x) and not as a Tex-command \var{x}.

12345\begin{variables}   \randint{x}{-5}{5} %create two random integers   \randint{y}{-5}{5}    \point{p1}{real}{var(x),var(y)} %creates a point on (x,y) depending on the values of x and y.\end{variables}