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}.

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