Chapter 1. ExpressionsWhen a graph is defined by an equation, Advanced Grapher offers the option of different types of operation, consisting of constants and variables and/or their functions, connected by operators. Operations
 arithmetical operations: +, , *, /, ^ (raising to power).
Example: 2+2^3=10
Hint: you can use the calculator to check the examples. Click button to show the calculator (Figure 1.1).  Figure 1.1: Calculator 
 logical operations. The result and operands of these operations may be true or false.
Advanced Grapher doesn't have special values for true and false. If the operand is negative or zero it's false, else it's true. The result of the operations is always 0 (false) or 1 (true). Advanced Grapher supports the following logical operations: AND, OR, XOR and NOT. NOT is an unary operator; AND, OR, XOR are binary operations. You can see results of the operations depending on the value of the operands in the following table:
Operand 1  Operand 2  AND  OR  XOR  NOT  0  0  0  0  0  1  0  1  0  1  1   1  0  0  1  1  0  1  1  1  1  0  
(The result for the not operation depends on the operand 1 only  not Operand 1). Examples: 1 or 0=1; 5 and 1=0; (not 3) + 2*(1 xor 0)=2  relational operations: >,<,>=,<=,=,<>. The result of these operations is 0 (false) or 1 (true). These operations are mostly used to graph systems of inequalities.
Examples: (2>3) = 0; (3<=3) = 1; (0<>1) = 1
Functions
You can use different functions in the expressions. If you'd like to use a function you should enter <name_of_function>(<argument>). Examples: sin(x+2); ln(ln(1/x)); sin(x)^3. Advanced Grapher allows to use the following functions: sin  sine cos  cosine tan  tangent cot  cotangent asin  inverse sine acos  inverse cosine atan  inverse tangent abs  absolute value sqrt  square root ln  natural logarithm lg  logarithm base 10 exp  exponent (exp(x)  e raised to the power x) int  integer part of number round  rounded value frac  fractional part of number sign  sign(x)=1 if x>0, sign(x)=0 if x=0 and sign(x)=1 if x<0 sinh  hyperbolic sine cosh  hyperbolic cosine tanh  hyperbolic tangent coth  hyperbolic cotangent asinh  hyperbolic inverse sine acosh  hyperbolic inverse cosine atanh  hyperbolic inverse tangent acoth  hyperbolic inverse cotangent random  random(x)=rnd*x, rnd is a random value, 0<=rnd<1 Priority of the operations and functions
1. Functions 2. ^ 3. *,/ 4. +, 5. >=,=,<=,<,>,<> 6. not 7. and, or, xor Functions have the largest priority; and, or, xor  the smallest. Example: not 1+2 and 0 = (not (1+2)) and 0 = 0 Constants
Advanced Grapher recognizes the constant PI which is directly available. If you wish to use the constant e (base of natural logarithm), type in exp(1). Variables
You can also use one or two variables, for example X, Y, A or T (it depends on the situation). Additional information You can leave out "*". Examples: xy, (x+1)(5y+x), xx, xsin(x).
