This page lists the various symbols which are used in our posts about dashed line theory. Some of them have been defined specifically for dashed line theory, while others are already known universally and are reported below just for reading convenience.
Symbol  Meaning 

a \mathrm{\ mod\ } b  Modulus: it indicates the remainder of the division between a and b.
For example, 20 \mathrm{\ mod\ } 7 = 6 indicates that the division between 20 and 7 gives 6 as remainder. Modulus has priority over additions and subtractions, while multiplications, divisions and powers have priority over it. Then, given the following expression: a + (b + c) x \mathrm{\ mod\ } d^2 + e
execution order of operations is: a + (((b + c) x) \mathrm{\ mod\ } (d^2)) + e

a \mathrm{\ mod^{\star}\ } b  Modulus Star: it’s defined as
a \mathrm{\ mod^{\star}\ } b := \begin{cases} b & \text{if }a \mathrm{\ mod\ } b = 0 \\ a \mathrm{\ mod\ } b & \text{otherwise} \end{cases}
It behaves like a \mathrm{\ mod\ } b, but returns b in place of 0. For example, if b = 5: 1 \mathrm{mod} 5 = 1 \mathrm{mod^{\star}} 5 = 1; Like modulus, it has priority only over additions and subtractions. 
(C) 
Integer value of a proposition: it’s defined as
(C) := \begin{cases} 1 &\text{if }C\text{ is true}\\ 0 &\text{if }C\text{ is false}\end{cases}
where C is a proposition. For example, (a \gt 10) is 1 if a \gt 10, 0 otherwise. 
\sigma_i(x_1, x_2, ... x_j) 
Elementary symmetric polynomials: they are defined as
\sigma_0(x_1, x_2, x_3, x_4, \ldots, x_j) = 1 Generally speaking, in order to compute \sigma_i(x_1, x_2, ... x_j) you have to list all the combinations i by i if the j arguments, transform each into a product, and then sum up the so obtained products: for example, \sigma_2(3, 5, 7) = 3 \cdot 5 + 3 \cdot 7 + 5 \cdot 7. If i is zero, the arguments are irrelevant, since the result is always 1. Similarly, we also agree that the result is 1 also when the argument list is empty, i.e. \sigma_i() = 1 for all i. 
[a, b]  Range: it’s the set of the integer numbers between a and b: [a,b] := \{n \in \mathbb{Z} \mid a \leq n \leq b\}. The number b  a + 1, that is the range cardinality, is defined width of the range. It’s supposed that a \leq b. 
p, q  The symbols p and q are used for indicating prime numbers, except if differently specified. 
p_i  The symbol p_i indicates the ith prime number, with i \geq 1, so that p_1 = 2, p_2 = 3, p_3 = 5, etcetera. 
q_i  The symbol q_i, with i \geq 1, indicates a number taken from a list of prime numbers, not necessarily sorted or complete. For example if the list is 5, 17, 3, then q_1 := 5, q_2 := 17 and q_3 := 3. 