Notation Standards

The following table provides a standard for the notation in the mathematical documentation and in the code.

Object	Math	Code
Graph	\(G,\, H,\, G_1,\, H_1\)	G, G1, H, H1, or graph, graph_1, subgraph
Framework	\(F\)	F, F1, framework
dimension	\(d\)	dim
Realization	\(p\)	realization or points depending on dict/list
Point	\((x_1,\dots,x_d)\in \RR^d\)	pos or point
Vertex Set	\(V\), \(V(G)\)	vertices
Edge Set	\(E\), \(E(G)\)	edges
Vertex	\(u,\, v, \, w,\, u_1,\, v_1,\, w_1\)	vertex, u, v,w,u1, v1,w1
Edge	\(e\), \(e_1\), \(uv\)	edge, e, e1
#V	\(n\) or \(|V|\)	n
#E	\(m\) or \(|E|\)	m
Rigidity Matrix	\(R(G,p)\)	rigidity_matrix
Infinitesimal flex	\(q\)	inf_flex
Equilibrium stress	\(\omega\)	stress
Stress Matrix	\(\Omega\)	stress_matrix
Motion	\(\alpha:[0,1]\rightarrow (\RR^d)^n\)	motion
\(d\)-rigidity matroid	\(\mathcal{R}_d\)	N/A
Symbolic bool	N/A	numerical
Tolerance float	N/A	tolerance

Iterator Variables are supposed to be denoted in the following order (with descending callback depth):

1. i

2. j

3. k (if k is not defined differently in the method)

4. L

5. ii…

If single-letter variables are part of the input parameters, that should be reflected in the method name. Examples of this are Graph.is_kl_sparse() or Graph.is_k_redundantly_rigid().

Otherwise, single-letter variables should be avoided whenever possible and descriptive variable names should be used instead. According to PEP8, the letters l (lower-case ell), O (upper-case oh) and I (upper-case eye) should generally be avoided due to their similarity to other characters.