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The signature of a non-degenerate quadratic form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2 of rank r is most often defined to be the ordered pair (p,q)=(p,r-p) of ...

An algorithm for determining the order of an elliptic curve E/F_p over the finite field F_p.

SNTP(n) is the smallest prime such that p#-1, p#, or p#+1 is divisible by n, where p# is the primorial of p. Ashbacher (1996) shows that SNTP(n) only exists 1. If there are ...

The upper half-plane is the portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]>0 i.e., {x+iy:x in (-infty,infty),y in (0,infty)}. Common notations ...

A two-dimensional grid graph, also known as a rectangular grid graph or two-dimensional lattice graph (e.g., Acharya and Gill 1981), is an m×n lattice graph that is the graph ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

A camel graph is a graph formed by all possible moves of a hypothetical chess piece called a "camel" which moves analogously to a knight except that it is restricted to moves ...

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

The cricket graph is the 5-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["CricketGraph"].