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An algebraic expression in variables {x_1,...,x_n} is an expression constructed with the variables and algebraic numbers using addition, multiplication, and rational powers.

Characterized by allowing only integer values.

A set S of positive integers is said to be Diophantine iff there exists a polynomial Q with integral coefficients in m>=1 indeterminates such that ...

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for ...

Consider a one-dimensional Hamiltonian map of the form H(p,q)=1/2p^2+V(q), (1) which satisfies Hamilton's equations q^. = (partialH)/(partialp) (2) p^. = ...

A quantified system of real algebraic equations and inequalities in variables {x_1,...,x_n} is an expression QS=Q_1(y_1)Q_2(y_2)...Q_m(y_m)S(x_1,...,x_n;y_1,...,y_m), where Q ...

For a given monic quartic equation f(x)=x^4+a_3x^3+a_2x^2+a_1x+a_0, (1) the resolvent cubic is the monic cubic polynomial g(x)=x^3+b_2x^2+b_1x+b_0, (2) where the coefficients ...

A classic arithmetical problem probably first posed by Euclid and investigated by various authors in the Middle Ages. The problem is formulated as a dialogue between the two ...

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...