$Assumptions is the default setting for the Assumptions option used in such functions as Simplify, Refine, and Integrate.

DiscretePlot[expr, {n, n_max}] generates a plot of the values of expr when n runs from 1 to n_max.DiscretePlot[expr, {n, n_min, n_max}] generates a plot of the values of expr ...

Hue[h] is a graphics directive which specifies that objects which follow are to be displayed, if possible, in a color corresponding to hue h. Hue[h, s, b] specifies colors in ...

RandomReal[] gives a pseudorandom real number in the range 0 to 1. RandomReal[{x_min, x_max}] gives a pseudorandom real number in the range x_min to x_max. RandomReal[x_max] ...

Fibonacci[n] gives the Fibonacci number F_n. Fibonacci[n, x] gives the Fibonacci polynomial F_n (x).

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...

Sec[z] gives the secant of z.

LinearRecurrence[ker, init, n] gives the sequence of length n obtained by iterating the linear recurrence with kernel ker starting with initial values ...

QuotientRemainder[m, n] gives a list of the quotient and remainder from division of m by n.