SatisfiabilityInstances[bf] attempts to find a choice of variables that makes the Boolean function bf yield True.SatisfiabilityInstances[expr, {a_1, a_2, ...}] attempts to ...
SquaredEuclideanDistance[u, v] gives the squared Euclidean distance between vectors u and v.
TrigExpand[expr] expands out trigonometric functions in expr.
In just one Mathematica command, you can easily specify a calculation that is far too complicated for any computer to do. For example, you could ask for ...
An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...
And
(Built-in Mathematica Symbol) e_1 && e_2 && ... is the logical AND function. It evaluates its arguments in order, giving False immediately if any of them are False, and True if they are all True.
ArcTan
(Built-in Mathematica Symbol) ArcTan[z] gives the arc tangent tan -1 (z) of the complex number z. ArcTan[x, y] gives the arc tangent of y/x, taking into account which quadrant the point (x, y) is in.
Assuming[assum, expr] evaluates expr with assum appended to $Assumptions, so that assum is included in the default assumptions used by functions such as Refine, Simplify, and ...
ClebschGordan[{j_1, m_1}, {j_2, m_2}, {j, m}] gives the Clebsch\[Dash]Gordan coefficient for the decomposition of \[VerticalSeparator] j, m\[RightAngleBracket] in terms of ...
Collect
(Built-in Mathematica Symbol) Collect[expr, x] collects together terms involving the same powers of objects matching x. Collect[expr, {x_1, x_2, ...}] collects together terms that involve the same powers ...