Point

Point

Point[line]

Point on line

Point[conic]

Point on conic section (e.g. circle, ellipse, hyperbola)

Point[function]

Point on function

Point[vector]

Point on vector

Point[point P, vector v]

Point P + v

Midpoint

Midpoint[point A, point B]

Midpoint of A and B

Midpoint[segment]

Midpoint of segment

Center

Center[conic]

Center of a conic section (e.g. circle, ellipse, hyperbola)

Focus

Focus[conic]

(All) foci of a conic section

Vertex

Vertex[conic]

(All) vertices of a conic section

Centroid

Centroid[polygon]

Centroid of a polygon

Intersect

Intersect[line g, line h]

Intersection point of lines g and h

Intersect[line g, conic c]

All Intersection points of g and c (max. 2)

Intersect[line g, conic c, number n]

n-th intersection point of g and c

Intersect[conic c, conic d]

All intersection points of c and d (max. 4)

Intersect[conic c, conic d, number n]

n-th intersection point of c and d

Intersect[polynomial f, polynomial g]

All intersection points of f and g

Intersect[polynomial f, polynomial g, number n]

n-th intersection point of f and g

Intersect[polynomial f, line g]

All intersection points of f and g

Intersect[polynomial f, line g, number n]

n-th intersection point of f and g

Intersect[function f, function g, point A]

Intersection point of f and g with initial value A (for Newton's method)

Intersect[function f, line g, point A]

Intersection point of f and g with initial value A (for Newton's method)

Root

Root[polynomial f]

All roots of polynomial f (as points)

Root[function f, number a]

One root of function f with initial value a (Newton's method)

Root[function f, number a, number b]

One root of function f with on interval [a, b] (regula falsi)

Extremum

Extremum[polynomial f]

All local extrema of polynomial f (as points)

InflectionPoint

InflectionPoint[polynomial f]

All inflection points of polynomial f