Intersect Command
 Intersect( <Object>, <Object> )

Yields the intersection points of two objects.

Let
a: 3x + 7y = 10
be a line andc: x^2 + 2y^2 = 8
be an ellipse.Intersect(a, c)
yields the intersection points E = (1.02, 1,87) and F = (2.81, 0.22) of the line and the ellipse. 
Intersect(y = x + 3, Curve(t, 2t, t, 0, 10))
yields A=(3,6). 
Intersect(Curve(2s, 5s, s,10, 10), Curve(t, 2t, t, 10, 10))
yields A=(0,0).
 Intersect( <Object>, <Object>, <Index of Intersection Point> )

Yields the n^{th} intersection point of two objects. Each object must be a line, conic, polynomial function or implicit curve.
Let a(x) = x^3 + x^2  x
be a function and b: 3x + 5y = 4
be a line. Intersect(a, b, 2)
yields the
intersection point C = (0.43, 0.54) of the function and the line.
 Intersect( <Object>, <Object>, <Initial Point> )

Yields an intersection point of two objects by using a numerical, iterative method with initial point.
Let a(x) = x^3 + x^2  x
be a function, b: 3x + 5y = 4
be a line, and C = (0, 0.8) be the initial point.
Intersect(a, b, C)
yields the intersection point D = (0.43, 0.54) of the function and the line by using a
numerical, iterative method.
 Intersect( <Function>, <Function>, <Start xValue>, <End xValue> )

Yields the intersection points numerically for the two functions in the given interval.
Let f(x) = x^3 + x^2  x
and g(x) = 4 / 5 + 3 / 5 x
be two functions. Intersect(f, g, 1, 2)
yields
the intersection points A = (0.43, 0.54) and B = (1.1, 1.46) of the two functions in the interval [ 1, 2 ].
 Intersect( <Curve 1>, <Curve 2>, <Parameter 1>, <Parameter 2> )

Finds one intersection point using a numerical, iterative method starting at the given parameters.
Let a = Curve(cos(t), sin(t), t, 0, π)
and b = Curve(cos(t) + 1, sin(t), t, 0, π)
.
Intersect(a, b, 0, 2)
yields the intersection point A = (0.5, 0.87).
CAS Syntax
 Intersect( <Function>, <Function> )

Yields a list containing the intersection points of two objects.
Let f(x):= x^3 + x^2  x
and g(x):= x
be two functions. Intersect(f(x), g(x))
yields the intersection
points list: {(1, 1), (0, 0), (2, 2)} of the two functions.
 Intersect( <Object>, <Object> )

Intersect( <Line> , <Object> )
creates the intersection point(s) of a line and a plane, segment, polygon, conic, etc. 
Intersect( <Plane> , <Object> )
creates the intersection point(s) of a plane and segment, polygon, conic, etc. 
Intersect( <Conic>, <Conic> )
creates the intersection point(s) of two conics 
Intersect( <Plane>, <Plane> )
creates the intersection line of two planes 
Intersect( <Plane>, <Polyhedron> )
creates the polygon(s) intersection of a plane and a polyhedron. 
Intersect( <Sphere>, <Sphere> )
creates the circle intersection of two spheres 
Intersect( <Plane>, <Quadric> )
creates the conic intersection of the plane and the quadric (sphere, cone, cylinder, …)
