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404 Functions and commands
orthocenter Shows the orthocenter of the triangle made with three points.
orthocenter((Pnt or Cplx),(Pnt or Cplx),(Pnt
or Cplx))
Example:
orthocenter(0,4i,4) returns (0,0)
orthogonal With a point (A) and a line (BC) as arguments, draws the
orthogonal plane of the line that passes through the point.
With a point (A) and a plane (BCD) as arguments, draws the
orthogonal line of the plane that passes through the point.
orthogonal(Pnt(A),(Line(BC) or Plane(BCD))
Example:
orthogonal(A,line(B,C)) draws the orthogonal
plane of line BC through A and
orthogonal(A,plane(B,C,D)) draws the orthogonal
line of plane(B,C,D) through A.
pa2b2 Takes a prime integer n congruent to 1 modulo 4 and returns
[a,b] such that a^2+b^2=n.
pa2b2(Intg(n))
Example:
pa2b2(17) gives [4,1]
pade Returns the Pade approximation i.e. a rational fraction P/Q
such that P/Q=Xpr mod x^(n+1) or mod N with degree(P)<p.
pade(Expr(Xpr), Var(x), (Intg(n) || Poly(N)),
Intg(p))
Example:
pade(exp(x),x,10,6) gives (-x^5-30*x^4-420*x^3-
3360*x^2-15120*x-30240)/(x^5-30*x^4+420*x^3-
3360*x^2+15120*x-30240)
parabola With two points (F, A) as arguments, draws a parabola of
focus F and top A. With three points (F, A and P) as
arguments, draws a parabola with focus F and top A in the
plane ABP. With a complex (A) and a real (c) as arguments,
draws a parabola of equation y=yA+c*(x–xA)^2. With one
second degree polynomial (P(x,y)) as argument, draws the
parabola when the polynomial is set to equal 0.
parabola(Pnt(F)||Pnt(xA+i*yA),Pnt(A)||Real(c)
,[Pnt(P)])