2D implicit curve

### 8.13.1 2D implicit curve

For an implicit plot in ℝ2:

- plotimplicit takes three mandatory arguments and three optional arguments:
  - expr, an expression of two variables implicitly defining a curve by expr=0.
  - vars, a list of the two variables, optionally with their ranges var=a..b. If a range is not given, the ranges are determined by WX-, WX+ and WY-, WY+ in the graphical configuration (see Section 3.5.8).
  - Optionally, xstep, which can be xstep=n to specify the discretization step in the x direction.
  - Optionally, ystep, which can be ystep=m to specify the discretization step in the y direction.
  - Optionally, unfactored.
- plotimplicity(expr,vars ⟨xstep,ystep,unfactored⟩) draws the graphic representation of the curve defined by the implicit equation expr=0 over the given ranges of the variables.

Examples.

- Input:
  plotimplicit(x^2+y^2-1,x,y)
  or:
  plotimplicit(x^2+y^2-1,x,y,unfactored)
  Output:
- Input:
  plotimplicit(x^2+y^2-1,x,y,xstep=0.2,ystep=0.3)
  or:
  plotimplicit(x^2+y^2-1,[x,y],xstep=0.2,ystep=0.3)
  or:
  plotimplicit(x^2+y^2-1,[x,y], xstep=0.2,ystep=0.3,unfactored)
  Output:
- Input:
  plotimplicit(x^2+y^2-1,x=-2..2,y=-2..2, xstep=0.2,ystep=0.3)
  Output: