Working with Implicit Functions in Mathematica

Question

Is it possible to build and handle implicit functions in Mathematica?

eg: -

x^3 + y^3 = 6xy

Is it possible to build such a function?

Answer 1

 ContourPlot[x^3 + y^3 == 6*x*y, {x, -2.7, 5.7}, {y, -7.5, 5}] 

Two comments:

• Pay attention to the double equal sign and the multiplication symbols.
• You can find this exact input through the WolframAlpha interface. This interface is more forgiving and accepts your input almost exactly - although I needed to point out that I needed some kind of plot.

Answer 2

Yes, using ContourPlot .

And it’s even possible to build the text x^3 + y^3 = 6xy along its own curve, replacing the Line primitive with several Text primitives:

 ContourPlot[x^3 + y^3 == 6 xy, {x, -4, 4}, {y, -4, 4}, Background -> Black, PlotPoints -> 7, MaxRecursion -> 1, ImageSize -> 500] /. { Line[s_] :> Map[ Text[Style["x^3+y^3 = 6xy", 16, Hue[RandomReal[]]], #, {0, 0}, {1, 1}] &, s] } 

Or you can animate the equation along a curve, for example:

 res = Table[ Normal[ ContourPlot[x^3 + y^3 == 6 xy, {x, -4, 4}, {y, -4, 4}, Background -> Black, ImageSize -> 600]] /. {Line[s_] :> {Line[s], Text[Style["x^3+y^3 = 6xy", 16, Red], s[[k]], {0, 0}, s[[k + 1]] - s[[k]]]}}, {k, 1, 448, 3}]; ListAnimate[res] 

Answer 3

I assume this is what you need:

http://reference.wolfram.com/mathematica/Compatibility/tutorial/Graphics/ImplicitPlot.html

 ContourPlot[x^3 + y^3 == 6 x*y, {x, -10, 10}, {y, -10, 10}]