Level Lines of a function of two variables. Graph of a function, defined implicitly

Graph definition for set of level lines of a 2-variable function F(x,y) has the following format:

 

F(x,y)=C1,C2, …

where

F(x,y) – is an expression which (after calculations), contains only variables, corresponding to coordinate axes. By default, variables names are x and y.

C1, Cetc. – are numbers or expressions which specify levels. If expressions are used, they (after evaluation) should not contain variables.  

 

Since an equation F(x,y)=C implicitly specifies a function y=y(x), this form of graph definition can be used to plot graph of a function, specified implicitly.

 

Examples:

x2-y2=-4,-1,-0,2,4                    ; a set of hyperboles and two intersecting straight lines

sin(x)*sin(y)=0.9                    ; a set of small circles

x^2-y^3=-20,-5,0,5,20            ; a set of implicitly specified functions

 

Remark on performance. Plotting of level lines sometimes requires long calculations, especially if there are many level. To break plotting press Alt+Break or use menu item Command -> Stop Processing.