I want to use SageMath to plot in 3D a function of two variables z=f(x,y) that is bound by a number of inequalities. As a simple example, say:
f(x,y) = x+2y
This is just a tilted plane; doesn't look too exciting. But now... Restrict it to only points that satisfy both of these inequalities:
y<x (so, boundary is line with slope 1)
y>-x (so, boundary is line with slope -1)
Note that these boundaries intersect at (x,y)=(0,0) I would like a 3D rotatable view of a plane with the edges at the boundary lines, and a corner at the origin.
Later I would like to add more inequalities, maybe a few other bondaries so that it is limited to a triangular or other polygonal region, or perhaps $x^2 + y^2 < 1$ so it would be a tilted stretch quarter-circle.
How do I set these boundaries? When I looked up plotting bondaries, my web search only found how to set min,max for (x,y) for the purposes of displaying the plot, and not how to confine the region itself.
Thanks for any help you can give.