Plotting the solution of inequalities with WolframAlpha or Maple

Question

I want to plot the solution of two inequalities and include them in a LaTeX paper. I really like they way this looks: Wolfram Alpha. Unfortunately, I have no idea how to export this into a LaTeX-suitable format and I don't have a version of Mathematica.

I have tried it with the implicitplot command of Maple but it does not look good at all. It displays the solutions of each of the inequalities but not both. Any ideas?

Answer 1

I would recommend that you plot these outside of Wolfram Alpha and just use LaTeX. Here is a pgfplots version that should get you started:

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}

    \begin{document}
    \begin{tikzpicture}
      \begin{axis}[
        thick,smooth,no markers,samples=100,
        ymin=-1.2,ymax=0.5,xmin=-1.5,xmax=1,
        xlabel=$x$, ylabel=$y$
        ]
            \addplot [domain=-1:0,fill=blue!20] {-sqrt(1-(x)^2)};
            \addplot [domain=-1:0]              {-x-1};
      \end{axis}
    \end{tikzpicture}
    \end{document}

Answer 2

Here's an option using PSTricks

\documentclass{article}
\usepackage{pst-plot}

\begin{document}

\psset{algebraic=true,unit=3cm}

\begin{pspicture}(-1.5,-1.2)(1,0.6)
  \psaxes[dx=0.5,Dx=0.5,dy=0.5,Dy=0.5]{<->}(0,0)(-1.5,-1.2)(1,0.6)[$x$,0][$y$,90]
\pscustom[fillstyle=solid,fillcolor=blue,opacity=0.4]{%
\psplot{-1}{0}{-sqrt(1-x^2)}
\psplot{-1}{0}{-x-1}
}
\end{pspicture}
\end{document}

I hope I don't get flamed for doing this, but here's some Maple code that does the same thing

with(plots):
f:=x->-sqrt(1-x^2):     # define f(x)
g:=x->-x-1:         # define g(x)
a:=-1:  b:=0:       # interval [a,b]

# plotting window
xmin:=-2:   xmax:=2:    ymin:=-1:   ymax:=4:
N:=50:

# define the points for f(x) and g(x)
fpoints := [seq([a+(b-a)/N*i,f(a+(b-a)/N*i) ],i=0..N)]:
gpoints := Reverse([seq([a+(b-a)/N*i,g(a+(b-a)/N*i) ],i=0..N)]):

# plot them!
p1:=(polygon([
        seq(fpoints[i],i=1..N+1),
        seq(gpoints[i],i=1..N+1)
        ]), 
            color=red,
            gridlines=true,
            view = [xmin..xmax,ymin..ymax]):
p2:=plot(f(x),x=xmin..xmax):
p3:=plot(g(x),x=xmin..xmax):
display(p1,p2,p3);

Answer 3

You mentioned having difficulty using Maple's implicitplot for this. You might well wish to use just latex packages such as pstricks or pgfplots, but here is a Maple code solution (tried in versions 13 and 15) since you mention that in both your post's title and body.

plots:-implicitplot( (x,y)->(y-(-sqrt(1-x^2)))*(y-(-x-1)),
                 -1..0,-1..0, view=[-1.5..1.5,-1.5..1.5],
                 gridrefine=3, filledregions=true, axes=boxed,
                 coloring=[COLOUR(RGB,.8,.8,.9),"white"],
                 labels=["x","y"] );

I zoomed in before exporting that image, which is why the axis labels look to small. If i hadn't panned in before exporting, those labels would be sized ok. (Sorry, first image insertion here.)

This post was imported from stackoverflow, where it had the maple tag, yes? Did that tag get lost, on import here? It may pr may not be the optimal solution, but the tag seems sensible as that software is mentioned in both title and text body.

Answer 4

The sagetex package is another option. Then you use Sage, which is free, instead of Mathematica or Maple.

\documentclass{article}
\usepackage{sagetex}
\begin{document}

\begin{sagesilent}
 var('x, y')
 P = region_plot([x+y+1<0,x^2+y^2-1<0], (x, -1, 1), (y, -1, 1), plot_points=300)
\end{sagesilent}

\sageplot[scale=.6]{P}

\end{document}