CoCalc -- 14-1 Functions of Several Variables.sagews

Sage examples from in-class

Project: MATH 202

Path: MATH 202 Spring 2016/Examples / 14-1 Functions of Several Variables.sagews

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var('x', 'y', 't')

(x, y, t)

plot3d(x^2 + y^2, (x, -2, 2), (y, -2, 2), adaptive = True) # False is the default

3D rendering not yet implemented

s = plot3d(x^2 + y^2, (x, -2, 2), (y, -2, 2))
p = [plot3d(c, (x, -3, 3), (y, -3, 3), opacity = 0.3, color = 'grey') for c in range(1, 8)]
c = [parametric_plot3d([sqrt(c)*cos(t), sqrt(c)*sin(t), c], (t, 0, 2*pi), color='red') for c in range(1, 8)]
show(s+sum(p)+sum(c))

3D rendering not yet implemented

plot3d(x*y^2 - x^3, (x, -1, 1), (y, -1, 1), mesh = True)

3D rendering not yet implemented

contour_plot(x*y^2 - x^3, (x, -1, 1), (y, -1, 1))
contour_plot(x*y^2 - x^3, (x, -1, 1), (y, -1, 1), contours = 20, colorbar = True)

help(show)

Help on function show in module smc_sagews.sage_salvus:

show(*objs, **kwds)
    Show a 2d or 3d graphics object (or objects), animation, or matplotlib figure, or show an
    expression typeset nicely using LaTeX.
    
       - display: (default: True); if True, use display math for expression (big and centered).
    
       - svg: (default: True); if True, show 2d plots using svg (otherwise use png)
    
       - d3: (default: True); if True, show graphs (vertices and edges) using an interactive D3 viewer
           for the many options for this viewer, type 'import graphics; graphics.graph_to_d3_jsonable?'
         If false, graphs are converted to plots and displayed as usual.
    
       - renderer: (default: 'webgl'); for 3d graphics
           - 'webgl' (fastest) using hardware accelerated 3d;
           - 'canvas' (slower) using a 2d canvas, but may work better with transparency;
           - 'tachyon' -- a ray traced static image.
    
       - spin: (default: False); spins 3d plot, with number determining speed (requires mouse over plot)
    
       - events: if given, {'click':foo, 'mousemove':bar}; each time the user clicks,
         the function foo is called with a 2-tuple (x,y) where they clicked.  Similarly
         for mousemove.  This works for Sage 2d graphics and matplotlib figures.
    
    ANIMATIONS:
    
       - animations are by default encoded and displayed using an efficiently web-friendly
         format (currently webm, which is **not supported** by Safari or IE).
    
            - ``delay`` - integer (default: 20); delay in hundredths of a
              second between frames.
    
            - gif=False -- if you set gif=True, instead use an animated gif,
              which is much less efficient, but works on all browsers.
    
         You can also use options directly to the animate command, e.g., the figsize option below:
    
              a = animate([plot(sin(x + a), (x, 0, 2*pi)) for a in [0, pi/4, .., 2*pi]], figsize=6)
              show(a, delay=30)
    
    
    EXAMPLES:
    
    Some examples:
    
        show(2/3)
        show([1, 4/5, pi^2 + e], 1+pi)
        show(x^2, display=False)
        show(e, plot(sin))
    
    Here's an example that illustrates creating a clickable image with events::
    
        @interact
        def f0(fun=x*sin(x^2), mousemove='', click='(0,0)'):
            click = sage_eval(click)
            g = plot(fun, (x,0,5), zorder=0) + point(click, color='red', pointsize=100, zorder=10)
            ymax = g.ymax(); ymin = g.ymin()
            m = fun.derivative(x)(x=click[0])
            b =  fun(x=click[0]) - m*click[0]
            g += plot(m*x + b, (click[0]-1,click[0]+1), color='red', zorder=10)
            def h(p):
                f0.mousemove = p
            def c(p):
                f0(click=p)
            show(g, events={'click':c, 'mousemove':h}, svg=True, gridlines='major', ymin=ymin, ymax=ymax)

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