Graphics in Axiom

The graphics commands are described in Chapter 7 of the AxiomBook. The syntax is:

    draw(f(x), x=a..b, options)
    draw(f(x,y), x=a..b, y=c..d, options)

axiom
vp1:=draw(sin(x), x=%pi/10..%pi)

Compiling function %B with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   FriCAS2D data being transmitted to the viewport manager...

(1)

This command creates a "view port" and would normally (on linux for example) also display the graph.

The draw command works only under an X-Windows environment (unix/linux). Work is underway to create a new user interface (AxiomUI) that among other things will allow graphics to be viewed under other operating systems. If you're interested in graphics, please pitch in!

Although due to technical limitations of this system (no Xwindows environment on the Web server) we are not yet able to display the graph here. However we description below a similar command named gnuDraw that can be used to generate similar graphics on this web site.

gnuDraw

It is possible to produce graphics similar to Axioms using gnuplot on this web site. To do this you need to include the GnuDraw (GDRAW) library

axiom
)lib GDRAW

GnuDraw is now explicitly exposed in frame initial GnuDraw will be automatically loaded when needed from /var/zope2/var/LatexWiki/GDRAW.NRLIB/code

The following examples are taken from Chapter 7 Graphics of the AxiomBook.

Section: 7.1 Two-Dimensional Graphics

The general format for drawing a function defined by a formula f(x) is:

  gnudraw(f(x), x = a..b, "filename.dat", options)

where a..b defines the range of x, options are additional draw options and "filename.dat" will contain the gnuplot script necessary to create the graph.

axiom
gnuDraw(sin(x), x=%pi/10..%pi,"AxiomGraphics1.dat")

Compiling function %F with type DoubleFloat -> DoubleFloat 
   Graph data being transmitted to the viewport manager...
   FriCAS2D data being transmitted to the viewport manager...

This file may be displayed on the web page using:

  !/begin{gnuplot}
  load "filename.dat"
  /end{gnuplot}

Technical Details

We can extract the graph data from the view port. For example we can display the list of data points that would be plotted in the graph.

(Note: we disable LaTeX output typesetting in order to save space.)

axiom
)set output tex off

axiom
)set output algebra on

g1:=getGraph(vp1,1)
   (3)  Graph with 1 point list

axiom
pointLists(g1)

   (4)
   [
     [[0.31415926535897931,0.3090169943749474,1.0,3.0],
      [0.37306412761378793,0.36447049987914965,1.0,3.0],
      [0.43196898986859655,0.41865973753742808,1.0,3.0],
      [0.49087385212340517,0.47139673682599764,1.0,3.0],
      [0.5497787143782138,0.5224985647159488,1.0,3.0],
      [0.60868357663302242,0.57178796022761225,1.0,3.0],
      [0.66758843888783104,0.61909394930983397,1.0,3.0],
      [0.72649330114263966,0.66425243791128175,1.0,3.0],
      [0.78539816339744828,0.70710678118654746,1.0,3.0],
      [0.8443030256522569,0.74750832686259672,1.0,3.0],
      [0.90320788790706552,0.78531693088074495,1.0,3.0],
      [0.96211275016187414,0.82040144352551359,1.0,3.0],
      [1.0210176124166828,0.85264016435409218,1.0,3.0],
      [1.0799224746714913,0.88192126434835494,1.0,3.0],
      [1.1388273369262998,0.90814317382508114,1.0,3.0],
      [1.1977321991811083,0.93121493475880346,1.0,3.0],
      [1.2566370614359168,0.95105651629515342,1.0,3.0],
      [1.3155419236907253,0.96759909236025965,1.0,3.0],
      [1.3744467859455338,0.98078528040323032,1.0,3.0],
      [1.4333516482003423,0.99056934044357714,1.0,3.0],
      [1.4922565104551508,0.99691733373312785,1.0,3.0],
      [1.5511613727099594,0.99980724048206482,1.0,3.0],
      [1.6100662349647679,0.99922903624072301,1.0,3.0],
      [1.6689710972195764,0.99518472667219704,1.0,3.0],
      [1.7278759594743849,0.98768834059513799,1.0,3.0],
      [1.7867808217291934,0.97676588132087272,1.0,3.0],
      [1.8456856839840019,0.96245523645364772,1.0,3.0],
      [1.9045905462388104,0.9448060464668786,1.0,3.0],
      [1.9634954084936189,0.92387953251128752,1.0,3.0],
      [2.0224002707484274,0.89974828405222229,1.0,3.0],
      [2.0813051330032359,0.87249600707279817,1.0,3.0],
      [2.1402099952580445,0.84221723371628776,1.0,3.0],
      [2.199114857512853,0.80901699437494878,1.0,3.0],
      [2.2580197197676615,0.77301045336273855,1.0,3.0],
      [2.31692458202247,0.73432250943568722,1.0,3.0],
      [2.3758294442772785,0.69308736254563774,1.0,3.0],
      [2.434734306532087,0.64944804833018577,1.0,3.0],
      [2.4936391687868955,0.60355594195357376,1.0,3.0],
      [2.552544031041704,0.55557023301960473,1.0,3.0],
      [2.6114488932965125,0.50565737337798722,1.0,3.0],
      [2.670353755551321,0.45399049973954964,1.0,3.0],
      [2.7292586178061295,0.40074883310314402,1.0,3.0],
      [2.7881634800609381,0.34611705707749618,1.0,3.0],
      [2.8470683423157466,0.29028467725446577,1.0,3.0],
      [2.9059732045705551,0.23344536385590897,1.0,3.0],
      [2.9648780668253636,0.17579627993435823,1.0,3.0],
      [3.0237829290801721,0.11753739745784152,1.0,3.0],
      [3.0826877913349806,0.058870803651193036,1.0,3.0],
      [3.1415926535897931,1.2246467991473532E-16,1.0,3.0]]
     ]

axiom
)set output algebra off

axiom
)set output tex on

Using lower level functions the points in such a graph can also be constructed as follows:

First we need this domain

axiom
)expose GraphImage
   GraphImage is now explicitly exposed in frame initial

axiom
lineSegments := [[point [sin(x*%pi/10)$DoubleFloat, _
                  x*%pi/10], point [sin((x+1)*%pi/10)$DoubleFloat, _
                 (x+1)*%pi/10]] for x in 1..10]

(2)

axiom
lineColors := [light blue() for i in 1..10]

(3)

axiom
pointColors  := [dark blue() for i in 1..10]

(4)

axiom
lineSize := [6 for i in 1..10]

(5)

axiom
g2:=makeGraphImage(lineSegments, lineColors, pointColors, lineSize)

Graph data being transmitted to the viewport manager...

(6)

axiom
)set output tex off

axiom
)set output algebra on

pointLists(g2)
   (10)
   [
     [[0.3090169943749474,0.31415926535897931,22.0,5.0],
      [0.58778525229247314,0.62831853071795862,22.0,5.0]]
     ,
     [[0.58778525229247314,0.62831853071795862,22.0,5.0],
      [0.80901699437494745,0.94247779607693793,22.0,5.0]]
     ,
     [[0.80901699437494745,0.94247779607693793,22.0,5.0],
      [0.95105651629515353,1.2566370614359172,22.0,5.0]]
     ,
     [[0.95105651629515353,1.2566370614359172,22.0,5.0],
      [1.0,1.5707963267948966,22.0,5.0]]
     ,
     [[1.0,1.5707963267948966,22.0,5.0],
      [0.95105651629515364,1.8849555921538759,22.0,5.0]]
     ,
     [[0.95105651629515364,1.8849555921538759,22.0,5.0],
      [0.80901699437494745,2.1991148575128552,22.0,5.0]]
     ,
     [[0.80901699437494745,2.1991148575128552,22.0,5.0],
      [0.58778525229247325,2.5132741228718345,22.0,5.0]]
     ,
     [[0.58778525229247325,2.5132741228718345,22.0,5.0],
      [0.30901699437494751,2.8274333882308138,22.0,5.0]]
     ,
     [[0.30901699437494751,2.8274333882308138,22.0,5.0],
      [1.2246467991473532E-16,3.1415926535897931,22.0,5.0]]
     ,
     [[1.2246467991473532E-16,3.1415926535897931,22.0,5.0],
      [- 0.3090169943749469,3.455751918948772,22.0,5.0]]
     ]

axiom
)set output algebra off

axiom
)set output tex on