Difference between revisions of "Rational functions"

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</script>
 
</script>
 
</html>
 
</html>
 +
 +
=== References ===
 +
* [http://en.wikipedia.org/wiki/Rational_function http://en.wikipedia.org/wiki/Rational_function]
 +
 +
=== The underlying JavaScript source code ===
 +
 +
<source lang="javascript">
 +
        board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
 +
        // Axes
 +
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
 +
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
 +
 +
        var p = [];
 +
        var q = [];
 +
        p[0] = board.createElement('point', [-1,2], {style:6});
 +
        p[1] = board.createElement('point', [3,-1], {style:6});
 +
        var polynomial = function(x) {
 +
                var i;
 +
                var y = 0.0;
 +
                var xc = [];
 +
                for (i=0;i<p.length;i++) {
 +
                  xc[i] = p[i].X();
 +
                }
 +
                for (i=0;i<p.length;i++) {
 +
                  var t = p[i].Y();
 +
                  for (var k=0;k<p.length;k++) {
 +
                    if (k!=i) {
 +
                      t *= (x-xc[k])/(xc[i]-xc[k]);
 +
                    }
 +
                  }
 +
                  y += t;
 +
                }
 +
                return y;
 +
            };
 +
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});
 +
 +
        function addPoint1() {
 +
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
 +
          board.update();
 +
        }
 +
 +
        board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25});
 +
        // Axes
 +
        b1axisx2 = board2.createElement('axis', [[0,0], [1,0]], {});
 +
        b1axisy2 = board2.createElement('axis', [[0,0], [0,1]], {});
 +
 +
        q[0] = board2.createElement('point', [-1,2], {style:6});
 +
        q[1] = board2.createElement('point', [3,-1], {style:6});
 +
        var polynomial2 = function(x) {
 +
                var i;
 +
                var y = 0.0;
 +
                var xc = [];
 +
                for (i=0;i<q.length;i++) {
 +
                  xc[i] = q[i].X();
 +
                }
 +
                for (i=0;i<q.length;i++) {
 +
                  var t = q[i].Y();
 +
                  for (var k=0;k<q.length;k++) {
 +
                    if (k!=i) {
 +
                      t *= (x-xc[k])/(xc[i]-xc[k]);
 +
                    }
 +
                  }
 +
                  y += t;
 +
                }
 +
                return y;
 +
            };
 +
        graph2 = board2.createElement('curve', ['x', polynomial2, 'x', -10, 10], {curveType:'graph'});
 +
 +
        function addPoint2() {
 +
          q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
 +
          board2.update();
 +
        }
 +
 +
        board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25});
 +
        // Axes
 +
        b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
 +
        b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
 +
        graph3 = board3.createElement('curve', ['x', function(x){return polynomial(x)/polynomial2(x);}, 'x', -10, 10], {curveType:'graph',strokeColor:'#ff0000'});
 +
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]

Revision as of 12:31, 16 December 2008

Polynomial f:

Polynomial g:

Rational function

f/g

:

References

The underlying JavaScript source code

        board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25});
        // Axes
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});

        var p = [];
        var q = [];
        p[0] = board.createElement('point', [-1,2], {style:6});
        p[1] = board.createElement('point', [3,-1], {style:6});
        var polynomial = function(x) {
                var i;
                var y = 0.0;
                var xc = [];
                for (i=0;i<p.length;i++) {
                  xc[i] = p[i].X();
                }
                for (i=0;i<p.length;i++) {
                  var t = p[i].Y();
                  for (var k=0;k<p.length;k++) {
                    if (k!=i) {
                      t *= (x-xc[k])/(xc[i]-xc[k]);
                    }
                  }
                  y += t;
                }
                return y;
            };
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});

        function addPoint1() {
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board.update();
        }

        board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25});
        // Axes
        b1axisx2 = board2.createElement('axis', [[0,0], [1,0]], {});
        b1axisy2 = board2.createElement('axis', [[0,0], [0,1]], {});

        q[0] = board2.createElement('point', [-1,2], {style:6});
        q[1] = board2.createElement('point', [3,-1], {style:6});
        var polynomial2 = function(x) {
                var i;
                var y = 0.0;
                var xc = [];
                for (i=0;i<q.length;i++) {
                  xc[i] = q[i].X();
                }
                for (i=0;i<q.length;i++) {
                  var t = q[i].Y();
                  for (var k=0;k<q.length;k++) {
                    if (k!=i) {
                      t *= (x-xc[k])/(xc[i]-xc[k]);
                    }
                  }
                  y += t;
                }
                return y;
            };
        graph2 = board2.createElement('curve', ['x', polynomial2, 'x', -10, 10], {curveType:'graph'});

        function addPoint2() {
          q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board2.update();
        }

        board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25});
        // Axes
        b1axisx3 = board3.createElement('axis', [[0,0], [1,0]], {});
        b1axisy3 = board3.createElement('axis', [[0,0], [0,1]], {});
        graph3 = board3.createElement('curve', ['x', function(x){return polynomial(x)/polynomial2(x);}, 'x', -10, 10], {curveType:'graph',strokeColor:'#ff0000'});