// Define the id of your board in BOARDID
const board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-5, 5, 5, -5], axis:false});
// Primal basis vectors
var b1 = board.create('point', [4,0], {size:6, name:'b_1', color:'blue', snaptogrid: true}),
b2 = board.create('point', [3,3], {size:6, name:'b_2', color:'blue', snaptogrid: true}),
v1 = board.create('arrow', [[0,0], b1], {strokeColor: 'black', fixed: true}),
v2 = board.create('arrow', [[0,0], b2], {strokeColor: 'red', fixed: true}),
w1, w2;
// Plot lattice points
for (let i = -5; i < 6; i++) {
for (let j = -5; j < 6; j++) {
if (!(i == 1 && j == 0) && !(i == 0 && j == 1)) {
board.create('point', [
() => i * b1.X() + j * b2.X(),
() => i * b1.Y() + j * b2.Y()
], {name:'', withLabel: false, size:2});
}
}
}
// Dual basis vectors
w1 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [b2.Y() / num, -b2.X() / num];
}], {strokeColor: 'black', name:"b_1'", withLabel:true, label:{position:'rt'}});
w2 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [-b1.Y() / num, b1.X() / num];
}], {strokeColor: 'red', name:"b_2'", withLabel:true, label:{position:'rt'}});
This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note that you have to mention The Center of Mobile Learning with Digital Technology in the credits.
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'your_div_id'; // Insert your id here!
const board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-5, 5, 5, -5], axis:false});
// Primal basis vectors
var b1 = board.create('point', [4,0], {size:6, name:'b_1', color:'blue', snaptogrid: true}),
b2 = board.create('point', [3,3], {size:6, name:'b_2', color:'blue', snaptogrid: true}),
v1 = board.create('arrow', [[0,0], b1], {strokeColor: 'black', fixed: true}),
v2 = board.create('arrow', [[0,0], b2], {strokeColor: 'red', fixed: true}),
w1, w2;
// Plot lattice points
for (let i = -5; i < 6; i++) {
for (let j = -5; j < 6; j++) {
if (!(i == 1 && j == 0) && !(i == 0 && j == 1)) {
board.create('point', [
() => i * b1.X() + j * b2.X(),
() => i * b1.Y() + j * b2.Y()
], {name:'', withLabel: false, size:2});
}
}
}
// Dual basis vectors
w1 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [b2.Y() / num, -b2.X() / num];
}], {strokeColor: 'black', name:"b_1'", withLabel:true, label:{position:'rt'}});
w2 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [-b1.Y() / num, b1.X() / num];
}], {strokeColor: 'red', name:"b_2'", withLabel:true, label:{position:'rt'}});
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
<div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>
<script type = "text/javascript">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'board-0';
const board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-5, 5, 5, -5], axis:false});
// Primal basis vectors
var b1 = board.create('point', [4,0], {size:6, name:'b_1', color:'blue', snaptogrid: true}),
b2 = board.create('point', [3,3], {size:6, name:'b_2', color:'blue', snaptogrid: true}),
v1 = board.create('arrow', [[0,0], b1], {strokeColor: 'black', fixed: true}),
v2 = board.create('arrow', [[0,0], b2], {strokeColor: 'red', fixed: true}),
w1, w2;
// Plot lattice points
for (let i = -5; i < 6; i++) {
for (let j = -5; j < 6; j++) {
if (!(i == 1 && j == 0) && !(i == 0 && j == 1)) {
board.create('point', [
() => i * b1.X() + j * b2.X(),
() => i * b1.Y() + j * b2.Y()
], {name:'', withLabel: false, size:2});
}
}
}
// Dual basis vectors
w1 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [b2.Y() / num, -b2.X() / num];
}], {strokeColor: 'black', name:"b_1'", withLabel:true, label:{position:'rt'}});
w2 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [-b1.Y() / num, b1.X() / num];
}], {strokeColor: 'red', name:"b_2'", withLabel:true, label:{position:'rt'}});
</script>
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Dual lattice" description="This construction was copied from JSXGraph examples database: https://jsxgraph.org/share/" useGlobalJS="false">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-5, 5, 5, -5], axis:false});
// Primal basis vectors
var b1 = board.create('point', [4,0], {size:6, name:'b_1', color:'blue', snaptogrid: true}),
b2 = board.create('point', [3,3], {size:6, name:'b_2', color:'blue', snaptogrid: true}),
v1 = board.create('arrow', [[0,0], b1], {strokeColor: 'black', fixed: true}),
v2 = board.create('arrow', [[0,0], b2], {strokeColor: 'red', fixed: true}),
w1, w2;
// Plot lattice points
for (let i = -5; i < 6; i++) {
for (let j = -5; j < 6; j++) {
if (!(i == 1 && j == 0) && !(i == 0 && j == 1)) {
board.create('point', [
() => i * b1.X() + j * b2.X(),
() => i * b1.Y() + j * b2.Y()
], {name:'', withLabel: false, size:2});
}
}
}
// Dual basis vectors
w1 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [b2.Y() / num, -b2.X() / num];
}], {strokeColor: 'black', name:"b_1'", withLabel:true, label:{position:'rt'}});
w2 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [-b1.Y() / num, b1.X() / num];
}], {strokeColor: 'red', name:"b_2'", withLabel:true, label:{position:'rt'}});
</jsxgraph>
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'your_div_id'; // Insert your id here!
const board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-5, 5, 5, -5], axis:false});
// Primal basis vectors
var b1 = board.create('point', [4,0], {size:6, name:'b_1', color:'blue', snaptogrid: true}),
b2 = board.create('point', [3,3], {size:6, name:'b_2', color:'blue', snaptogrid: true}),
v1 = board.create('arrow', [[0,0], b1], {strokeColor: 'black', fixed: true}),
v2 = board.create('arrow', [[0,0], b2], {strokeColor: 'red', fixed: true}),
w1, w2;
// Plot lattice points
for (let i = -5; i < 6; i++) {
for (let j = -5; j < 6; j++) {
if (!(i == 1 && j == 0) && !(i == 0 && j == 1)) {
board.create('point', [
() => i * b1.X() + j * b2.X(),
() => i * b1.Y() + j * b2.Y()
], {name:'', withLabel: false, size:2});
}
}
}
// Dual basis vectors
w1 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [b2.Y() / num, -b2.X() / num];
}], {strokeColor: 'black', name:"b_1'", withLabel:true, label:{position:'rt'}});
w2 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [-b1.Y() / num, b1.X() / num];
}], {strokeColor: 'red', name:"b_2'", withLabel:true, label:{position:'rt'}});
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
<div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>
<script type = "text/javascript">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'board-0';
const board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-5, 5, 5, -5], axis:false});
// Primal basis vectors
var b1 = board.create('point', [4,0], {size:6, name:'b_1', color:'blue', snaptogrid: true}),
b2 = board.create('point', [3,3], {size:6, name:'b_2', color:'blue', snaptogrid: true}),
v1 = board.create('arrow', [[0,0], b1], {strokeColor: 'black', fixed: true}),
v2 = board.create('arrow', [[0,0], b2], {strokeColor: 'red', fixed: true}),
w1, w2;
// Plot lattice points
for (let i = -5; i < 6; i++) {
for (let j = -5; j < 6; j++) {
if (!(i == 1 && j == 0) && !(i == 0 && j == 1)) {
board.create('point', [
() => i * b1.X() + j * b2.X(),
() => i * b1.Y() + j * b2.Y()
], {name:'', withLabel: false, size:2});
}
}
}
// Dual basis vectors
w1 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [b2.Y() / num, -b2.X() / num];
}], {strokeColor: 'black', name:"b_1'", withLabel:true, label:{position:'rt'}});
w2 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [-b1.Y() / num, b1.X() / num];
}], {strokeColor: 'red', name:"b_2'", withLabel:true, label:{position:'rt'}});
</script>
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Dual lattice" description="This construction was copied from JSXGraph examples database: https://jsxgraph.org/share/" useGlobalJS="false">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-5, 5, 5, -5], axis:false});
// Primal basis vectors
var b1 = board.create('point', [4,0], {size:6, name:'b_1', color:'blue', snaptogrid: true}),
b2 = board.create('point', [3,3], {size:6, name:'b_2', color:'blue', snaptogrid: true}),
v1 = board.create('arrow', [[0,0], b1], {strokeColor: 'black', fixed: true}),
v2 = board.create('arrow', [[0,0], b2], {strokeColor: 'red', fixed: true}),
w1, w2;
// Plot lattice points
for (let i = -5; i < 6; i++) {
for (let j = -5; j < 6; j++) {
if (!(i == 1 && j == 0) && !(i == 0 && j == 1)) {
board.create('point', [
() => i * b1.X() + j * b2.X(),
() => i * b1.Y() + j * b2.Y()
], {name:'', withLabel: false, size:2});
}
}
}
// Dual basis vectors
w1 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [b2.Y() / num, -b2.X() / num];
}], {strokeColor: 'black', name:"b_1'", withLabel:true, label:{position:'rt'}});
w2 = board.create('arrow', [[0,0], function() {
var num = b1.X() * b2.Y() - b2.X() * b1.Y();
return [-b1.Y() / num, b1.X() / num];
}], {strokeColor: 'red', name:"b_2'", withLabel:true, label:{position:'rt'}});
</jsxgraph>