[IMP] web: add math_utils to core

math_utils is a small library that exports two
functions:

    - cartesian: allows to compute the cartesian
                products of any numbers of arrays
                while preserving the internal
                structures of their elements.
    - sections: returns an array with all
                the initial sections of the
                array passed as parameter.

addons/web/static/src/js/core/math_utils.js

@@ -0,0 +1,73 @@
+odoo.define('web.mathUtils', function () {
+"use strict";
+
+/**
+ * Same values returned as those returned by cartesian function for case n = 0
+ * and n > 1. For n = 1, brackets are put around the unique parameter elements.
+ *
+ * @returns {Array}
+ */
+function _cartesian() {
+    var args = Array.prototype.slice.call(arguments);
+    if (args.length === 0) {
+        return [undefined];
+    }
+    var firstArray = args[0].map(function (elem) {
+        return [elem];
+    });
+    if (args.length === 1) {
+        return firstArray;
+    }
+    var productOfOtherArrays = _cartesian.apply(null, args.slice(1));
+    var result = firstArray.reduce(
+        function (acc, elem) {
+            return acc.concat(productOfOtherArrays.map(function (tuple) {
+                return elem.concat(tuple);
+            }));
+        },
+        []
+    );
+    return result;
+}
+
+/**
+ * Returns the product of any number n of arrays.
+ * The internal structures of their elements is preserved.
+ * For n = 1, no brackets are put around the unique parameter elements
+ * For n = 0, the singleton [undefined] is returned since it is the unit
+ * of the cartesian product (up to isomorphism).
+ *
+ * @returns {Array}
+ */
+function cartesian() {
+    var args = Array.prototype.slice.call(arguments);
+    if (args.length === 0) {
+        return [undefined];
+    } else if (args.length === 1) {
+        return args[0];
+    } else {
+        return _cartesian.apply(null, args);
+    }
+}
+
+/**
+ * Returns all initial sections of a given array, e.g. for [1, 2] the array
+ * [[], [1], [1, 2]] is returned.
+ *
+ * @param {Array} array
+ * @returns {Array[]}
+ */
+function sections(array) {
+    var sections = [];
+    for (var i = 0; i < array.length + 1; i++) {
+        sections.push(array.slice(0, i));
+    }
+    return sections;
+}
+
+return {
+    cartesian: cartesian,
+    sections: sections,
+};
+
+});

addons/web/static/tests/core/math_utils_tests.js

@@ -0,0 +1,56 @@
+odoo.define('web.math_utils_tests', function(require) {
+"use strict";
+
+var mathUtils = require('web.mathUtils');
+var cartesian = mathUtils.cartesian;
+
+QUnit.module('mathUtils', function () {
+
+    QUnit.module('cartesian');
+
+
+    QUnit.test('cartesian product of zero arrays', function(assert) {
+        assert.expect(1);
+        assert.deepEqual(cartesian(), [undefined],
+            "the unit of the product is a singleton");
+    });
+
+    QUnit.test('cartesian product of a single array', function(assert) {
+        assert.expect(5);
+        assert.deepEqual(cartesian([]), []);
+        assert.deepEqual(cartesian([1]), [1],
+            "we don't want unecessary brackets");
+        assert.deepEqual(cartesian([1, 2]), [1, 2]);
+        assert.deepEqual(cartesian([[1, 2]]), [[1, 2]],
+            "the internal structure of elements should be preserved");
+        assert.deepEqual(cartesian([[1, 2], [3, [2]]]), [[1, 2], [3, [2]]],
+            "the internal structure of elements should be preserved");
+    });
+
+    QUnit.test('cartesian product of two arrays', function(assert) {
+        assert.expect(5);
+        assert.deepEqual(cartesian([], []), []);
+        assert.deepEqual(cartesian([1], []), []);
+        assert.deepEqual(cartesian([1], [2]), [[1, 2]]);
+        assert.deepEqual(cartesian([1, 2], [3]), [[1, 3], [2, 3]]);
+        assert.deepEqual(cartesian([[1], 4], [2, [3]]), [[[1], 2], [[1], [3]], [4, 2], [4, [3]] ],
+            "the internal structure of elements should be preserved");
+    });
+
+    QUnit.test('cartesian product of three arrays', function(assert) {
+        assert.expect(4);
+        assert.deepEqual(cartesian([], [], []), []);
+        assert.deepEqual(cartesian([1], [], [2, 5]), []);
+        assert.deepEqual(cartesian([1], [2], [3]), [[1, 2, 3]],
+            "we should have no unecessary brackets, we want elements to be 'triples'");
+        assert.deepEqual(cartesian([[1], 2], [3], [4]), [[[1], 3, 4], [2, 3, 4]],
+            "the internal structure of elements should be preserved");
+    });
+
+    QUnit.test('cartesian product of four arrays', function(assert) {
+        assert.expect(1);
+        assert.deepEqual(cartesian([1], [2], [3], [4]), [[1, 2, 3, 4]]);
+    });
+
+});
+});

addons/web/views/webclient_templates.xml

@@ -250,6 +250,7 @@
         <script type="text/javascript" src="/web/static/src/js/_deprecated/data.js"></script>
         <script type="text/javascript" src="/web/static/src/js/core/context.js"></script>
         <script type="text/javascript" src="/web/static/src/js/core/data_comparison_utils.js"></script>
+        <script type="text/javascript" src="/web/static/src/js/core/math_utils.js"></script>
         <script type="text/javascript" src="/web/static/src/js/core/misc.js"></script>
         <script type="text/javascript" src="/web/static/src/js/services/crash_manager_service.js"></script>
         <script type="text/javascript" src="/web/static/src/js/services/data_manager.js"></script>
@@ -664,6 +665,7 @@
                 <script type="text/javascript" src="/web/static/tests/core/rpc_tests.js"></script>
                 <script type="text/javascript" src="/web/static/tests/core/domain_tests.js"></script>
                 <script type="text/javascript" src="/web/static/tests/core/data_comparison_utils_tests.js"></script>
+                <script type="text/javascript" src="/web/static/tests/core/math_utils_tests.js"></script>
                 <script type="text/javascript" src="/web/static/tests/core/mixins_tests.js"></script>
                 <script type="text/javascript" src="/web/static/tests/core/time_tests.js"></script>
                 <script type="text/javascript" src="/web/static/tests/core/concurrency_tests.js"></script>