.. role:: xml(code)
   :language: xml

default
=============

.. code-block:: xml

  <question type="default">
   ...
  </question>

Can be used when the answer is a symbolic or numeric expression in a
set of variables, possibly vector or matrix-valued. Student answers
are graded by comparing them with the correct expression, optionally
by random sampling. 

Vectors and matrices are defined using square brackets and can be
unitful. For example a 3-vector can be written as ``[1,2,3]``. A
matrix is similarly entered as ``[[1,0], [0,1]]``, where the inner
vectors corresponds to the rows of the matrix. There are a number of
vector operators available (see the help button for a default
question for the full list) such as ``cross(v1,v2)``, ``dot(v1,v2)``
and ``norm(v)``.

Scalar variables can be defined as random sampled using the function
``sample(value1, value2, ...)``. The answer will be compared using
random sampling in a neighbourhood around each value.


For example to correctly grade an answer containing the absolute value
function,

.. code-block:: xml

  <question type="default">
    <variables>
      x = sample(1, -1)
    </variables>
    <text>
     What is $\sqrt(x^2)$?
    </text>
    <expression>abs(x)</expression>
  </question>

The following tags can be used inside a **default** block.

.. only:: latex

   .. tabularcolumns:: |p{0.15\linewidth}|p{0.40\linewidth}|p{0.35\linewidth}|

.. rst-class:: tight-table

.. list-table::
  :header-rows: 1
  :widths: 20 10 70

  * - Tag
    - Attributes
    - Description
  * - ``<text>``
    -
    - Question text shown in viscinity of the input field.
  * - ``<expression>``
    -
    - Expression for the correct answer
  * - ``<variables>``
    -
    - Variables in semicolon separated list of var=value, e.g. ``x=1;y=2;``
  * - ``<blacklist>``
    -
    - List of subtags ``<token></token>`` containing tokens
      (variables, functions or operators) that are not allowed in the
      answer.

Examples
--------

Basic
^^^^^

.. code-block:: xml

  <question type="default">
    <text>What is 1+1?</text>
    <expression>2</expression>
  </question>

Variables
^^^^^^^^^

.. code-block:: xml

  <question type="default">
    <variables>
      omega=[1,0,0]; r=[0,1,0];
    </variables>
    <text>
      What is the velocity of a particle at a point $\vec{r}$ rotating around the origin with angular velocity $\vec{omega}$?
    </text>
    <expression>cross(omega, r)</expression>
  </question>

Global variables, multiple questions, latex, units
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. code-block:: xml

  <exercise>
    <exercisename>Momentum and energy</exercisename>
    <text>
      A particle with mass $m$ is moving with velocity $\vec{v}$.
    </text>

    <global type="default">
      x = sample(1)
      m = kg; v = [x, 0, 0] meter / second;
    </global>

    <question type="default">
      <text>
        What is the linear momentum of the particle?
      </text>
      <expression>m*v</expression>
    </question>

    <question type="default">
      <text>
        What is the kinetic energy of the particle?
      </text>
      <expression>m*dot(v, v)/2</expression>
    </question>
  </exercise>