<textline> (While <textline /> is supported, its use is extremely discouraged. We urge usage of <formulaequationinput />. See the opening paragraphs of the Numerical Response section for more information.)
.. image:: ../Images/numericalresponse5.png
Math Expression Syntax
----------------------
In NumericalResponses, the student's input may be more complicated than a
simple number. Expressions like ``sqrt(3)`` and even ``1+e^(sin(pi/2)+2*i)``
are valid, and evaluate to 1.73 and -0.13 + 2.47i, respectively.
A summary of the syntax follows:
Numbers
~~~~~~~
Accepted number types:
- Integers: '2520'
- Normal floats: '3.14'
- With no integer part: '.98'
- Scientific notation: '1.2e-2' (=0.012)
- More s.n.: '-4.4e+5' = '-4.4e5' (=-440,000)
- Appending SI suffixes: '2.25k' (=2,250). The full list:
====== ========== ===============
Suffix Stands for One of these is
====== ========== ===============
% percent 0.01 = 1e-2
k kilo 1000 = 1e3
M mega 1e6
G giga 1e9
T tera 1e12
c centi 0.01 = 1e-2
m milli 0.001 = 1e-3
u micro 1e-6
n nano 1e-9
p pico 1e-12
====== ========== ===============
The largest possible number handled currently is exactly the largest float
possible (in the Python language). This number is 1.7977e+308. Any expression
containing larger values will not evaluate correctly, so it's best to avoid
this situation.
Default Constants
~~~~~~~~~~~~~~~~~
Simple and commonly used mathematical/scientific constants are included by
default. These include:
- ``i`` and ``j`` as ``sqrt(-1)``
- ``e`` as Euler's number (2.718...)
- ``pi``
- ``k``: the Boltzmann constant (~1.38e-23 in Joules/Kelvin)
- ``c``: the speed of light in m/s (2.998e8)
- ``T``: the positive difference between 0K and 0°C (285.15)
- ``q``: the fundamental charge (~1.602e-19 Coloumbs)
Operators and Functions
~~~~~~~~~~~~~~~~~~~~~~~
As expected, the normal operators apply (with normal order of operations):
``+ - * / ^``. Also provided is a special "parallel resistors" operator given
by ``||``. For example, an input of ``1 || 2`` would represent the resistance
of a pair of parallel resistors (of resistance 1 and 2 ohms), evaluating to 2/3
(ohms).
At the time of writing, factorials written in the form '3!' are invalid, but there is a workaround. Students can specify ``fact(3)`` or ``factorial(3)`` to
access the factorial function.
The default included functions are the following:
- Trig functions: sin, cos, tan, sec, csc, cot
- Their inverses: arcsin, arccos, arctan, arcsec, arccsc, arccot
- Other common functions: sqrt, log10, log2, ln, exp, abs
- Factorial: ``fact(3)`` or ``factorial(3)`` are valid. However, you must take
care to only input integers. For example, ``fact(1.5)`` would fail.
- Hyperbolic trig functions and their inverses: sinh, cosh, tanh, sech, csch, coth, arcsinh, arccosh, arctanh, arcsech, arccsch, arccoth
.. raw:: latex
\newpage %
...
...
@@ -513,6 +589,13 @@ mathematical expression from the student and evaluates the input for equivalence
to a mathematical expression provided by the grader. Correctness is based on
numerical sampling of the symbolic expressions.
The syntax of the answers is shared with that of the Numerical Response,
including default variables and functions. The difference between the two
response types is that the Formula Response grader may specify unknown
variables. The student's response is compared against the instructor's
response, with the unknown variable(s) sampled at random values, as specified
by the problem author.
The answer is correct if both the student-provided response and the grader's
mathematical expression are equivalent to specified numerical tolerance, over a
specified range of values for each variable.
...
...
@@ -522,6 +605,15 @@ an extra burden on the problem author to specify the allowed variables in the
expression and the numerical ranges over which the variables must be sampled in
order to test for correctness.
A further note about the variables: when the following Greek letters are typed
