Introduction
Please skip this paragraph if you are searching for the rules
for writing a formula answering a question.
QCmath is a language the purpose of which is to allow quizzes
with questions to be answered with simple mathematical
formulas such as (a' + b)*(a' - b) eller a'*a' - b^2.
Please notice that these two formulas are equivalent.
QCmath is useful on quiz servers which do not have
access to a more advanced mathematical program for analysis
of answers with a formula.
Quite a large number of questions within applied natural science
can be answered with an expression in QCmath.
The simplicity of the language has an advantage, namely that
errors in answers are less likely.
Rules
A syntactically correct expression in QCmath iss
either an algebraic expression according to rules stated below
or a function call with arguments, each being such
an algebraic expression.
Algebraic operators
The only semantic rules of the language are associated with the
algebraic operators addition '+'. subtraction '-',
multiplication '*', division '/'
together with raising to a unsigned single digit power '^' and grouping
via parentheses.
It is these semantic rules which render (a' + b)*(a' + b) and b^2 + a'*a'
equivalent.
Numbers
QCmath "understands" unsigned integers whereas numbers
with a decimal point are not permitted.
An unsigned integer is a sequence of digits.
No names known
QCmath knows no names and has,
accordingly, no semantic rules for functions.
A specification of an answer in the form of a function call
consists of the name of the function followed by a
parenthesis containing an algebraic expression,
e.g. sqrt( (x2 - x1)^2 + (y2 - y1)^2 ).
A corresponding correct answer has the same form with the same
function name and an equivalent algebraic expression.
The quiz author must ensure that the answerers know what names
of functions, variables and constants, to use in the answers,
and also that between all possible answers using these names
only one group of equivalent answers is correct. Operands in an algebraic expression are represented by names,
unsigned integers and algebraic expressions in parentheses.
For expressions beginning with minus '-' a preceeding 0 is understood.
Syntax for names
A name is either simple or extended.
A simple name consists of a letter followed by letters
and/or digits and apostrophes
(the latter for indicating a differentiation, for example).
An extended name has the format f(x,y,..) in which
f is a simple name and x,y,.. is a list of simple names
separated by commas, thus the same form as a function call. No space is permitted between f and (x,y,..)
and neither numbers nor expressions in the list.
Extended names are included in QCmath to allow questions to be answered
with such expressions as (cos(u)*cos(v) - sin(u)*sin(v)).
(But notice that the same question cannot be answered with cos(u+v)
since QCmath knows nothing about trigonometry).
Obviously, the quiz author must in the question state that the
answer must be written using cos(u), cos(v), sin(u) and sin(v).
Maybe, in many cases, banal errors in answers can be avoided by using
simple rather than extended names, e.g. cu in place of cos(u).
Omissions
Multiplication signs may be omitted between a number and a simple name,
between a number and a left parenthesis, between a right and a left
parenthesis and, finally, between a left parenthesis and a name,
as for example in 3x, 3(a+b),(a+b)(c-d) and (2+x)d.
In all other cases, set a multiplication sign.
