Options

Options affect the behaviour of each question.

Question Level Simplify

See the entry on simplification. Default is true.

Assume Positive

This option sets the value of Maxima's

assume_pos

variable.

If true and the sign of a parameter $x$ cannot be determined from the current context or other considerations, sign and asksign(x) return true. This may forestall some automatically-generated asksign queries, such as may arise from integrate or other computations

Default is False

Question Penalty

This is the percentage of the marks deducted from each different and valid attempt which is not completely correct, when the penalty mark modification scheme is in use. The default is $10\%$ of the marks available for this question, entered at $0.1$.

Note that Moodle stores scores to 7 decimal places, so, $1/3$ should be entered as $0.3333333$, and $2/3$ as $0.6666667$. If you input any number close to $1/3$, but with less precision, then the extra digits will automatically be added. The exact range affected is that any penalty $\ge 0.33$ and $\le 0.34$ is changed to $0.3333333$, and any penalty $\ge 0.66$ and $\le 0.67$ is changed to $0.6666667$.

Output

The following options affect how mathematics is displayed.

Decimal separator

Choose the symbol for the decimal separator used by student input. There are currently two choices.

• ., the British decimal point.
• ,, the comma, as used in much of Europe.

The design of this option is discussed further in the developer docs.

Teachers must always use strict Maxima syntax, which requires ., including in test case construction.

Scientific notation formal

Choose the format for display of scientific notation.

• '*10', numbers will be displayed as $3.14 \times 10^{3}$.
• 'E', numbers will be displayed as $3.14 E^{3}$.

Multiplication Sign

• (none), e.g. $x(x+1)$
• Dot, e.g. $x\cdot(x+1)$
• Cross, e.g. $x\times (x+1)$
• Numbers only, e.g. $3\times 5\, x$.

In practice it is very helpful to have some kind of multiplication sign displayed to the student. The difference between $$xe^x \text{ and } x\,e^x$$ is very subtle. Notice the spacing? The first means xe^x=(xe)^x the second is x*e^x. Could be quite confusing to students if there is no multiplication sign. Using $x\cdot e^x$ neatly solves this problem.

Internally the display of multiplication signs is controlled by the STACK function make_multsgn(ex), where the argument can be one of the strings "cross", "dot" or "blank". This can be switched part-way through a session. E.g. consider the following castext.

Default: {@a*b@}.
Switch to cross: {@(make_multsgn("cross"), a*b)@}.
Cross remains: {@a*b@}.

The expression (make_multsgn("cross"), a*b) uses parentheses as an abbreviation for Maxima's block command. So, the first expression make_multsgn("cross") is evaluated which changes the display option to a cross. Then the second expression is evaluated and displayed as $a\times b$. The new option persists in the next expression.

The value of this option onum will only put a multiplication sign between numbers. This means you will see $3\times 5\, x$ and not $3\, 5\, x$ as you would if you have "none".

There is a special atom which controls the multiplication symbol used with option onum. If you would like a dot then define

texput(multsgnonlyfornumberssym, "\\cdot");

in the question variables.

Logic symbols

How logical symbols should be displayed. The values are language, e.g. $A \text{ and } B$ or symbol, e.g. $A\land B$.

Surd for Square Root

This option sets the value of Maxima's

sqrtdispflag

When false the prefix function sqrt(x) will be displayed as $x^{1/2}$. This setting is global to the question, and having both notations co-exist in one question is very tricky. You need to have simp:false throughout the question.

By default Maxima does not like to use the $\sqrt{}$ symbol. The internal representation favours fractional powers, for very good reasons. In Maxima we get:

(%i1) 4*sqrt(2);
(%o1) 2^(5/2)
(%i2) 6*sqrt(2);
(%o2) 3*2^(3/2)

Furthermore, if you execute this in a Maxima session

simp:true;
p:1+sqrt(x);
?print(p);

Then the displayed value of p is $\sqrt{x}+1$ whereas the internal representation of p is

((MPLUS SIMP) 1 ((MEXPT SIMP) $X ((RAT SIMP) 1 2)))

This means that internally Maxima has converted sqrt(x) to x^(1/2), even though it is by default displayed as sqrt. This is an example where the displayed form (text and LaTeX) does not match Maxima's internal representation.

Do you really want to continue using $\sqrt{}$ in your teaching? In his Elements of Algebra, L. Euler wrote the following.

$\S 200$ We may therefore entirely reject the radical signs at present made use of, and employ in their stead the fractional exponents which we have just explained: but as we have been long accustomed to those signs, and meet with them in most books of Algebra, it might be wrong to banish them entirely from calculations; there is, however, sufficient reason also to employ, as is now frequently done, the other method of notation, because it manifestly corresponds with the nature of the thing. In fact we see immediately that $a^\frac12$ is the square root of $a$, because we know that the square of $a^\frac12$, that is to say $a^\frac12$ multiplied by $a^\frac12$ is equal to $a^1$, or $a$.

A lot of elementary mathematics involves converting from one form to another and back again. Sometimes these forms have important differences of use, e.g. factored form or completed square form for a quadratic. However, sometimes these equivalent forms are more customary than because it "manifestly corresponds with the nature of the thing" in question. I digress...

STACK defines an $n$th root function root(x,n) which is a noun form for $\sqrt[n]{x}$. This can be used by students, but if teachers wish to use this in question variables etc. then they must prefix this with the apostophie to create the nounform 'root(x,n) to prevent immediate evaluation to x^(1/n).

sqrt(-1)

In Maxima %i is the complex unit satisfying %i^2=-1. However, students would like to type i and physicists and engineers j. We also sometimes need to use symbols i and j for vectors. To accommodate these needs we have an option ComplexNo which provides a context for these symbols and affects the way they are displayed.

Option	Interpretation	Display	~	~	~	~
	%i^2	i^2	j^2	%i	i	j
--------	----------------	---------	-----	----	-----	-----
i	-1	-1	j^2	i	i	j
j	-1	i^2	-1	j	i	j
symi	-1	i^2	j^2	i	i	j
symj	-1	i^2	j^2	j	i	j

Note the use of both Roman and italic symbols in this table.

If you are using $i,j,k$ as basis vectors then consider the following in your question variables

/* Below means set the ComplexNo option in the question to "symi". */
make_complexJ("symi");
ordergreat(i,j,k);
texput(i,"\\vec{i}");
texput(j,"\\vec{j}");
texput(k,"\\vec{k}");
%_stack_preamble_end;
/* These are examples. */
p:3*i+4*j+5*k;
q:a*i+b*j+c*k;

Then, your expressions p and q will be displayed repectively as $${3\cdot \vec{i}+4\cdot \vec{j}+5\cdot \vec{k}}$$ and $${a\cdot \vec{i}+b\cdot \vec{j}+c\cdot \vec{k}}.$$ Further examples are given in the vectors.documentation.

Matrix parentheses

See the entry on matrices.

Inline and displayed fractions.

The display of fractions can take two forms: inline $1/x$ and displayed $\frac{1}{x}$.

The default behaviour is displayed, i.e. using LaTeX \frac{}{}.

The function stack_disp_fractions(ex) can be used to control the display.

• stack_disp_fractions("i") switches display to inline.
• stack_disp_fractions("d") switches display to display.

Note, for CASText the display is controlled by the prevailing setting at the moment the text is displayed, not when a variable is defined in the question variables. Hence, if you would like a single inline fraction within a CASText you will need to use

Normally fractions are displayed {@1/x@}. This switches to inline {@(stack_disp_fractions("i"), 1/x)@}, which persists {@1/a@}.  Switch explicitly back to displayed {@(stack_disp_fractions("d"),1/x)@}.