Subscripts

Atoms, subscripts and fine tuning the LaTeX display

Everything in Maxima is either an atom or an expression. Atoms are either an integer number, float, string or a name. You can use the predicate atom() to decide if its argument is an atom. Expressions have an operator and a list of arguments. Note that the underscore symbol is not an operator. Thus a_1 is an atom in maxima. Hence, the atoms a1 and a_1 are not considered to be algebraically equivalent. If you would like to consolidate subscripts in students' input see the documentation on the input option consolidatesubscripts in the extra options. Also note that since the underscore is not an operator, an expression such as (a_b)_c is not valid Maxima syntax, but a_b_c is a valid name for an atom.

You can change the TeX output for an atom with Maxima's texput command. E.g. texput(blob, "\\diamond") will display the atom blob as $\diamond$. If you place texput commands in the question variables, this affects the display everywhere in the question including the inputs. E.g. if a student types in blob then the validation feedback should say something like "your last answer was: $\diamond$".

Display with subscripts is a subtle and potentially confusing issue because subscript notation in mathematics has many different uses. For example,

1. Subscripts denote a function of the natural numbers, e.g. when defining terms in a sequence $a_1, a_2, a_3$. That is the subscript denotes function application. $a_n = a(n)$.
2. Subscripts denote differentiation, e.g. $x_t$ is the derivative of $x$ with respect to $t$.
3. Subscripts denote coordinates in a vector, in $\vec{v} = (v_1, v_2, \cdots, v_n)$.

There are many other possible uses for subscripts, especially in other subjects e.g. in physics or actuarial studies.

Because Maxima considers subscripted expressions to be atoms, the default TeX output of an atom V_alpha from Maxima is ${\it V\_alpha}$ (literally {\it V\_alpha}) and not $V_{\alpha}$ as a user might expect. For this reason STACK intercepts and redefines how atoms with the underscore are displayed. In particular STACK (but not core Maxima) takes an atom A_B, applies the tex() command to A and B separately and concatenates the result using subscripts. For example, if you define

texput(A, "{\\mathcal A}");
texput(B, "\\diamond");

then A_B is now displayed as ${{{\mathcal A}}_{\diamond}}$.

Below are some examples.

Maxima code	Maxima's tex() command (raw output and displayed)	STACK (raw output and displayed)
A_B	{\it A\_B} ${\it A\_B}$	{{A}_{B}} ${{A}_{B}}$
A[1]	A_{1} $A_{1}$	{A_{1}} ${A_{1}}$
A1	A_{1} $A_{1}$	{A_{1}} ${A_{1}}$
A_1	A_{1} $A_{1}$	{A_{1}} ${A_{1}}$
A_x1	{\it A\_x}_{1} ${\it A\_x}_{1}$	{{A}_{x_{1}}} ${{A}_{x_1}}$
A_BC	{\it A\_BC} ${\it A\_BC}$	{{A}_{{\it BC}}} ${{A}_{{\it BC}}}$
A_alpha	{\it A\_alpha} ${\it A\_alpha}$	{{A}_{\alpha}} ${{A}_{\alpha}}$
A_B_C	{\it A\_B\_C} ${\it A\_B\_C}$	{{{A}_{B}}_{C}} ${A_B}_C$
x_t(1)	{\it x\_t}\left(1\right) ${\it x\_t}\left(1\right)$	{{\it x\_t}\left(1\right)} ${{\it x\_t}\left(1\right)}$
A[1,2]	A_{1,2} $A_{1,2}$	{A_{1,2}} ${A_{1,2}}$

Notes

1. The maxima atoms A1 and A_1 are different, and are not algebraically equivalent. If student input is using both forms, and this causes problems, look at the documentation on consolidatesubscripts in the extra options.
2. in the above examples three different expressions (atoms A1, A_1 and the expression A[1]) generate the same tex code A_{1} $A_{1}$, and so are indistinguishable at the display level.
3. The expression x_t(1) refers to the function x_t which is not an atom, and hence STACK's logic for displaying atoms with underscores does not apply (by design). If you want to display a function name including a subscript you can explicitly use, e.g. texput(x_t, "x_t"); to control the display, this is just not done automatically.
4. When we split up atoms for display we have two separate atoms. E.g. x_h will be split into atoms x and h temporarily and the TeX display of x and h evaluated. For this reason, student's input will validate the parts of the subscript sparately. In particular, if h is a question variable and a student types in the atom x_h then since h is forbidden input the student's x_h will be invalid as well. This might cause problems, but these can be avoided when the teacher uses appropriate variable names.

One situation where this design is not satisfactory is when you want to use both of the atoms F and F_1 but with different display. For example F should display as ${\mathcal F}$ but F_1 should display as $F_1$. Such a situation is not hard to imagine, as it is often considered good style to have things like $F_1 \in {\mathcal F}$. The above design always splits up the atom F_1 into F and 1, so that the atom F_1 will display as ${\mathcal F}_1$. (This is actually what you normally expect, especially with the Greek letter subscripts.) To avoid this problem the logic which splits up atoms containing an underscore checks the texput properties list. If an entry has been made for a specific atom then STACK's display logic uses the entry, and does not split an atom over the underscore. In the above example, use the following texput commands.

texput(F, "{\\mathcal F}");
texput(F_1, "{F_1}");

With this code F displays as ${\mathcal F}$, the atom F_1 displays as $F_1$, and every subscript will display with calligraphic, e.g. F_alpha displays as ${\mathcal F}_{\alpha}$. There is no way to code the reverse logic, i.e. define a special display only for the unique atom F.

Note that the scientific units code redefines and then assumes that symbols represent units. E.g. F is assumed to represent Farad, and all units are typeset in Roman type, e.g. $\mathrm{F}$ rather than the normal $F$. This is typically the right thing to do, but it does restrict the number of letters which can be used for variable names in a particular question. To overcome this problem you will have to redefine some atoms with texput. For example,

stack_unit_si_declare(true);
texput(F_a, "F_a");

will display the atom F_a as $F_a$, i.e. not in Roman. If you texput(F, "F") the symbol F is no longer written in Roman, as you would expect from units. This may be sensible if Farad could not possibly appear in context, but students might type a range of subscripted atoms involving F.

The use of texput is global to a question. There is no way to display a particular atom differently in different places (except perhaps in the feedback variables, which is currently untested: assume texput is global).

How would you generate the tex like $A_{1,2}$? STACK's sequence command (see below) does output its arguments separated by a comma, so sequence(1,2) is displayed as ${1,2}$, however the Maxima command A_sequence(1,2) refers to the function A_sequence, (since the underscore is not an operator). Hence STACK's logic for splitting up atoms containing the underscore does not apply. (In any case, even if the display logic did split up function names we would still have the issue of binding power to sort out, i.e. do we have the atom with parts A and sequence(1,2) or the function named A and sequence?) To create an output like $A_{1,2}$ you have no option but to work at the level of display. Teachers can create an inert function which displays using subscripts.

texsub(a,b)

is typeset as ${a}_{b}$ i.e. {a}_{b} in LaTeX. For example,

• texsub(A, sequence(1,2)) will display as ${{A}_{1, 2}}$,
• with simplification off, texsub(F,1-2) will be displayed as ${F}_{1-2}$.

Note that the process of converting theta_07 into the intermediate texsub form internally results in the texsub(theta,7) which removes the leading zero. This is a known issue, for which a work around is to directly use texput(theta_07, "{{\\theta}_{07}}") or texsub(theta,"07"). The second option does not produce optimal LaTeX, since it uses TeX mbox, e.g. {{\theta}_{\text{07}}}.