DP Notes

Handling Equations

We obtain an inline math expression using the math directive as \(y = f(x)\). If we define math as the default role, then we do not need to precede each math directive with “:math:”. A math expression can be defined once at the top of the document (as for \(\hat{\mathbf{n}}_\mathbf{c}\)), and then placed within bars in a paragraph or table. Such a math expression cannot be used within an equation. The standard way to do this in TeX is to define the expression as a command, and then use this command in the equation; we have not worked out how to do this within the Sphinx system.

The following equation contains commonly used symbols to denote scalar and vector quantities:

(1)\[\begin{split}\begin{array}{c} \{ x, x_c, \mathbf{x}, \mathbf{x_c}, \dot{\mathbf{x}}_\mathbf{c}, \hat{\mathbf{n}}_\mathbf{c} \} \\ \{ \dot{\mathbf{x}}_\mathbf{c}^{(b)}, \pmb{ω}^{(b)} \} \\ \{ \delta, \theta, \delta_s, \theta_b, \pmb{ω}, \pmb{δ}, \pmb{θ}, \pmb{δ}_\mathbf{s}, \pmb{θ}_\mathbf{b} \} \end{array}\end{split}\]

The mathbf-command operates on letters, numbers and upper-case Greek letters. The pmb-command (Poor Man’s Bold) operates on lower-case Greek letters, and to make them non-italic we must insert their UTF-8 encoding. The hat- and dot-commands typically operate on a single character.

A typical left-aligned equation using a “with” expression is given here:

(2)\[\begin{split}\begin{array}{l} y = f(x),\quad z = g(F_n) \\[3mm] \mbox{with }\quad x = 27 \\ \hskip{12mm} F_n = 34 \end{array}\end{split}\]

A typical equation that contains “(2D model: expr)”:

(3)\[y = f(x) \quad \left( \mbox{2D model: } x = 2 \right).\]

(4)\[ \begin{align}\begin{aligned}y = f(x)\\\begin{split} \mathbf{M^r} = \left\{ \begin{array}{l} {\qquad \mathbf{M^r},\qquad \left\| \mathbf{M^{r}} \right\| \le M^{*} } \\ {\qquad M^{*} \left( \mathbf{M^r} / \left\| \mathbf{M^{r}} \right\| \right),\qquad {\rm otherwise.}} \end{array} \right.\end{split}\\\begin{split}s_r = \left\{ \begin{array}{l} {\qquad {\rm true},\qquad \left\| \mathbf{M^{r}} \right\| =M^{*} } \\ {\qquad {\rm false},\qquad {\rm otherwise.}} \end{array} \right.\end{split}\end{aligned}\end{align} \]

Case Statement

The following equation demonstrates how to create a case statement with TeX (using the cases construct) and with LaTeX (using the array construct). Note the use of hfill to get right-alignment of the first column with the cases construct. The column alignment for the array construct is specified by the arguments after the begin-array term. For the array construct, the dot following the right term gives us no right delimiter.

(5)\[\begin{split}|x| = \cases{ \hfill x, & if $x > 0$; \cr -x, & otherwise. \cr} = \left\{ \begin{array}{rl} x, & \mbox{if $x > 0$;} \\ -x, & \mbox{otherwise.} \end{array} \right.\end{split}\]

Handling Commands and Other Things

We can refer to an equation using the eq-directive as in Eq. (5) is given above. We can refer to an equation in another document with the ref-directive as in this equation. We can refer to a command with the cmd-directive as in: model calm does a neat thing. We can refer to a FISH function with the func-directive as in the FISH function measure.list does a cool thing. We can refer to the command without linking to the command description using the lcmd-directive as in model calm. We can refer to the FISH function or variable without linking to the function or variable descriptions using the sym-directive as in measure.list and myVar.

We can refer to an integer argument with the int-directive, and the argument value with the lint-directive as in this command takes an integer argument i that may have a value of 3. The same convention applies to other types as well, such as bool, int, flt, vec, etc. For example, a vector argument v may take the value of f, and a string argument s may take the value of fred.

We can insert a flagged remark into the text using the directives flag, flag2 and flag3. The flag-directive adds the remark in red text. The flag2-directive marks a block of text, it is not marked in the output document. The flag3-directive adds a comment for internal review, it does not appear in the output document.

We can refer to a marked location in another document using the ref-directive. (1) Material Modeling Support For PFC puts in the link and the name of that section. (2) mat sup puts in the link and the word “mat sup”.