illuminating markup for
instructional mathematics

3 x23 + 13
mathrobatics provides highly instructional answers, tutoring, and help for students in algebra, trigonometry, & calculus, aswell as support for anyone wanting to use the markup language to create illuminated solution with both correctly formatted mathematic symbols and built-in graphical gestures
let's try a simple integral; mouse over, or click on, this description this solution might be more overt than typical; it shows not only how elaborate the markup can be but also how explicit a description can get

it uses the i-teg tag for integrals:

<i-teg>
  <b>9x<sup>2</sup></b>
  <b>dx</b>
  <b></b><!--opt from -->
  <b></b><!--opt to   -->
</i-teg>
9x2 dx
we see it's a product, then note the exponent any extra, or at-length, commentary will appear when touching, or mousing-over a <c‑omm> tag like this one
9x2 dx
this can be solved using the power rule! first increase the exponent by one, then also divide everything by that value - mathrobatics allows this illuminated notation with a simple i-pow tag:

<i‑pow>9x<sup>2</sup></i-pow>
9x2 dx
exponent and denominator are both two-plus-one the fraktion was created with an f-rak tag: 
<f-rak>
    <b> numerator   </b>
    <b> denominator </b> <!-- b optional -->
</f-rak>

the second b tag is option if the denominator contains no other tags; for instance, this is 3/5:

<f‑rak><b>3</b>5</f‑rak>
9x 2+1 2+1 dx
add two-plus-one in the exponent an <e‑kwa> tag ghosts out a statement and places another illuminated value overtop of it 
<e-kwa>
    <b> old value </b>
    <b> new value </b>
</e-kwa>
9x 2 + 1 =3 2 + 1
all of these parenthesis can be dropped now parenthetical groups can be made with a p-ren tag; these use the ghost option:

<p‑ren data-ghost>
9x3 2 + 1
perform the addition in the denominator by default, the <e‑kwa> tag uses the larger, handwritten, illuminated font
9x3 2 + 1 =3
can this be faktored at all? this note is tacked on to the end using a <n‑ote> tag
9x3 3 faktor
???
look at faktors of both nine and three an i-fak tag allows the illuminated display of a value's faktors: 
<i-fak>
    <b> value </b>
    <b>
        faktor list
    </b>
</i-fak>
9 3, 3 x3 3 1, 3
we could cancel-out one of the threes and reduce mathro~batics has several types of canceling; this was done with the r-dux tag, allowing for cancelling and display of the reduced value:

<r‑dux> value <b> reduced </b> </r‑dux>
93  x3 31
rewrite using the reduced values these use the v-iva tag to illuminate values; there are several tags that color and illuminate; some are:

<v‑iva> illuminate </v‑iva>
<v‑ers> invert </v‑ers>
<g‑ost> ghost </g‑ost>
<v‑por> vaporize </v‑por>
3x3 1
one in the denominator can go away most mathro~batic tags have parameters to illuminate, ghost, or vaporize them;

this f-rak tag uses the [data-ghost] parameter, while the denominator uses a <g‑ost> tag
3x3 1
this looks good so far; let's check it a <g‑ood> tag puts a check-mark at the side of it's enclosure
3x3
use the power rule of derivatives to verify a <p‑owr> tag will create all the illuminated gestures needed for the power rule for derivatives, recognizing a <sup> tag in the statement 
<p-owr> 3x<sup>3<sup> </p-owr>
3x3
multiply by the exponent, then subtract one from it there's an <n‑ote> note infront used to indicate the multiplication by the exponent
33x 3 - 1
do the mathrobatics in the exponent
33x 3 - 1 =2
those first two values need to be multiplied groupings in curly brakettes can be indicated with a <c‑url> tag; this one uses the [data-lo] option to place it on the bottom
33 x2
use a computron brand comptometer to multiply
33 =9 x2
that all checks out!
9x2 = 9x2
looks like the original calculation was correct using a <s‑tar> tag gives people a shiny star as a reward
3x3