Rewrite MathTex to make it more robust regarding splitting

[henrikmidtiby]

Overview: What does this pull request change?

This PR changes a large part of the implementation of the MathTex class.
The reason is to deal with the issues related to splitting the tex string and then try to match the generated objects with parts of the original tex string.
The idea for the PR is based on this discussion on discord.
https://discord.com/channels/581738731934056449/1406977902788218892

Motivation and Explanation: Why and how do your changes improve the library?

This PR changes how MathTex objects are created / rendered.
To illustrate the changes in the process, please look at the following example
of calling MathTex.

exp1 = MathTex("{a}^2+{b}^2", 
               "=", 
               "{c}^2", 
               substrings_to_isolate=["a", "b", "c"])

The first step in rendering the MathTex equation, is to join the three separate strings to a single string and add some markup to the string that will allow manim to extract certain parts of the equation afterwards. Each of the three input strings are put in the following markup.

\special{dvisvgm:raw <g id='unique000'>} < input string > \special{dvisvgm:raw </g>}

This ends up looking like the following:

\special{dvisvgm:raw <g id='unique000'>}{a}^2+{b}^2 \special{dvisvgm:raw </g>}
\special{dvisvgm:raw <g id='unique001'>}= \special{dvisvgm:raw </g>}
\special{dvisvgm:raw <g id='unique002'>}{c}^2\special{dvisvgm:raw </g>}

This allows us to access a named group in the formed svg file corresponding to each of the three tex strings.
For each string, the elements of substrings_to_isolate is also located, and marked up with a similar markup.
E.g. the a in the equation ends up like this, where the element is placed in the named group 'unique000ss'.

\special{dvisvgm:raw <g id='unique000ss'>}a\special{dvisvgm:raw </g>}

All there marked up strings are joined to the following string (newlines were added to increase readability).

\special{dvisvgm:raw <g id='unique000'>}{
\special{dvisvgm:raw <g id='unique000ss'>}a
\special{dvisvgm:raw </g>}}^2+{
\special{dvisvgm:raw <g id='unique001ss'>}b
\special{dvisvgm:raw </g>}}^2 
\special{dvisvgm:raw </g>}
\special{dvisvgm:raw <g id='unique001'>}= 
\special{dvisvgm:raw </g>}
\special{dvisvgm:raw <g id='unique002'>}{
\special{dvisvgm:raw <g id='unique002ss'>}c
\special{dvisvgm:raw </g>}}^2
\special{dvisvgm:raw </g>}

This string is then saved to a tex file and converted to first a .dvi and then a .svg file using the latex and dvisvgm command line tools.
Finally the svg file is loaded by a SVGMobject from which the named groups can be accessed as demonstrated here.

exp1.scale(2)
exp1.set_color_by_tex("a", BLUE)
exp1[2].set_color(ORANGE)
self.add(exp1)

The full code for this example is provided here

class Scene27(Scene):
    def construct(self):
        exp1 = MathTex("{a}^2+{b}^2", 
                       "=", 
                       "{c}^2", 
                       substrings_to_isolate=["a", "b", "c"])
        exp1.scale(2)
        exp1.set_color_by_tex("a", BLUE)
        exp1[2].set_color(ORANGE)
        self.add(exp1)

and it renders as follows

Links to added or changed documentation pages

Further Information and Comments

This PR is an extension of #4473 "Maintain groups when importing svg files"

Reviewer Checklist

• The PR title is descriptive enough for the changelog, and the PR is labeled correctly
• If applicable: newly added non-private functions and classes have a docstring including a short summary and a PARAMETERS section
• If applicable: newly added functions and classes are tested

[henrikmidtiby]

And here are some example code and the generated output.

class ExampleScene8(Scene):
    def construct(self):
        formula = MathTex(
            r"P(X=k) =",
            r"\binom{12}{k}",
            r"0.5^{k}",
            r"(1-0.5)^{12-k}",
            substrings_to_isolate=["k", "1", "12", "0.5"],
        ).scale(1.3)

        formula.set_color_by_tex("k", GREEN)
        formula.set_color_by_tex("12", RED)
        formula.set_color_by_tex("1", YELLOW)
        formula.set_color_by_tex("0.5", BLUE_D)
        self.add(formula)

class ExampleScene11(Scene):
    def construct(self):
        t2cm = {"n": RED, "1": GREEN, "x": YELLOW}
        eq = MathTex(r"\sum_{1}^{n} x", tex_to_color_map=t2cm).scale(1.3)

        self.add(eq)

[henrikmidtiby]

I have located a minor issue related to the "Using text" guide.
https://docs.manim.community/en/stable/guides/using_text.html#substrings-and-parts

In the example IncorrectLaTeXSubstringColoring, the equation is no longer colored as in the current documentation.