Fails to turn into correct MathJSON

I went through some mathematics notes and found the following interesting equations. I tested them on the compute engine demo page https://cortexjs.io/compute-engine/demo/

(Information for myself: Page 1 of ANA_UE_SS_21_Mo_1.pdf , meaning there are a few more testcases)

• \begin{equation*} N(\varepsilon)\coloneq\lceil\frac{4}{\varepsilon^2}\rceil \end{equation*} turns into "" syntax-error

• \begin{equation*} x_{1,2}=1,2 \end{equation*} turns into ["Equal", ["Subscript", "x", {num: "12"}], {num: "12"}]. Notice how the comma is missing

• \begin{equation*} \{1,2\} \end{equation*} turns into ["Multiply", "\\{", {num: "12"}, "\\}"]. I assume this happens because sets haven’t been implemented yet

• \begin{equation*} [1,2] \end{equation*} turns into "" syntax-error. I assume this happens because vectors/matrices and the like haven’t been implemented yet.

• \begin{equation*} \frac{2}{\sqrt{n}}\Leftrightarrow n>\frac{5}{n^2} \end{equation*} turns into the following, notice how \\Leftrightarrow doesn’t have a special meaning and its precedence is off

[
  "Greater",
  [
    "Multiply",
    ["Divide", 
      {num: "2"}, ["Sqrt", "n"]],
    "\\Leftrightarrow",
    "n"
  ],
  ["Divide", 
    {num: "5"}, ["Power", "n", 2]]
]

• \begin{equation*} |a_n|\le\frac{2}{\sqrt{n}}\Rightarrow a_n\to0=0 \end{equation*} turns into the following, notice how \\Rightarrow doesn’t have a special meaning (implies) and its precedence is off.

[
  "LessEqual",
  ["Abs", ["Subscript", "a", "n"]],
  [
    "Equal",
    [
      "To",
      [
        "Multiply",
        ["Divide", 
          {num: "2"}, ["Sqrt", "n"]],
        "\\Rightarrow",
        ["Subscript", "a", "n"]
      ],
      
      {num: "0"}
    ],
    
    {num: "0"}
  ]
]

• \begin{equation*} 3\equiv5\mod7 \end{equation*} or also \begin{equation*} 3\equiv 5 (\mod 7) \end{equation*} This is a congruence relation. I assume this is simply something that hasn’t been implemented yet. Hopefully it’s a good test case for round-tripping

• \begin{equation*} a={\displaystyle \lim_{n\to\infin}a_n} \end{equation*} turns into

["Equal", "a", "Missing"]
syntax-error

• \begin{equation*} \forall x\in\C^2:|x|<0 \end{equation*} turns into the following

[
  "Element",
  ["Multiply", "\\forall", "x"],
  ["Power", "ComplexNumber", 2]
]
syntax-error

• \begin{equation*} \forall n\colon a_n\le c_n\le b_n\implies\lim_{n\to\infin}c_n=a \end{equation*} turns into the following, note how a few operators aren’t parsed and how the precedences for other operators are slightly off. I think the correct order of operations in this case would start at the :, then the => and then the normal rules. Another interesting tidbit here are the two <= signs. While a comparison would usually return a boolean value (true/false), here the comparisons are more like a range. The expression is a part of the squeeze theorem.

[
  "LessEqual",
  [
    "Multiply",
    "\\forall",
    "n",
    "\\colon",
    ["Subscript", "a", "n"]
  ],
  [
    "LessEqual",
    ["Subscript", "c", "n"],
    [
      "Equal",
      [
        "Multiply",
        ["Subscript", "b", "n"],
        "\\implies",
        ["Subscript", "\\lim", ["To", "n", "\\infin"]],
        ["Subscript", "c", "n"]
      ],
      "a"
    ]
  ]
]

[arnog]

Yes, it’s considered a punctuation character and so has a small padding on its right.

Note also that you can configure which character (or rather which LaTeX command sequence) is used with the groupSeparator option.

That said, some people have very strong opinions about this: http://wordpress.mrreid.org/2014/05/27/stop-putting-commas-in-your-numbers/

Maybe I should reconsider the default value for groupSeparator… 😃

[stefnotch]

I found another case where the compute-engine doesn’t quite work: Logarithms.

For example \begin{equation*} \log_3(7) \end{equation*} gets parsed as

[
  "Multiply",
  ["Subscript", "\\log", 3],
  ["Parentheses", 
    {num: "7"}]
]

@phcreery