Make Mathematica input things on a website and take the data out

Question

So I found a website that calculates polynomials that I need it intakes a word of a's and b's say aabba and outputs a polynomial. Here is the website: http://www.math.stonybrook.edu/~moira/NewApps/Fricke%20Polynomial/fricke.html

I do not know how to use javascript,html,css or anything like that so I am not sure how to import this into Mathematica. I have asked it on stackoverflow with hopes of putting jt into Mathematica but no answer thus far. Thus I was wondering if I can perhaps write code in Mathematica that goes on that website, inputs a word, and outputs the polynomial. An API of a sort. Is that possible?

Answer 1

• ConfigureNodeJSForExternalEvaluate

ClearAll[x, y, z]

session = StartExternalSession@"NodeJS";

sources = Import[#, "Text"] & /@ {
    "http://www.math.stonybrook.edu/~moira/NewApps/Fricke%20Polynomial/Word.js",
    "http://www.math.stonybrook.edu/~moira/NewApps/Fricke%20Polynomial/Polynomial.js"
};

ExternalEvaluate[session, sources];

fricke = ExternalEvaluate[session, "Fricke"];

frickeStringToExpr[str_String]:= str // 
  StringReplace[ x : LetterCharacter ~~ n : DigitCharacter .. :> ( StringTemplate[" ``^``"][x, n]) ] // 
  ToExpression

---

string = "aabba";

fricke[string]["data"] // frickeStringToExpr

3 x - x^3 - x y^2 - y z + x^2 y z