dualize.js

function DualizeError() {}
DualizeError.prototype = new Error();

function parseInequality(str) {
    var m = str.match(/^(.+?)(\s*(?:\\leq?|=)\s*)(.+)$/);
    if (m) {
        return [m[1], m[2], m[3]];
    } else {
        throw new DualizeError("cannot parse it");
    }
}

function dualizeInvariant(str) {
    var m;
    if (m = str.match(/^(\s+)(.+)$/)) {
        return m[1] + dualizeInvariant(m[2]);
    }
    if (m = str.match(/^\\cov\((.+)\)$/)) {
        return "\\non("+m[1]+")";
    }
    if (m = str.match(/^\\non\((.+)\)$/)) {
        return "\\cov("+m[1]+")";
    }
    if (m = str.match(/^\\add\((.+)\)$/)) {
        return "\\cof("+m[1]+")";
    }
    if (m = str.match(/^\\cof\((.+)\)$/)) {
        return "\\add("+m[1]+")";
    }
    if (m = str.match(/^\\frakb$/)) {
        return "\\frakd";
    }
    if (m = str.match(/^\\frakd$/)) {
        return "\\frakb";
    }
    if (m = str.match(/^\\min(\s*)\\{(.+)\\}$/)) {
        return "\\max"+m[1]+"\\{"+m[2].split(",").map((x) => dualizeInvariant(x)).join(",")+"\\}";
    }
    if (m = str.match(/^\\max(\s*)\\{(.+)\\}$/)) {
        return "\\min"+m[1]+"\\{"+m[2].split(",").map((x) => dualizeInvariant(x)).join(",")+"\\}";
    }
    throw new DualizeError("cannot dualize it");
}

function dualizeInequality(str) {
    var parsed = parseInequality(str);
    var lhs = parsed[0];
    var op = parsed[1];
    var rhs = parsed[2];
    if (op.match(/^\s*=\s*$/)) {
        return dualizeInvariant(lhs) + op + dualizeInvariant(rhs);
    } else {
        return dualizeInvariant(rhs) + op + dualizeInvariant(lhs);
    }
}

var line = editor.text(cursor.lineNumber());
var re = /\$([^$]+)\$([^$]*)$/g;
var matched = re.exec(line);
if (matched) {
    var to = re.lastIndex;
    var from = to - matched[0].length;
    var result;
    try {
        var result = dualizeInequality(matched[1]);
    } catch(e) {
        alert(e);
        var result = null;
    }
    if (result) {
        cursor.beginEditBlock();
        cursor.eraseLine();
        cursor.insertText(line.slice(0, from));
        cursor.insertText("$"+matched[1]+"$");
        cursor.insertText(" and $"+result+"$"+matched[2]);
        cursor.insertText(line.slice(to, -1));
        cursor.insertLine();
        cursor.endEditBlock();
        cursor.movePosition(1, cursorEnums.Left);
    }
}