(function () {
    "use strict";
    if (typeof window.bigRat !== "function") {
        throw new Error("bh_bigrat.js muss vor bh_de_minplex.js geladen werden.");
    }
    var STYLE_ID = "bh-ratplex-style";
    var WRAP_ID = "bh-ratplex-wrap";
    var scriptEl = document.currentScript || (function () {
        var xs = document.getElementsByTagName("script");
        return xs[xs.length - 1];
    })();
    var mountNode = null;
    function ensureStyle() {
        if (document.getElementById(STYLE_ID))
            return;
        var style = document.createElement("style");
        style.id = STYLE_ID;
        style.textContent = `/* Ratplex-spezifische Ergänzungen */
#bh-ratplex-wrap {
  margin: 0 auto !important;
  padding: 0 !important;
  background: #D6D2CE !important;
  display: flex;
  flex-direction: column;
  align-items: center;
  width: 100%;
}

#bh-ratplex-wrap form,
#bh-ratplex-wrap table,
#bh-ratplex-wrap tr,
#bh-ratplex-wrap td,
#bh-ratplex-wrap .row,
#bh-ratplex-wrap .form-row,
#bh-ratplex-wrap .controls,
#bh-ratplex-wrap .slider-block,
#bh-ratplex-wrap .dropdown-block,
#bh-ratplex-wrap .button-block {
  background: #D6D2CE !important;
}

#bh-ratplex-wrap h1 {
  margin: 0 0 8px 0;
  font-size: 1.2em;
}

#bh-ratplex-wrap .note {
  display: block;
  margin: 0 0 12px 0;
  font-size: 14px;
}

#bh-ratplex-wrap #runtime {
  display: block;
  margin-top: 8px;
  font-size: 14px;
  width: 100%;
  max-width: 1080px;
  text-align: left;
}}

#bh-ratplex-wrap form[name="ratplex"] {
  width: 100%;
  max-width: 1080px;
  margin: 0 auto !important;
}

#bh-ratplex-wrap textarea {
  width: 100%;
  box-sizing: border-box;
  font-family: "Courier New", Courier, monospace;
  font-size: 14px;
}

#bh-ratplex-wrap textarea[name="data"] {
  min-height: 245px;
}

#bh-ratplex-wrap textarea[name="result"] {
  min-height: 425px;
}

#bh-ratplex-wrap .row {
  display: flex;
  flex-wrap: wrap;
  align-items: center;
  gap: 20px;
  margin-bottom: 10px;
}

#bh-ratplex-wrap .arrow-row {
  justify-content: center;
}

#bh-ratplex-wrap .controls label {
  white-space: nowrap;
}

#bh-ratplex-wrap button,
#bh-ratplex-wrap input[type="button"],
#bh-ratplex-wrap select {
  font: inherit;
}`;
        document.head.appendChild(style);
    }
    function getMountNode() {
        if (mountNode)
            return mountNode;
        var wrap = document.getElementById(WRAP_ID);
        if (wrap) {
            mountNode = wrap;
            return wrap;
        }
        wrap = document.createElement("div");
        wrap.id = WRAP_ID;
        var anchor = scriptEl;
        var p = anchor && anchor.closest ? anchor.closest("p") : null;
        if (p && p.parentNode) {
            p.parentNode.insertBefore(wrap, p);
        } else if (anchor && anchor.parentNode) {
            anchor.parentNode.insertBefore(wrap, anchor);
        } else {
            document.body.appendChild(wrap);
        }
        mountNode = wrap;
        return wrap;
    }
    function formMarkup() {
        return `<form name="ratplex" autocomplete="off">
  <textarea name="data" rows="16" cols="132" wrap="off"></textarea>

  <div class="row arrow-row">
    <div><input type="button" value="↓" title="Berechnen" id="btn-arrow" /></div>
  </div>

  <textarea name="result" rows="28" cols="132" wrap="off" readonly></textarea>
  <div class="footer" id="runtime"></div>

  <div class="row">
    <div><input type="button" class="button" value="Zufalls-LP" id="btn-random"></div>

    <div class="slider-block">
      <label for="slider-m">Zeilen:</label>
      <div class="slider-container">
        <input type="range" name="m" id="slider-m" min="2" max="100" value="8">
        <div class="slider-thumb" id="thumb-m">8</div>
      </div>
    </div>

    <div class="slider-block">
      <label for="slider-n">Spalten:</label>
      <div class="slider-container">
        <input type="range" name="n" id="slider-n" min="2" max="100" value="8">
        <div class="slider-thumb" id="thumb-n">8</div>
      </div>
    </div>

    <div>
      <label for="x">Beispiele:</label>
      <select name="x" id="x">
        <option selected></option>
        <option>Beispiel 1</option><option>Beispiel 2</option><option>Beispiel 3</option>
        <option>Beispiel 4</option><option>Beispiel 5</option><option>Beispiel 6</option>
        <option>Beispiel 7</option><option>Beispiel 8</option><option>Beispiel 9</option>
        <option>Beispiel 10</option>
      </select>
    </div>
  </div>

  <div class="row controls">
    <div><input type="button" value="Berechnen" id="btn-compute" /></div>
    <label><input type="checkbox" name="output"> detaillierte Ausgabe</label>

    <label><input type="radio" name="prog" value="1" checked> primal</label>
    <label><input type="radio" name="prog" value="2"> dual</label>

    <label><input type="radio" name="rule" value="1" checked> steilste Kante</label>
    <label><input type="radio" name="rule" value="2"> größter Wert</label>
    <label><input type="radio" name="rule" value="3"> kleinster Winkel</label>

    <label><input type="radio" name="opt" value="1" checked> Maximum</label>
    <label><input type="radio" name="opt" value="2"> Minimum</label>

    <label><input type="radio" name="op" value="1" checked> ≤</label>
    <label><input type="radio" name="op" value="2"> ≥</label>
  </div>

  <div class="row controls">
    <div><input type="button" value="Felder leeren" id="btn-clear"></div>
    <label><input type="checkbox" name="red"> redundante Restriktionen bestimmen</label>
    <label><input type="checkbox" name="few" checked> Restriktionsanzahl minimieren</label>
    <label><input type="checkbox" name="nor1"> 1. Normierung</label>
    <label><input type="checkbox" name="scal"> Skalierung</label>
    <label><input type="checkbox" name="nor2"> 2. Normierung</label>
  </div>
</form>`;
    }
    function bindUI() {
        document.ratplex = document.forms.ratplex;
        var debouncedRandomCompute = debounce(function () {
            random(true);
        }, 180);
        document.getElementById("slider-m").addEventListener("input", function () {
            updateThumb(this, "thumb-m");
        });
        document.getElementById("slider-n").addEventListener("input", function () {
            updateThumb(this, "thumb-n");
        });
        document.getElementById("slider-m").addEventListener("change", debouncedRandomCompute);
        document.getElementById("slider-n").addEventListener("change", debouncedRandomCompute);
        document.getElementById("btn-random").addEventListener("click", function () {
            random(true);
        });
        document.getElementById("btn-compute").addEventListener("click", compute);
        document.getElementById("btn-arrow").addEventListener("click", compute);
        document.getElementById("btn-clear").addEventListener("click", function () {
            document.ratplex.data.value = "";
            document.ratplex.result.value = "";
            sourceState.text = "";
            sourceState.matrix = null;
            document.ratplex.x.selectedIndex = 0;
            document.getElementById("runtime").textContent = "";
        });
        document.getElementById("x").addEventListener("change", function () {
            var idx = this.selectedIndex;
            if (idx > 0) {
                setSourceText(EXAMPLES[idx]);
                compute();
            }
        });
        var recomputeOnChange = document.querySelectorAll('#' + WRAP_ID + ' input[type="checkbox"], #' + WRAP_ID + ' input[type="radio"]');
        recomputeOnChange.forEach(function (el) {
            el.addEventListener("change", function () {
                if (document.ratplex.data.value.trim() !== "")
                    compute();
            });
        });
        updateThumb(document.getElementById("slider-m"), "thumb-m");
        updateThumb(document.getElementById("slider-n"), "thumb-n");
        document.ratplex.x.selectedIndex = 0;
        document.ratplex.data.value = EXAMPLES[1];
        sourceState.text = "";
        sourceState.matrix = null;
        compute();
    }
    function initMinplex() {
        ensureStyle();
        var node = getMountNode();
        node.innerHTML = formMarkup();
        bindUI();
    }
    var EPSILON = bigRat(1, 10000000000),
    FACTOR = 25,
    INFINITY,
    TAB = 7,
    ZERO = bigRat(0),
    a = [],
    b = [],
    e = [],
    n1 = [],
    n2 = [],
    s = [],
    bv = [],
    mbv = [],
    nbv = [],
    tab = [],
    i,
    j,
    k,
    l,
    m,
    n,
    beq,
    bet,
    ble,
    cb,
    cn,
    ms,
    ns,
    prog = 1,
    rule = 1,
    op = 1,
    opt = 1,
    max,
    min,
    few = true,
    less,
    nor1 = false,
    nor2 = false,
    output = false,
    perts,
    red = false,
    scal = false,
    solve,
    steps,
    status,
    str,
    tmp,
    nul = 0,
    phase1 = false;
    function nines() {
        var big = "99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999";
        big += big;
        return bigRat(big + big);
    }
    INFINITY = nines();
    var sourceState = {
        text: "",
        matrix: null
    };
    var EXAMPLES = {
        1: "15  17 -12  -2 15  -6  -4  21\n16  15 -13  -4 -1  -7  -8   0\n-8 -12  -3  -5 16  -6  22  -4\n17  -3 -12  -1 -1  21  14   0\n-7  -9  14 -11 23 -12  21  21\n21 -11  19  -2 -9  -2  16  14\n 0  -2  -3  22 16  16  -3 -11\n14 -10  17  -6 23  23 -12  24\n 0  23  23  24 -6  18  -5 -12",
        2: "30 1 3 2\n25 4 2 1\n45 3 4 4\n50 2 3 5\n 0 5 8 4",
        3: "  1  1 -8 -2  0  0\n 28  2  8 -2  0  0\n 42  1 -6  1  0  0\n  1  0  1  0  0  0\n0,6  0  0  1 -1  0\n8,5 -1  8  2  0 -1\n  1 -1  8  1  0  0\n0,1 -1 -9  2  0  0\n  0  1  0  0  0  0",
        4: "   1  0  1 -8  0 -2  0  0  0  0\n  28  0  2  8  0 -2  0  0  0  0\n  42  0  1 -6  0  1  0  0  0  0\n   1  0  0  1  0  0  0  0  0  0\n 0,6  0  0  0  0  1  0 -1  0  0\n 8,5  0 -1  8  0  2  0  0  0 -1\n   1  0 -1  8  0  1  0  0  0  0\n 0,1  0 -1 -9  0  2  0  0  0  0\n   1  1 -8  0 -2  0  0  0  0  0\n 700  2  8  0 -2  0  0  0  0  0\n1050  1 -6  0  1  0  0  0  0  0\n 0,6  0  0  0  1  0 -1  0  0  0\n 8,5 -1  8  0  2  0  0  0 -1  0\n   1 -1  8  0  1  0  0  0  0  0\n 0,1 -1 -9  0  2  0  0  0  0  0\n   0  0  1  0  0  0  0  0  0  0",
        5: "-2 -2  1  0  0 -1\n 1 -1 -2  0  0 -2\n-5  0  0  1 -1 -1\n 1  0  0 -1  1 -2\n 0 -4 -6 -2 -2 -4",
        6: "0  -2 -9    1   9\n0 1/3  1 -1/3  -2\n1   1  1    1   1\n0   2  3   -1 -12",
        7: "-4 -2 -1  0  0\n-6  1 -2  0  0\n-2  0  0  1 -1\n-2  0  0 -1  1\n-4 -1 -2 -1 -2\n 0 -2  1 -5  1",
        8: "   4  1  1 -1\n  -4 -1 -1 -1\n-0,5 -1 -1  0\n   3 -1  0  0\n   3  0 -1  0\n   3  0  0 -1\n   0  1  2  1",
        9: "     5   1   0  0  0  0 0 0 0\n    25   4   1  0  0  0 0 0 0\n   125   8   4  1  0  0 0 0 0\n   625  16   8  4  1  0 0 0 0\n  3125  32  16  8  4  1 0 0 0\n 15625  64  32 16  8  4 1 0 0\n 78125 128  64 32 16  8 4 1 0\n390625 256 128 64 32 16 8 4 1\n     0 128  64 32 16  8 4 2 1",
        10: "              1        1       0      0     0    0   0  0 0\n            100       20       1      0     0    0   0  0 0\n          10000      200      20      1     0    0   0  0 0\n        1000000     2000     200     20     1    0   0  0 0\n      100000000    20000    2000    200    20    1   0  0 0\n    10000000000   200000   20000   2000   200   20   1  0 0\n  1000000000000  2000000  200000  20000  2000  200  20  1 0\n100000000000000 20000000 2000000 200000 20000 2000 200 20 1\n              0 10000000 1000000 100000 10000 1000 100 10 1"
    };
    function debounce(fn, ms) {
        var t = 0;
        return function () {
            var args = arguments;
            clearTimeout(t);
            t = setTimeout(function () {
                fn.apply(null, args);
            }, ms || 150);
        };
    }
    function cloneRat(r) {
        return new Rat(r.n, r.d);
    }
    function deepCloneMatrix(M) {
        var R = new Array(M.length);
        for (var ii = 0; ii < M.length; ii++) {
            R[ii] = new Array(M[ii].length);
            for (var jj = 0; jj < M[ii].length; jj++)
                R[ii][jj] = cloneRat(M[ii][jj]);
        }
        return R;
    }
    function decimal(val) {
        return val.toDecimal(16).replace(/\./, ",").toUpperCase();
    }
    function format(val) {
        var arg = String(val).replace(/\./, ",").toUpperCase();
        return (arg.length > 2 && arg.indexOf("/1") == arg.length - 2) ? arg.substr(0, arg.length - 2) : arg;
    }
    var SPACE_CACHE = " ".repeat(512);
    function space(val) {
        val = Math.max(0, Math.min(val, 512));
        return SPACE_CACHE.substr(0, val);
    }
    function finite() {
        return solve = true;
    }
    function updateThumb(slider, thumbId) {
        const thumb = document.getElementById(thumbId);
        const percent = (slider.value - slider.min) / (slider.max - slider.min);
        const sliderWidth = slider.offsetWidth || 260;
        const thumbWidth = thumb.offsetWidth || 24;
        const x = percent * (sliderWidth - thumbWidth) + thumbWidth / 2;
        thumb.style.left = x + "px";
        thumb.textContent = slider.value;
    }
    function matrixToText(M) {
        var mm = M.length,
        nn = M[0].length,
        out = "";
        var len = new Array(nn),
        maxs = new Array(nn),
        maxv,
        mem;
        for (j = 0; j < nn; j++) {
            len[j] = new Array(mm);
            maxv = 0;
            for (i = 0; i < mm; i++) {
                mem = format(M[i][j]).length;
                if (mem > maxv)
                    maxv = mem;
                len[j][i] = mem;
            }
            maxs[j] = maxv + 1;
        }
        for (i = 1; i < mm; i++) {
            for (j = 0; j < nn; j++)
                out += space(maxs[j] - len[j][i]) + format(M[i][j]);
            out += "\n";
        }
        for (j = 0; j < nn; j++)
            out += space(maxs[j] - len[j][0]) + format(M[0][j]);
        return out;
    }
    function parseTextMatrix(input) {
        input = (input || "").trim();
        var rest = input.replace(/[\d\-\/,eE\.\s+]/g, "");
        if (rest !== "")
            throw new Error("Es sind unzulässige Zeichen enthalten.");
        input = input.replace(/,/g, ".").replace(/[\r]/g, "").replace(/[ \t]+$/gm, "");
        var rows = input.split(/\n+/).filter(function (x) {
            return x.trim() !== "";
        });
        if (rows.length < 2)
            throw new Error("Es sind mindestens zwei Zeilen erforderlich.");
        var raw = new Array(rows.length);
        var rex = /([+\-]?(?:\d+(?:\.\d*)?|\.\d+)(?:[eE][+\-]?\d+)?(?:\/[+\-]?(?:\d+(?:\.\d*)?|\.\d+)(?:[eE][+\-]?\d+)?)?|[+\-]?\d+(?:[eE][+\-]?\d+)?(?:\/\d+(?:[eE][+\-]?\d+)?)?)/g;
        var cols = 0;
        for (var r = 0; r < rows.length; r++) {
            var toks = rows[r].match(rex);
            if (!toks || toks.length < 2)
                throw new Error("Die Eingabe ist nicht ausreichend oder nicht zulässig.");
            if (r === 0)
                cols = toks.length;
            if (toks.length !== cols)
                throw new Error("Die Matrix hat in Zeile " + (r + 1) + " leider " + toks.length + " Spalten statt " + cols + ".");
            raw[r] = new Array(cols);
            for (var c = 0; c < cols; c++)
                raw[r][c] = bigRat(toks[c]);
        }
        var M = new Array(rows.length);
        M[0] = raw[rows.length - 1];
        for (var rr = 0; rr < rows.length - 1; rr++)
            M[rr + 1] = raw[rr];
        return M;
    }
    function setSourceMatrix(M) {
        sourceState.matrix = deepCloneMatrix(M);
        sourceState.text = matrixToText(M);
        document.ratplex.data.value = sourceState.text;
    }
    function setSourceText(text) {
        var M = parseTextMatrix(text);
        setSourceMatrix(M);
    }
    function makeRandomMatrix(mm, nn) {
        var M = new Array(mm);
        for (var ii = 0; ii < mm; ii++) {
            M[ii] = new Array(nn);
            for (var jj = 0; jj < nn; jj++) {
                var x = Math.random();
                var v = (x > 0.5) ? Math.round(FACTOR * x) : -Math.round(FACTOR * x);
                M[ii][jj] = bigRat(v);
            }
            M[ii][0] = M[ii][0].abs();
        }
        M[0][0] = ZERO;
        return M;
    }
    function random(renderOnly) {
        m = parseInt(document.ratplex.m.value, 10);
        n = parseInt(document.ratplex.n.value, 10);
        document.ratplex.x.selectedIndex = 0;
        setSourceMatrix(makeRandomMatrix(m, n));
        if (renderOnly !== false)
            compute();
    }
    function check() {
        try {
            var txt = document.ratplex.data.value;
            if (sourceState.matrix && txt === sourceState.text) {
                a = deepCloneMatrix(sourceState.matrix);
            } else {
                a = parseTextMatrix(txt);
                sourceState.matrix = deepCloneMatrix(a);
                sourceState.text = txt;
            }
            m = a.length;
            n = a[0].length;
            if (m < 2 || n < 2) {
                alert("Es sind mindestens zwei Zeilen und mindestens zwei Spalten erforderlich.");
                return false;
            }
            if (finite())
                return true;
        } catch (err) {
            alert(err.message || String(err));
            return false;
        }
        return false;
    }
    function redundant() {
        var test;
        for (i = 1; i < m; i++) {
            test = bv[i];
            if (mbv[test]) {
                for (j = 1; j < n && a[i][j].leq(ZERO); j++);
                if (j == n) {
                    mbv[test] = false;
                    if (test < ns)
                        cn++;
                    else
                        cb++;
                }
            }
        }
    }
    function trans(row, col) {
        k = row;
        l = col;
        solve = false;
        tableau("", 2, true);
        str += "Die Rechengrenze wurde überschritten.\n";
    }
    function norm_scale() {
        var minv,
        obj,
        sca;
        if (nor1 || nor2) {
            if (output)
                str += "Die 1. Normierung wird durchgeführt.\n";
            for (i = 1; i < m; i++) {
                sca = ZERO;
                for (j = 1; j < n; j++)
                    sca = sca.add(a[i][j].times(a[i][j]));
                sca = bigRat(Math.sqrt(sca.toNumber() || 0));
                if (sca.eq(ZERO))
                    sca = bigRat(1);
                for (j = 0; j < n; j++)
                    a[i][j] = a[i][j].divide(sca);
                n1[i] = sca.reciprocate();
            }
        }
        if (scal) {
            if (output)
                str += "Die Skalierung wird durchgeführt.\n";
            for (j = 1; j < n; j++) {
                minv = INFINITY;
                for (i = 1; i < m; i++) {
                    obj = a[i][j].abs();
                    if (obj.gt(ZERO) && obj.lt(minv))
                        minv = obj;
                }
                minv = minv.reciprocate();
                for (i = 0; i < m; i++)
                    a[i][j] = a[i][j].times(minv);
                e[tab[j]] = minv;
            }
            if (nor1 && nor2) {
                if (output)
                    str += "Die 2. Normierung wird durchgeführt.\n";
                for (i = 1; i < m; i++) {
                    sca = ZERO;
                    for (j = 1; j < n; j++)
                        sca = sca.add(a[i][j].times(a[i][j]));
                    sca = bigRat(Math.sqrt(sca.toNumber() || 0));
                    if (sca.eq(ZERO))
                        sca = bigRat(1);
                    for (j = 0; j < n; j++)
                        a[i][j] = a[i][j].divide(sca);
                    n2[i] = sca.reciprocate();
                }
            }
        }
    }
    function pivot(inc, mem, v) {
        var ele = a[0][v],
        dif,
        pro,
        quo,
        sca,
        sum;
        switch (rule) {
        case 1:
            sum = bigRat(1);
            for (i = 1; i < m; i++)
                sum = sum.add(a[i][v].times(a[i][v]));
            pro = ele.times(ele);
            quo = pro.divide(sum);
            if (quo.gt(max)) {
                k = mem;
                l = v;
                max = quo;
            } else if (quo.eq(max)) {
                pro = ele.times(inc);
                if (pro.gt(bet)) {
                    k = mem;
                    l = v;
                    bet = pro;
                }
            }
            break;
        case 2:
            pro = ele.times(inc);
            if (pro.gt(max)) {
                k = mem;
                l = v;
                max = pro;
            } else if (pro.eq(max)) {
                sum = bigRat(1);
                for (i = 1; i < m; i++)
                    sum = sum.add(a[i][v].times(a[i][v]));
                pro = ele.times(ele);
                quo = pro.divide(sum);
                if (quo.gt(bet)) {
                    k = mem;
                    l = v;
                    bet = quo;
                }
            }
            break;
        case 3:
            quo = ele.divide(a[mem][v]);
            sum = quo;
            sca = quo.times(quo);
            for (j = 1; j < n; j++) {
                pro = a[mem][j].times(quo);
                dif = a[0][j].subtract(pro);
                sum = sum.add(dif);
                pro = dif.times(dif);
                sca = sca.add(pro);
            }
            sum = sum.times(sum.abs());
            quo = sum.divide(sca);
            if (quo.lt(min)) {
                k = mem;
                l = v;
                min = quo;
            } else if (quo.eq(min)) {
                pro = ele.times(inc);
                if (pro.gt(max)) {
                    k = mem;
                    l = v;
                    max = pro;
                }
            }
            break;
        }
    }
    var scratchPline = [];
    function transform(val) {
        var rowel,
        pivotv = a[k][l].reciprocate(),
        ak = a[k],
        i,
        j,
        r;
        a[k][l] = pivotv;
        rowel = pivotv.times(ak[0]).negate();
        if (val == 0) {
            for (i = 0; i < k; i++)
                a[i][0] = a[i][0].add(rowel.times(a[i][l]));
            for (i = k + 1; i < m; i++)
                a[i][0] = a[i][0].add(rowel.times(a[i][l]));
        } else {
            for (i = 0; i < val; i++) {
                r = s[i];
                a[r][0] = a[r][0].add(rowel.times(a[r][l]));
            }
        }
        ak[0] = rowel.negate();
        scratchPline.length = n;
        for (j = 1; j < l; j++) {
            scratchPline[j] = ak[j];
            ak[j] = pivotv.times(ak[j]);
        }
        for (j = l + 1; j < n; j++) {
            scratchPline[j] = ak[j];
            ak[j] = pivotv.times(ak[j]);
        }
        pivotv = pivotv.negate();
        for (i = 0; i < k; i++) {
            a[i][l] = pivotv.times(a[i][l]);
            rowel = a[i][l];
            for (j = 1; j < l; j++)
                a[i][j] = a[i][j].add(rowel.times(scratchPline[j]));
            for (j = l + 1; j < n; j++)
                a[i][j] = a[i][j].add(rowel.times(scratchPline[j]));
        }
        for (i = k + 1; i < m; i++) {
            a[i][l] = pivotv.times(a[i][l]);
            rowel = a[i][l];
            for (j = 1; j < l; j++)
                a[i][j] = a[i][j].add(rowel.times(scratchPline[j]));
            for (j = l + 1; j < n; j++)
                a[i][j] = a[i][j].add(rowel.times(scratchPline[j]));
        }
        if ((red || few))
            redundant();
    }
    function tableau(string, piv, force) {
        if (!force && !output) {
            str += string;
            return;
        }
        var i,
        j,
        len = [],
        maxs = [],
        nbvl = [],
        maxw = TAB,
        mem;
        if (opt == 1)
            a[0][0] = a[0][0].negate();
        str += string;
        len[n] = new Array(m);
        nbvl[n] = maxw;
        for (i = 1; i < m; i++) {
            mem = String(bv[i]).length;
            if (mem > maxw)
                maxw = mem;
            len[n][i] = mem;
        }
        maxs[n] = ++maxw;
        if (l > 0) {
            len[0] = new Array(m);
            maxw = TAB;
            nbvl[0] = maxw;
            for (i = 0; i < m; i++) {
                tmp = a[i][0];
                mem = format(tmp).length;
                if (mem > maxw)
                    maxw = mem;
                len[0][i] = mem;
            }
            maxs[0] = ++maxw;
        } else {
            len[0] = new Array(m);
            maxs[0] = TAB + 1;
            nbvl[0] = TAB;
            for (i = 0; i < m; i++)
                len[0][i] = format(a[i][0]).length;
        }
        for (j = 1; j < l; j++) {
            len[j] = new Array(m);
            maxw = String(nbv[j]).length;
            nbvl[j] = maxw;
            for (i = 0; i < m; i++) {
                tmp = a[i][j];
                mem = format(tmp).length;
                if (mem > maxw)
                    maxw = mem;
                len[j][i] = mem;
            }
            maxs[j] = ++maxw;
        }
        len[l] = new Array(m);
        maxw = l > 0 ? String(nbv[l]).length : TAB;
        nbvl[l] = maxw;
        for (i = 0; i < k; i++) {
            tmp = a[i][l];
            mem = format(tmp).length;
            if (mem > maxw)
                maxw = mem;
            len[l][i] = mem;
        }
        tmp = a[k] && a[k][l] ? a[k][l] : ZERO;
        mem = format(tmp).length + piv;
        if (mem > maxw)
            maxw = mem;
        len[l][k] = mem;
        for (i = k + 1; i < m; i++) {
            tmp = a[i][l];
            mem = format(tmp).length;
            if (mem > maxw)
                maxw = mem;
            len[l][i] = mem;
        }
        maxs[l] = ++maxw;
        for (j = l + 1; j < n; j++) {
            len[j] = new Array(m);
            maxw = String(nbv[j]).length;
            nbvl[j] = maxw;
            for (i = 0; i < m; i++) {
                tmp = a[i][j];
                mem = format(tmp).length;
                if (mem > maxw)
                    maxw = mem;
                len[j][i] = mem;
            }
            maxs[j] = ++maxw;
        }
        str += space(maxs[n] - TAB) + "    BV:";
        str += space(maxs[0] - TAB) + "RS\\NBV:";
        for (j = 1; j < n; j++)
            str += space(maxs[j] - nbvl[j]) + nbv[j];
        str += "\n";
        for (i = 1; i < k; i++) {
            str += space(maxs[n] - len[n][i]) + bv[i];
            for (j = 0; j < n; j++)
                str += space(maxs[j] - len[j][i]) + format(a[i][j]);
            str += "\n";
        }
        if (k > 0) {
            str += space(maxs[n] - len[n][k]) + bv[k];
            for (j = 0; j < l; j++)
                str += space(maxs[j] - len[j][k]) + format(a[k][j]);
            str += (piv == 2) ? space(maxs[l] - len[l][k]) + "»" + format(a[k][l]) + "«" : space(maxs[l] - len[l][k]) + format(a[k][l]);
            for (j = l + 1; j < n; j++)
                str += space(maxs[j] - len[j][k]) + format(a[k][j]);
            str += "\n";
        }
        for (i = k + 1; i < m; i++) {
            str += space(maxs[n] - len[n][i]) + bv[i];
            for (j = 0; j < n; j++)
                str += space(maxs[j] - len[j][i]) + format(a[i][j]);
            str += "\n";
        }
        str += (prog == 1) ? ((opt == 1) ? space(maxs[n] - TAB) + "PP Max:" : space(maxs[n] - TAB) + "PP Min:") : ((opt == 1) ? space(maxs[n] - TAB) + "DP Min:" : space(maxs[n] - TAB) + "DP Max:");
        for (j = 0; j < l; j++)
            str += space(maxs[j] - len[j][0]) + format(a[0][j]);
        str += (piv == 2 && k == 0) ? space(maxs[l] - len[l][0]) + "»" + format(a[0][l]) + "«" : space(maxs[l] - len[l][0]) + format(a[0][l]);
        for (j = l + 1; j < n; j++)
            str += space(maxs[j] - len[j][0]) + format(a[0][j]);
        str += "\n";
        if (opt == 1)
            a[0][0] = a[0][0].negate();
    }
    function loop(last) {
        var t = [],
        u = [],
        o,
        p,
        q,
        r,
        v,
        ele,
        inc,
        man,
        mem,
        per,
        pro,
        quo,
        sca;
        l = 0;
        nul = 0;
        do {
            k = 0;
            q = 0;
            for (j = 1; j < n; j++)
                if (a[0][j].gt(ZERO))
                    u[q++] = j;
            if (q > 0) {
                o = 0;
                bet = ZERO;
                max = ZERO;
                pro = ZERO;
                min = INFINITY;
                if (nul == 0) {
                    p = 0;
                    for (i = 1; i < m; i++)
                        if (a[i][0].eq(ZERO))
                            s[o++] = i;
                        else
                            t[p++] = i;
                } else {
                    for (i = 1; i < m; i++)
                        if (a[i][0].eq(ZERO))
                            o++;
                }
                if (o > 0 || nul > 0) {
                    if (nul == 0)
                        nul = o;
                    if (o > 0) {
                        for (i = 0; i < nul && solve; i++) {
                            sca = ZERO;
                            r = s[i];
                            for (j = 1; j < n; j++)
                                sca = sca.add(a[r][j].times(a[r][j]));
                            a[r][0] = a[r][0].add(bigRat(Math.sqrt(sca.toNumber() || 0)));
                        }
                    }
                    for (j = 0; j < q; j++) {
                        v = u[j];
                        for (i = 0; i < nul && a[s[i]][v].leq(ZERO); i++);
                        if (i == nul) {
                            inc = INFINITY;
                            for (i = 0; i < p; i++) {
                                r = t[i];
                                ele = a[r][v];
                                if (ele.gt(ZERO)) {
                                    quo = a[r][0].divide(ele);
                                    if (quo.lt(inc)) {
                                        inc = quo;
                                        mem = r;
                                    }
                                }
                            }
                            if (inc.lt(INFINITY))
                                pivot(inc, mem, v);
                        }
                    }
                    if (k > 0) {
                        for (i = 0; i < nul; i++)
                            a[s[i]][0] = ZERO;
                        nul = 0;
                    }
                } else {
                    for (j = 0; j < q; j++) {
                        v = u[j];
                        inc = INFINITY;
                        for (i = 1; i < m; i++) {
                            ele = a[i][v];
                            if (ele.gt(ZERO)) {
                                quo = a[i][0].divide(ele);
                                if (quo.lt(inc)) {
                                    inc = quo;
                                    mem = i;
                                }
                            }
                        }
                        if (inc.lt(INFINITY))
                            pivot(inc, mem, v);
                    }
                }
                if (nul > 0) {
                    bet = ZERO;
                    max = ZERO;
                    min = INFINITY;
                    for (j = 0; j < q; j++) {
                        v = u[j];
                        inc = INFINITY;
                        for (i = 0; i < nul; i++) {
                            r = s[i];
                            ele = a[r][v];
                            if (ele.gt(ZERO)) {
                                quo = a[r][0].divide(ele);
                                if (quo.lt(inc)) {
                                    inc = quo;
                                    mem = r;
                                }
                            }
                        }
                        if (inc.lt(INFINITY))
                            pivot(inc, mem, v);
                    }
                    per = (k > 0) ? ++perts : false;
                } else
                    per = false;
                if (k > 0) {
                    mem = bv[k];
                    bv[k] = nbv[l];
                    nbv[l] = mem;
                    steps++;
                    if (output) {
                        tableau("", 2);
                        str += "Das Pivotelement ist a[" + k + "][" + (l + 1) + "] = " + format(a[k][l]) + ".\n";
                        if (per)
                            str += "Eine Perturbation war erforderlich.\n";
                    }
                    man = a[0][0];
                    transform(nul);
                    if (last && a[0][0].neq(man))
                        return;
                    if (!solve) {
                        trans(i, j);
                        k = 0;
                    }
                }
            }
        } while (k > 0);
        if (nul > 0 && solve) {
            if (output)
                tableau("", 0);
            for (i = 0; i < nul; i++)
                a[s[i]][0] = ZERO;
            if (output)
                str += "Tableau ohne Perturbationen:\n";
        }
    }
    function numbers(string) {
        if (steps == 1)
            str += "Es wurden" + string + " ein Pivotschritt und ";
        else
            str += "Es wurden" + string + " " + steps + " Pivotschritte und ";
        if (perts == 0)
            str += "keine Perturbationen benötigt.\n";
        else
            str += (perts == 1) ? "eine Perturbation benötigt.\n" : perts + " Perturbationen benötigt.\n";
    }
    function compute() {
        var t0 = performance.now();
        function results() {
            var br = new Array(ms - 1),
            ng = [];
            numbers("");
            if (prog == 1)
                str += (opt == 1) ? "Das Maximum liegt bei " + format(a[0][0].negate()) + " (" + decimal(a[0][0].negate()) + ")." : "Das Minimum liegt bei " + format(a[0][0]) + " (" + decimal(a[0][0]) + ").";
            else
                str += (opt == 1) ? "Das Minimum liegt bei " + format(a[0][0].negate()) + " (" + decimal(a[0][0].negate()) + ")." : "Das Maximum liegt bei " + format(a[0][0]) + " (" + decimal(a[0][0]) + ").";
            for (j = 1; j < ns; j++)
                x[j] = ZERO;
            for (i = 1; i < ms; i++) {
                y[i] = ZERO;
                if (bv[i] < ns)
                    x[bv[i]] = a[i][0];
            }
            if (scal)
                for (j = 1; j < n; j++)
                    x[tab[j]] = x[tab[j]].times(e[tab[j]]);
            if (few && ble) {
                for (i = m; i < ms; i++) {
                    bv[i] -= ns - 1;
                    br[i] = b[bv[i]][0];
                    for (j = 1; j < ns; j++)
                        br[i] = br[i].subtract(b[bv[i]][j].times(x[j]));
                    ng[i] = br[i].lt(ZERO);
                }
                for (j = n; j < ns; j++) {
                    min = ZERO;
                    for (i = m; i < ms; i++) {
                        if (ng[i] && b[bv[i]][nbv[j]].lt(ZERO)) {
                            tmp = br[i].divide(b[bv[i]][nbv[j]]);
                            if (tmp.gt(min)) {
                                min = tmp;
                                ng[i] = false;
                            }
                        }
                    }
                    x[nbv[j]] = min;
                }
                for (i = m; i < ms; i++)
                    bv[i] += ns - 1;
            }
            str += (prog == 1) ? "\n1. primale rationale Lösung: " : "\n1. duale   rationale Lösung: ";
            for (j = 1; j < ns; j++) {
                str += format(x[j]) + " ";
                if (nbv[j] >= ns)
                    y[nbv[j] - ns + 1] = a[0][j].negate();
            }
            str += (prog == 1) ? "\n1. primale Fließkommalösung: " : "\n1. duale   Fließkommalösung: ";
            for (j = 1; j < ns; j++)
                str += decimal(x[j]) + " ";
            if (nor1 || nor2)
                for (i = 1; i < m; i++)
                    y[i] = y[i].times(n1[i]);
            if (nor1 && scal && nor2)
                for (i = 1; i < m; i++)
                    y[i] = y[i].times(n2[i]);
            if (ms == 1) {
                str += (prog == 1) ? "\n1. duale   rationale Lösung: Existiert nicht.\n1. duale   Fließkommalösung: Existiert nicht." : "\n1. primale rationale Lösung: Existiert nicht.\n1. primale Fließkommalösung: Existiert nicht.";
            } else {
                str += (prog == 1) ? "\n1. duale   rationale Lösung: " : "\n1. primale rationale Lösung: ";
                for (i = 1; i < ms; i++)
                    str += format(y[i]) + " ";
                str += (prog == 1) ? "\n1. duale   Fließkommalösung: " : "\n1. primale Fließkommalösung: ";
                for (i = 1; i < ms; i++)
                    str += decimal(y[i]) + " ";
            }
            str += (m < ms || less) ? "\nDie Restriktionsanzahl wurde verringert.\n" : "\n";
        }
        var index = document.ratplex.x.selectedIndex;
        if (index > 0 && (!sourceState.matrix || document.ratplex.data.value !== sourceState.text)) {
            try {
                setSourceText(EXAMPLES[index]);
            } catch (_) {}
        }
        str = "";
        if (check()) {
            k = 0;
            l = 0;
            opt = Number(document.querySelector('input[name="opt"]:checked').value);
            op = Number(document.querySelector('input[name="op"]:checked').value);
            prog = Number(document.querySelector('input[name="prog"]:checked').value);
            if (opt == 1)
                a[0][0] = a[0][0].negate();
            else
                for (j = 1; j < n; j++)
                    a[0][j] = a[0][j].negate();
            if (op == 2)
                for (i = 1; i < m; i++)
                    for (j = 0; j < n; j++)
                        a[i][j] = a[i][j].negate();
            if (prog == 2) {
                opt = (opt == 1) ? 2 : 1;
                min = Math.min(m, n);
                for (i = 0; i < min; i++) {
                    for (j = 0; j <= i; j++) {
                        tmp = a[i][j];
                        a[i][j] = a[j][i].negate();
                        a[j][i] = tmp.negate();
                    }
                }
                if (m != n) {
                    if (m < n) {
                        for (j = m; j < n; j++) {
                            a[j] = new Array(m);
                            for (i = 0; i < m; i++)
                                a[j][i] = a[i][j].negate();
                        }
                    } else {
                        for (i = n; i < m; i++)
                            for (j = 0; j < n; j++)
                                a[j][i] = a[i][j].negate();
                    }
                    tmp = m;
                    m = n;
                    n = tmp;
                }
            }
            for (j = 1; j < n; j++)
                nbv[j] = j;
            for (i = 1; i < m; i++)
                bv[i] = n + i - 1;
            str += "Das lineare Programm hat " + m + " Zeilen und " + n + " Spalten.\n";
            for (i = 1; i < m && solve; i++) {
                for (j = 1; j < n && a[i][j].geq(ZERO); j++);
                if (j == n && a[i][0].lt(ZERO)) {
                    k = i;
                    solve = false;
                    tableau("", 2, true);
                    str += "Das lineare Programm ist nicht lösbar.\n";
                }
            }
            var abs,
            ele,
            f = [],
            g = [],
            ar = [],
            cj = 0,
            eq = [],
            le = [],
            h,
            hco,
            hgi,
            hli,
            heq,
            hsi,
            hge,
            hle,
            ind,
            leng = [],
            maxs = [],
            lco,
            lgi,
            lli,
            llim,
            lsi,
            mem,
            none = true,
            one,
            q = 0,
            r,
            ri = 0,
            sca,
            too,
            ulim;
            red = document.ratplex.red.checked;
            few = document.ratplex.few.checked;
            less = false;
            if (red || few) {
                b[0] = [];
                for (j = 0; j < n; j++)
                    b[0][j] = a[0][j];
                for (i = 1; i < m; i++) {
                    b[i] = [];
                    b[i][0] = a[i][0];
                    max = ZERO;
                    sca = ZERO;
                    for (j = 1; j < n; j++) {
                        b[i][j] = a[i][j];
                        abs = b[i][j].abs();
                        if (abs.gt(max))
                            max = abs;
                    }
                    max = (max.eq(ZERO)) ? bigRat(1) : max.reciprocate();
                    b[i][0] = b[i][0].times(max);
                    for (j = 1; j < n; j++) {
                        b[i][j] = b[i][j].times(max);
                        sca = sca.add(b[i][j].times(b[i][j]));
                    }
                    sca = (sca.gt(ZERO)) ? bigRat(1 / Math.sqrt(sca.toNumber() || 1)) : bigRat(1);
                    for (j = 0; j < n; j++)
                        b[i][j] = b[i][j].times(sca);
                    f[i] = b[i][0].geq(ZERO);
                    if (f[i]) {
                        for (j = 1; j < n && b[i][j].leq(ZERO); j++);
                        f[i] = j == n;
                    }
                }
                if (m > 2) {
                    for (i = 1; i < m; i++) {
                        hsi = b[i][0];
                        hgi = hsi.gt(ZERO);
                        hli = hsi.lt(ZERO);
                        hge = hsi.geq(ZERO);
                        hle = hsi.leq(ZERO);
                        heq = hsi.eq(ZERO);
                        for (k = i + 1; !f[i] && k < m; k++) {
                            if (!f[k]) {
                                lsi = b[k][0];
                                if (hle && lsi.geq(ZERO))
                                    l = i;
                                else if (hge && lsi.leq(ZERO))
                                    l = k;
                                else
                                    l = 0;
                                h = (l == i) ? k : i;
                                if (l != 0) {
                                    llim = ZERO;
                                    ulim = INFINITY;
                                } else {
                                    l = k;
                                    if (hgi) {
                                        llim = ZERO;
                                        ulim = hsi.divide(lsi);
                                    } else {
                                        llim = hsi.divide(lsi);
                                        ulim = INFINITY;
                                    }
                                }
                                one = true;
                                for (j = 1; one && j < n; j++) {
                                    hco = b[h][j];
                                    lco = b[l][j];
                                    var hgo = hco.gt(ZERO),
                                    hlo = hco.lt(ZERO),
                                    lgo = lco.gt(ZERO),
                                    llo = lco.lt(ZERO);
                                    if ((hgo && lgo) || (hlo && llo)) {
                                        hco = hco.divide(lco);
                                        if (lgo && llim.lt(hco))
                                            llim = hco;
                                        else if (llo && ulim.gt(hco))
                                            ulim = hco;
                                        if (llim.gt(ulim.add(EPSILON)))
                                            one = false;
                                    } else {
                                        if (hgo && lco.leq(ZERO))
                                            one = false;
                                        else if (hco.geq(ZERO) && llo)
                                            one = false;
                                    }
                                }
                                f[h] = one;
                                if (!one && ((hgi && lsi.gt(ZERO)) || (hli && lsi.lt(ZERO)) || (heq && lsi.eq(ZERO)))) {
                                    llim = (hli) ? lsi.divide(hsi) : ZERO;
                                    ulim = (hgi) ? lsi.divide(hsi) : INFINITY;
                                    one = true;
                                    for (j = 1; one && j < n; j++) {
                                        hco = b[h][j];
                                        lco = b[l][j];
                                        var hgo2 = hco.gt(ZERO),
                                        hlo2 = hco.lt(ZERO),
                                        lgo2 = lco.gt(ZERO),
                                        llo2 = lco.lt(ZERO);
                                        if ((hgo2 && lgo2) || (hlo2 && llo2)) {
                                            lco = lco.divide(hco);
                                            if (hgo2 && llim.lt(lco))
                                                llim = lco;
                                            else if (hlo2 && ulim.gt(lco))
                                                ulim = lco;
                                            if (llim.gt(ulim.add(EPSILON)))
                                                one = false;
                                        } else {
                                            if (hlo2 && lco.leq(ZERO))
                                                one = false;
                                            else if (hco.leq(ZERO) && lgo2)
                                                one = false;
                                        }
                                    }
                                    f[l] = one;
                                }
                            }
                        }
                    }
                }
                for (i = 1; i < m; i++)
                    if (f[i])
                        g[q++] = i;
                if (q > 0) {
                    str += (q == 1) ? "Folgende Zeile ist" : "Folgende Zeilen sind";
                    str += " überflüssig:\n";
                    for (j = 0; j < n; j++) {
                        leng[j] = new Array(q);
                        max = 0;
                        for (i = 0; i < q; i++) {
                            tmp = a[g[i]][j];
                            mem = format(tmp).length;
                            if (mem > max)
                                max = mem;
                            leng[j][i] = mem;
                        }
                        maxs[j] = ++max;
                    }
                    for (i = 0; i < q; i++) {
                        ind = g[i];
                        for (j = 0; j < n; j++)
                            str += space(maxs[j] - leng[j][i]) + format(a[ind][j]);
                        str += "\n";
                    }
                    q = 1;
                    for (i = 1; i < m; i++) {
                        if (!f[i]) {
                            for (j = 0; j < n; j++)
                                a[q][j] = a[i][j];
                            q++;
                        }
                    }
                    m = q;
                    less = true;
                }
                cb = 0;
                cn = 0;
                for (i = 0; i < m + n - 1; i++)
                    mbv[i] = true;
            }
            ms = m;
            ns = n;
            beq = false;
            ble = false;
            for (i = 1; i < m; i++)
                ar[i] = false;
            for (j = 1; j < n; j++) {
                eq[j] = a[0][j].eq(ZERO);
                if (eq[j]) {
                    for (i = 1; i < m && a[i][j].eq(ZERO); i++);
                    eq[j] = i == m;
                    if (eq[j] && !beq)
                        beq = cj = j;
                    else {
                        for (i = 1; i < m && a[i][j].leq(ZERO); i++);
                        le[j] = i == m;
                        if (le[j]) {
                            if (!ble)
                                ble = cj = j;
                            for (i = 1; i < m; i++)
                                if (a[i][j].lt(ZERO))
                                    ar[i] = true;
                        }
                    }
                }
            }
            if (few) {
                if (ble || beq) {
                    q = 1;
                    r = n;
                    for (j = 1; j < n; j++) {
                        if (le[j] || eq[j]) {
                            r--;
                            for (i = 0; i < m; i++)
                                b[i][r] = a[i][j];
                            nbv[r] = j;
                        } else {
                            for (i = 0; i < m; i++)
                                a[i][q] = a[i][j];
                            tab[q] = j;
                            nbv[q++] = j;
                        }
                    }
                    for (j = r; j < n; j++)
                        for (i = 0; i < m; i++)
                            a[i][j] = b[i][j];
                    n = q;
                    nbv[0] = 0;
                    if (ble) {
                        q = 1;
                        r = ms;
                        for (i = 1; i < ms; i++) {
                            if (ar[i]) {
                                r--;
                                for (j = 0; j < ns; j++)
                                    b[r][j] = a[i][j];
                                bv[r] = i + ns - 1;
                            } else {
                                for (j = 0; j < ns; j++)
                                    a[q][j] = a[i][j];
                                bv[q++] = i + ns - 1;
                            }
                        }
                        for (i = r; i < ms; i++)
                            for (j = 0; j < ns; j++)
                                a[i][j] = b[i][j];
                        m = q;
                    }
                    q = ns - 1;
                    for (i = 1; i < ms; i++)
                        for (j = 0; j < ns; j++)
                            b[bv[i] - q][nbv[j]] = bigRat(a[i][j]);
                } else {
                    for (i = 1; i < m; i++)
                        for (j = 0; j < n; j++)
                            b[i][j] = a[i][j];
                    for (j = 1; j < n; j++)
                        tab[j] = j;
                }
            } else {
                for (j = 1; j < n; j++)
                    tab[j] = j;
            }
            for (i = 1; i < m && ri == 0; i++) {
                if (a[i][0].eq(ZERO)) {
                    for (j = 1; j < n && a[i][j].geq(ZERO); j++);
                    if (j == n)
                        ri = i;
                }
            }
            if (solve) {
                var allp = 0,
                alls = 0,
                c = new Array(n),
                index2,
                limit = true,
                p = n,
                u = new Array(n),
                v = new Array(m),
                w = new Array(n),
                min0 = ZERO,
                hadPhase1 = false,
                obj,
                x = new Array(ns - 1),
                y = new Array(ms - 1);
                ind = 0;
                mem = a[0][0];
                for (j = 1; j < n && limit; j++) {
                    if (a[0][j].gt(ZERO)) {
                        for (i = 1; i < m && a[i][j].lt(ZERO); i++);
                        limit = i < m;
                    }
                }
                if (limit && m > 1) {
                    rule = Number(document.querySelector('input[name="rule"]:checked').value);
                    output = document.ratplex.output.checked;
                    nor1 = document.ratplex.nor1.checked;
                    scal = document.ratplex.scal.checked;
                    nor2 = document.ratplex.nor2.checked;
                    perts = 0;
                    steps = 0;
                    min0 = ZERO;
                    for (i = 1; i < m; i++) {
                        ele = a[i][0];
                        if (ele.lt(min0)) {
                            k = i;
                            min0 = ele;
                        }
                    }
                    if (min0.lt(ZERO)) {
                        hadPhase1 = true;
                        l = 0;
                        if (output)
                            tableau("", 0);
                        norm_scale();
                        for (i = 1; i < m; i++)
                            a[i][n] = bigRat(-1);
                        for (j = 1; j < n; j++) {
                            c[j] = a[0][j];
                            a[0][j] = ZERO;
                            none &= c[j].eq(ZERO);
                        }
                        nbv[n] = bv[k];
                        bv[k] = 0;
                        a[0][0] = ZERO;
                        c[0] = ZERO;
                        a[0][n] = bigRat(-1);
                        l = n++;
                        steps++;
                        if (output) {
                            tableau("Phase I:\n", 2);
                            str += "Das Pivotelement ist a[" + k + "][" + (l + 1) + "] = -1/1.\n";
                        }
                        transform(0);
                        if (solve) {
                            index2 = k;
                            loop(false);
                            if (solve) {
                                if (a[0][0].abs().gt(EPSILON)) {
                                    solve = false;
                                    k = 0;
                                    l = 0;
                                    tableau("", 2, true);
                                    str += "Das lineare Programm ist nicht lösbar.\n";
                                    numbers("");
                                } else {
                                    k = index2;
                                    if (output)
                                        tableau("", 0);
                                    if (nbv[l] != 0) {
                                        for (l = n - 1; l > 0 && a[k][l].eq(ZERO); l--);
                                        bv[k] = nbv[l];
                                        nbv[l] = 0;
                                        steps++;
                                        transform(0);
                                        if (output)
                                            tableau("Das Pivotelement ist a[" + k + "][" + (l + 1) + "] = " + format(a[k][l].reciprocate()) + ".\n", 2);
                                    }
                                    if (solve) {
                                        phase1 = false;
                                        n--;
                                        if (nbv[l] == 0 && l < n) {
                                            for (i = 1; i < m; i++)
                                                a[i][l] = a[i][n];
                                            nbv[l] = nbv[n];
                                        }
                                        a[0][0] = mem;
                                        if (none) {
                                            l = 0;
                                            if (output)
                                                tableau("Ende Phase I:\n", 0);
                                            results();
                                        } else {
                                            none = false;
                                            for (j = 1; j < n; j++) {
                                                l = nbv[j];
                                                a[0][j] = (l < ns) ? c[l] : ZERO;
                                            }
                                            for (i = 1; i < m; i++) {
                                                l = bv[i];
                                                if (l < ns) {
                                                    obj = c[l].negate();
                                                    for (j = 0; j < n; j++)
                                                        a[0][j] = a[0][j].add(obj.times(a[i][j]));
                                                }
                                            }
                                            for (j = 0; j < n; j++)
                                                if (a[0][j].abs().lt(EPSILON))
                                                    a[0][j] = ZERO;
                                            if (red || few)
                                                redundant();
                                            if (output)
                                                str += "Ende Phase I:\n";
                                        }
                                    } else {
                                        str += "Die Rechengrenze wurde überschritten.\n";
                                        numbers("");
                                    }
                                }
                            } else
                                numbers("");
                        } else {
                            str += "Die Rechengrenze wurde überschritten.\n";
                            numbers("");
                        }
                    } else {
                        none = false;
                        k = 0;
                        l = 0;
                        if (output && (nor1 || nor2 || scal))
                            tableau("", 0);
                        norm_scale();
                    }
                    if (solve && !none) {
                        phase1 = false;
                        for (j = 1; j < n && a[0][j].leq(ZERO); j++);
                        if (j < n) {
                            if (hadPhase1) {
                                if (output) {
                                    numbers("");
                                    str += "Phase II:\n";
                                }
                                allp = perts;
                                alls = steps;
                                perts = 0;
                                steps = 0;
                            }
                            loop(false);
                            if (solve) {
                                for (j = 1; j < n && a[0][j].leq(ZERO); j++);
                                if (j < n) {
                                    solve = false;
                                    l = j;
                                    tableau("", 2, true);
                                    str += "Das lineare Programm ist unbeschränkt in Spalte " + (++j) + ".\n";
                                    numbers("");
                                } else {
                                    if (output)
                                        tableau("", 0);
                                    results();
                                }
                            } else
                                numbers("");
                            if (hadPhase1) {
                                perts += allp;
                                steps += alls;
                                numbers(" insgesamt");
                            }
                        } else {
                            k = 0;
                            l = 0;
                            if (output)
                                tableau("", 0);
                            results();
                        }
                    }
                } else {
                    if (m > 1 && !limit) {
                        solve = false;
                        k = 0;
                        l = j - 1;
                        tableau("", 2, true);
                        str += "Das lineare Programm ist unbeschränkt in Spalte " + j + ".\n";
                    }
                    if (prog == 2)
                        opt = (opt == 1) ? 2 : 1;
                }
            }
            if (red || few) {
                if (m == 1) {
                    for (j = 1; j < n && a[0][j].eq(ZERO); j++);
                    if (j < n && a[0][j].gt(ZERO)) {
                        solve = false;
                        k = 0;
                        l = j;
                        tableau("", 2, true);
                        str += "Das lineare Programm ist unbeschränkt in Spalte " + j + ".\n";
                    } else {
                        k = 0;
                        l = 0;
                        perts = 0;
                        steps = 0;
                        if (output)
                            tableau("", 0);
                        results();
                    }
                }
                m = ms;
                n = ns;
                if (cb > 0) {
                    too = (q > 0) ? " ebenfalls" : "";
                    str += (cb == 1) ? "Folgende Zeile ist" : "Folgende Zeilen sind";
                    str += too + " überflüssig:\n";
                    for (j = 0; j < n; j++) {
                        leng[j] = new Array(m);
                        max = 0;
                        for (i = 1; i < m; i++) {
                            tmp = b[i][j];
                            mem = format(tmp).length;
                            if (mem > max)
                                max = mem;
                            leng[j][i] = mem;
                        }
                        maxs[j] = ++max;
                    }
                    for (i = 1; i < m; i++)
                        if (!mbv[i + n - 1]) {
                            for (j = 0; j < n; j++)
                                str += space(maxs[j] - leng[j][i]) + format(b[i][j]);
                            str += "\n";
                        }
                }
                if (!mbv[0])
                    cn--;
                if (cn > 0) {
                    str += (cn == 1) ? "Folgende Variable bedarf" : "Folgende Variablen bedürfen";
                    str += " keiner Nichtnegativitätsbedingung:\n";
                    for (j = 1; j < n; j++)
                        if (!mbv[j])
                            str += j + " ";
                    str += "\n";
                }
            }
            if (solve) {
                q = 0;
                mem = a[0][0];
                for (i = 1; i < m; i++) {
                    if (a[i][0].eq(ZERO)) {
                        v[++q] = bv[i];
                        for (j = 1; j < n; j++)
                            b[q][j] = a[i][j];
                    }
                }
                l = 0;
                for (j = 1; j < n; j++) {
                    u[j] = a[0][j];
                    w[j] = nbv[j];
                    if (u[j].eq(ZERO)) {
                        if (j > ++l) {
                            nbv[l] = nbv[j];
                            for (i = 1; i < m; i++)
                                a[i][l] = a[i][j];
                        }
                        a[0][l] = bigRat(1);
                    }
                }
                if (ble || beq) {
                    none = false;
                    l = 0;
                    x[cj] = x[cj].add(bigRat(1));
                } else
                    none = true;
                if (l > 0) {
                    n = ++l;
                    none = red;
                    output = false;
                    red = false;
                    loop(true);
                    red = none;
                    none = mem.eq(a[0][0]);
                    for (j = 1; j < n && (a[0][j].leq(ZERO) || nbv[j] >= ns); j++);
                    for (i = 1; i < ns; i++)
                        x[i] = ZERO;
                    for (i = 1; i < ms; i++)
                        if (bv[i] < ns)
                            x[bv[i]] = a[i][0];
                    if (scal)
                        for (i = 1; i < ns; i++)
                            x[tab[i]] = x[tab[i]].times(e[tab[i]]);
                    if (none && j < n)
                        none = !decimal(x[nbv[j]] = bigRat(1));
                }
                if (none) {
                    str += (prog == 1) ? "2. primale rationale Lösung: Existiert nicht.\n2. primale Fließkommalösung: Existiert nicht." : "2. duale   rationale Lösung: Existiert nicht.\n2. duale   Fließkommalösung: Existiert nicht.";
                } else {
                    str += (prog == 1) ? "2. primale rationale Lösung: " : "2. duale   rationale Lösung: ";
                    for (j = 1; j < ns; j++)
                        str += format(x[j]) + " ";
                    str += (prog == 1) ? "\n2. primale Fließkommalösung: " : "\n2. duale   Fließkommalösung: ";
                    for (j = 1; j < ns; j++)
                        str += decimal(x[j]) + " ";
                }
                if (ri > 0) {
                    none = false;
                    q = 0;
                    y[ri] = y[ri].add(bigRat(1));
                } else
                    none = true;
                if (q > 0) {
                    m = p;
                    n = ++q;
                    a = new Array(m);
                    a[0] = new Array(n);
                    a[0][0] = mem;
                    for (i = 1; i < m; i++) {
                        a[i] = new Array(n);
                        a[i][0] = u[i].negate();
                        bv[i] = w[i];
                        for (j = 1; j < n; j++)
                            a[i][j] = b[j][i].negate();
                    }
                    for (j = 1; j < n; j++) {
                        nbv[j] = v[j];
                        a[0][j] = bigRat(1);
                    }
                    none = red;
                    output = false;
                    red = false;
                    loop(true);
                    red = none;
                    none = mem.eq(a[0][0]);
                    for (i = 1; i < ms; i++)
                        y[i] = ZERO;
                    for (j = 1; j < n && (a[0][j].leq(ZERO) || nbv[j] < ns); j++);
                    for (i = 1; i < m; i++)
                        if (bv[i] >= ns)
                            y[bv[i] - ns + 1] = a[i][0];
                    if (nor1 || nor2)
                        for (i = 1; i < ms; i++)
                            y[i] = y[i].times(n1[i]);
                    if (nor1 && scal && nor2)
                        for (i = 1; i < ms; i++)
                            y[i] = y[i].times(n2[i]);
                    if (none && j < n)
                        none = !decimal(y[nbv[j] - ns + 1] = bigRat(1));
                }
                if (none) {
                    str += (prog == 1) ? "\n2. duale   rationale Lösung: Existiert nicht.\n2. duale   Fließkommalösung: Existiert nicht." : "\n2. primale rationale Lösung: Existiert nicht.\n2. primale Fließkommalösung: Existiert nicht.";
                } else {
                    str += (prog == 1) ? "\n2. duale   rationale Lösung: " : "\n2. primale rationale Lösung: ";
                    for (i = 1; i < ms; i++)
                        str += format(y[i]) + " ";
                    str += (prog == 1) ? "\n2. duale   Fließkommalösung: " : "\n2. primale Fließkommalösung: ";
                    for (i = 1; i < ms; i++)
                        str += decimal(y[i]) + " ";
                }
            }
        }
        document.ratplex.result.value = str;
        document.getElementById("runtime").textContent = "Laufzeit: " + (performance.now() - t0).toFixed(1) + " ms";
    }
    window.compute = compute;
    window.random = random;
    window.updateThumb = updateThumb;
    window.initBhDeMinplex = initMinplex;
    if (document.readyState === "loading") {
        document.addEventListener("DOMContentLoaded", initMinplex);
    } else {
        initMinplex();
    }
})();