Gleichungen

MATHEMATIK-Lernprogramme
Projekt "Gleichungen"

Primfaktoren, GGT, KGV (zahlen.html)
Rechnen mit Variablen (variable.html)
Lineare Gleichungen (gleichungen2.html)
Lineare Gleichungen (gleichungen3.html)
Eine Gerade in der Ebene (gerade1.html)
Schnitt von zwei Geraden (gerade2.html)
Textgleichungen (textglei1.html)
Textgleichungen (textglei2.html)

Programm starten mit Klick auf einen Programm-Schalter.
Programm beenden mit Klick auf [X] im Dateinamen-Feld
in der ersten Zeile des Internet-Browsers.

<!DOCTYPE html>
<html lang="de">
<head>
<title>zahlen.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="ggt,kgv,Primfaktoren">
<meta name="keywords" content="ggt,kgv,Primfaktoren">

var a,b;    // Aufgaben-Parameter
var a1,a2;  // Antwort-Werte
var r1,r2;  // Lösungen

function primFakt(x) {
  var zahlen = new Array(1000);

function Init() {
    for (var i = 0; i < 1000; i++) { zahlen[i] = 0; }
  }

function ausgabe(j) {
    aus = '';
    for (var i = 1; i < j; i++) { aus = aus + zahlen[i] + '*'; }
    aus = aus.substring(0,aus.length-1);
    return aus; 
  }

function Teiler() {
    while (((x % t) == 0) && (x > 1)) {
      n = n + 1;
      zahlen[n] = t;
      x = (x / t);
    }
  }

Init();

n = 0;
  if (x < 0) { x = -x; }
  m = x / 2;
  t = 2;
  Teiler();
  t = 3;
  do {
    Teiler();
    t = t + 2;
  } while (t <= m);

if (n == 0) { n = 1; zahlen[n] = x; }
  return ausgabe(n+1);
}

function ggt(a,b) {
  let r;
  let x = a;
  let y = b;
  do {
    r = x % y;
    x = y;
    y = r;
  } while (r > 0);
  return x;
}

function kgv(a,b) {
  let x = ggt(a,b);
  let y = a * b / x;
  return y;
}

function showPrim() {
  let x = document.MyForm.ein1.value.trim();
  let y = document.MyForm.ein2.value.trim();
  if (zahlTest(x,y) == - 1) { alert('Eingabefehler - Abbruch !'); return; }
  x = 1 * x;
  y = 1 * y;
  document.MyForm.ein3.value =  primFakt(x);
  document.MyForm.ein4.value =  primFakt(y);
}

function Neu() {
  document.MyForm.reset();
  let z = 2 + 19 * Math.random();
  let p1 = 6 * Math.round(z); 
  document.MyForm.ein1.value = p1;
  z = 2 + 19 * Math.random();
  let p2 = 6 * Math.round(z); 
  document.MyForm.ein2.value = p2;
  document.MyForm.ein3.value = '';
  document.MyForm.ein4.value = '';
  document.MyForm.aus1.value = '';
  document.MyForm.aus2.value = '';
  document.MyForm.erg1.value = '';
  document.MyForm.erg2.value = '';
  document.MyForm.rech.focus();
}

function zahlTest(x,y) {
  if ( (x > 1000000) || (y > 1000000) ) { return -1; }
  if ( (x == '') || (y == '') ) { return -1; }
  if ( isNaN(x) || isNaN(y) ) { return -1; }

x1 = x.includes('-');
  y1 = y.includes('-'); 
  if (x1 || y1) { return -1; }

x1 = x.includes('.');
  y1 = y.includes('.'); 
  if (x1 || y1) { return -1; }
}

</script>
</head>

<body id="body">
<form name="MyForm">
<h2>GGT und KGV</h2>
Gegeben (Zahlen < 1 000 000):<br>
<div id = "eins">
Erste Zahl a =    <input type="text" name="ein1" value="90" size="7" class="cd1"><br> 
Zweite Zahl b = <input type="text" name="ein2" value="60" size="7" class="cd1"><br>
</div>
<br>
<input type="button" name="prim" value="Primfaktoren anzeigen" class="cd2" onclick="showPrim()">
<br>
Primfaktoren von a:<br> 
<input type="text" name="ein3" value="" size="24" class="cd1">
<br> 
Primfaktoren von b:<br>
<input type="text" name="ein4" value="" size="24" class="cd1">
<br><br>
Gesucht:<br>
<div id = "zwei">
GGT(a,b) = <input type=text" name="aus1" value="" size="10" class="cd1"><br>
KGV(a,b) = <input type=text" name="aus2" value="" size="10" class="cd1"><br>
</div>
<br>
<input type="button" name="rech" value="Rechnung überprüfen" class="cd2" onclick="Pruef()">
<br>
GGT <input type=text" name="erg1" value="" size="20" class="cd1" readonly="true"><br>
KGV <input type=text" name="erg2" value="" size="20" class="cd1" readonly="true"><br>
<br>
<input type="button" name="knopf" value="Rechnung wiederholen" class="cd2" onclick=Neu()>
<br>
<span id="last"> GGT(a,b) * KGV(a,b) = a * b </span>
</form>

if (smallScr) { smart(); }

if (!smallScr) { document.addEventListener("contextmenu", (e) => {e.preventDefault()}); }

</script>

</body>
</html>

<!DOCTYPE html>
<html lang = "de">
<head>
<title>variable.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="Variable, Mathematikparser">
<meta name="keywords" content="Variable, Mathematikparser">

function clearVar() {
    a = 0; b = 0; c = 0; d = 0; e = 0; f = 0; g = 0; h = 0; i = 0; j = 0; k = 0; l = 0; m = 0; 
    n = 0; o = 0; p = 0; q = 0; r = 0; s = 0; t = 0; u = 0; v = 0; w = 0; x = 0; y = 0; z = 0;
}

// ------------------------------------------------
// "parser.js", Universeller Mathematik-Parser (HP)
// ------------------------------------------------
// HP0

// 26 einfache Variable
var a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z;

function myTrim(x) { return x.replace(/^\s+|\s+$/gm,'') }
function round2(x) { return Math.round(100*x)/100 }
function round4(x) { return Math.round(10000*x)/10000 }

function fun(s,x)  {
// Ein geparster Funktionterm "s" in nur EINER Variablen x.
   if (s == '') { s = '0'; }
   var t,z;
   t = Parser.parse(s);
   z = t.evaluate({ x: x });
   return z;
}

// --------------------------------------------------------------------------

var Parser = (function (scope) {
  function object(o) {
    function F() {}
    F.prototype = o;
    return new F();
  }

var TNUMBER = 0;
  var TOP1 = 1;
  var TOP2 = 2;
  var TVAR = 3;
  var TFUNCALL = 4;

function Expression(tokens, ops1, ops2, functions) {
    this.tokens = tokens;
    this.ops1 = ops1;
    this.ops2 = ops2;
    this.functions = functions;
  }

// Based on http://www.json.org/json2.js
    var cx = /[\u0000\u00ad\u0600-\u0604\u070f\u17b4\u17b5\u200c-\u200f\u2028-\u202f\u2060-\u206f\ufeff\ufff0-\uffff]/g,
        escapable = /[\\\'\x00-\x1f\x7f-\x9f\u00ad\u0600-\u0604\u070f\u17b4\u17b5\u200c-\u200f\u2028-\u202f\u2060-\u206f\ufeff\ufff0-\uffff]/g,
        meta = { // table of character substitutions
            '\b': '\\b',
            '\t': '\\t',
            '\n': '\\n',
            '\f': '\\f',
            '\r': '\\r',
            "'" : "\\'",
            '\\': '\\\\'
        };

Expression.prototype = {
    simplify: function (values) {
      values = values || {};
      var nstack = [];
      var newexpression = [];
      var n1;
      var n2;
      var f;
      var L = this.tokens.length;
      var item;
      var i = 0;
      for (i = 0; i < L; i++) {
        item = this.tokens[i];
        var type_ = item.type_;
        if (type_ === TNUMBER) {
          nstack.push(item);
        }
        else if (type_ === TVAR && (item.index_ in values)) {
          item = new Token(TNUMBER, 0, 0, values[item.index_]);
          nstack.push(item);
        }
        else if (type_ === TOP2 && nstack.length > 1) {
          n2 = nstack.pop();
          n1 = nstack.pop();
          f = this.ops2[item.index_];
          item = new Token(TNUMBER, 0, 0, f(n1.number_, n2.number_));
          nstack.push(item);
        }
        else if (type_ === TOP1 && nstack.length > 0) {
          n1 = nstack.pop();
          f = this.ops1[item.index_];
          item = new Token(TNUMBER, 0, 0, f(n1.number_));
          nstack.push(item);
        }
        else {
          while (nstack.length > 0) {
            newexpression.push(nstack.shift());
          }
          newexpression.push(item);
        }
      }
      while (nstack.length > 0) {
        newexpression.push(nstack.shift());
      }

return new Expression(newexpression, object(this.ops1), object(this.ops2), object(this.functions));
    },

substitute: function (variable, expr) {
      if (!(expr instanceof Expression)) {
        expr = new Parser().parse(String(expr));
      }
      var newexpression = [];
      var L = this.tokens.length;
      var item;
      var i = 0;
      for (i = 0; i < L; i++) {
        item = this.tokens[i];
        var type_ = item.type_;
        if (type_ === TVAR && item.index_ === variable) {
          for (var j = 0; j < expr.tokens.length; j++) {
            var expritem = expr.tokens[j];
            var replitem = new Token(expritem.type_, expritem.index_, expritem.prio_, expritem.number_);
            newexpression.push(replitem);
          }
        }
        else {
          newexpression.push(item);
        }
      }

var ret = new Expression(newexpression, object(this.ops1), object(this.ops2), object(this.functions));
      return ret;
    },

evaluate: function (values) {
      values = values || {};
      var nstack = [];
      var n1;
      var n2;
      var f;
      var L = this.tokens.length;
      var item;
      var i = 0;
      for (i = 0; i < L; i++) {
        item = this.tokens[i];
        var type_ = item.type_;
        if (type_ === TNUMBER) {
          nstack.push(item.number_);
        }
        else if (type_ === TOP2) {
          n2 = nstack.pop();
          n1 = nstack.pop();
          f = this.ops2[item.index_];
          nstack.push(f(n1, n2));
        }
        else if (type_ === TVAR) {
          if (item.index_ in values) {
            nstack.push(values[item.index_]);
          }
          else if (item.index_ in this.functions) {
            nstack.push(this.functions[item.index_]);
          }
          else {
            // alert('PAU 1');
            return 'NaN';
            throw new Error("undefined variable: " + item.index_);
          }
        }
        else if (type_ === TOP1) {
          n1 = nstack.pop();
          f = this.ops1[item.index_];
          nstack.push(f(n1));
        }
        else if (type_ === TFUNCALL) {
          n1 = nstack.pop();
          f = nstack.pop();
          if (f.apply && f.call) {
            if (Object.prototype.toString.call(n1) == "[object Array]") {
              nstack.push(f.apply(undefined, n1));
            }
            else {
              nstack.push(f.call(undefined, n1));
            }
          }
          else {
            throw new Error(f + " is not a function");
          }
        }
        else {
          throw new Error("invalid Expression");
        }
      }
      if (nstack.length > 1) {
        throw new Error("invalid Expression (parity)");
      }
      return nstack[0];
    },

toString: function (toJS) {
      var nstack = [];
      var n1;
      var n2;
      var f;
      var L = this.tokens.length;
      var item;
      var i = 0;
      for (i = 0; i < L; i++) {
        item = this.tokens[i];
        var type_ = item.type_;
        if (type_ === TNUMBER) {
          nstack.push(escapeValue(item.number_));
        }
        else if (type_ === TOP2) {
          n2 = nstack.pop();
          n1 = nstack.pop();
          f = item.index_;
          if (toJS && f == "^") {
            nstack.push("Math.pow(" + n1 + "," + n2 + ")");
          }
          else {
            nstack.push("(" + n1 + f + n2 + ")");
          }
        }
        else if (type_ === TVAR) {
          nstack.push(item.index_);
        }
        else if (type_ === TOP1) {
          n1 = nstack.pop();
          f = item.index_;
          if (f === "-") {
            nstack.push("(" + f + n1 + ")");
          }
          else {
            nstack.push(f + "(" + n1 + ")");
          }
        }
        else if (type_ === TFUNCALL) {
          n1 = nstack.pop();
          f = nstack.pop();
          nstack.push(f + "(" + n1 + ")");
        }
        else {
          throw new Error("invalid Expression");
        }
      }
      if (nstack.length > 1) {
        throw new Error("invalid Expression (parity)");
      }
      return nstack[0];
    },

variables: function () {
      var L = this.tokens.length;
      var vars = [];
      for (var i = 0; i < L; i++) {
        var item = this.tokens[i];
        if (item.type_ === TVAR && (vars.indexOf(item.index_) == -1)) {
          vars.push(item.index_);
        }
      }

return vars;
    },

toJSFunction: function (param, variables) {
      var f = new Function(param, "with(Parser.values) { return " + this.simplify(variables).toString(true) + "; }");
      return f;
    }
  };

function neg(a) {
    return -a;
  }

function random(a) {
    return Math.random() * (a || 1);
  }
  function fac(a) { //a!
    a = Math.floor(a);
    var b = a;
    while (a > 1) {
      b = b * (--a);
    }
    return b;
  }

function lg(a) {
    return Math.log(a)/Math.log(10);
  }
  
  function rd2(a) {
    return Math.round(100*a)/100;
  }

function rd4(a) {
    return Math.round(10000*a)/10000;
  }
 
  function rad(a) {
    return a * Math.PI / 180;
  }

function deg(a) {
    return a * 180 / Math.PI;
  }

// TODO: use hypot that doesn't overflow
  function pyt(a, b) {
    return Math.sqrt(a * a + b * b);
  }

function append(a, b) {
    if (Object.prototype.toString.call(a) != "[object Array]") {
      return [a, b];
    }
    a = a.slice();
    a.push(b);
    return a;
  }

function Parser() {
    this.success = false;
    this.errormsg = "";
    this.expression = "";

this.pos = 0;

this.tokennumber = 0;
    this.tokenprio = 0;
    this.tokenindex = 0;
    this.tmpprio = 0;

this.ops1 = {
      "sin": Math.sin,
      "cos": Math.cos,
      "tan": Math.tan,
      "asin": Math.asin,
      "acos": Math.acos,
      "atan": Math.atan,
      "sqrt": Math.sqrt,
      "log": Math.log,
      "abs": Math.abs,
      "ceil": Math.ceil,
      "floor": Math.floor,
      "round": Math.round,
      "-": neg,
      "exp": Math.exp
    };

this.ops2 = {
      "+": add,
      "-": sub,
      "*": mul,
      "/": div,
      "%": mod,
      "^": Math.pow,
      ",": append,
      "||": concat
    };

this.functions = {
      "random": random,
      "fac": fac,
      "min": Math.min,
      "max": Math.max,
      "pyt": pyt,
      "pow": Math.pow,
      "atan2": Math.atan2,
      "lg": lg,
      "rd2": rd2,
      "rd4": rd4,
      "rad": rad,
      "deg": deg 
    };

this.consts = {
      "E": Math.E,
      "PI": Math.PI
    };
  }

Parser.parse = function (expr) {
    return new Parser().parse(expr);
  };

Parser.evaluate = function (expr, variables) {
    return Parser.parse(expr).evaluate(variables);
  };

Parser.Expression = Expression;

Parser.values = {
    sin: Math.sin,
    cos: Math.cos,
    tan: Math.tan,
    asin: Math.asin,
    acos: Math.acos,
    atan: Math.atan,
    sqrt: Math.sqrt,
    log: Math.log,
    abs: Math.abs,
    ceil: Math.ceil,
    floor: Math.floor,
    round: Math.round,
    random: random,
    fac: fac,
    exp: Math.exp,
    min: Math.min,
    max: Math.max,
    pyt: pyt,
    pow: Math.pow,
    atan2: Math.atan2,
    lg: lg,
    rd2: rd2, 
    rd4: rd4, 
    rad: rad,
    deg: deg, 
    E: Math.E,
    PI: Math.PI
  };

var PRIMARY  = 1 << 0;
  var OPERATOR = 1 << 1;
  var FUNCTION = 1 << 2;
  var LPAREN   = 1 << 3;
  var RPAREN   = 1 << 4;
  var COMMA    = 1 << 5;
  var SIGN     = 1 << 6;
  var CALL     = 1 << 7;

Parser.prototype = {
    parse: function (expr) {
      this.errormsg = "";
      this.success = true;
      var operstack = [];
      var tokenstack = [];
      this.tmpprio = 0;
      var expected = (PRIMARY | LPAREN | FUNCTION | SIGN);
      var noperators = 0;
      this.expression = expr;
      this.pos = 0;

while (this.pos < this.expression.length) {
        if (this.isOperator()) {
          if (this.isSign() && (expected & SIGN)) {
            if (this.isNegativeSign()) {
              this.tokenprio = 2;
              this.tokenindex = "-";
              noperators++;
              this.addfunc(tokenstack, operstack, TOP1);
            }
            expected = (PRIMARY | LPAREN | FUNCTION | SIGN);
          }
          else if (this.isComment()) {

}
          else {
            if ((expected & OPERATOR) === 0) {
              this.error_parsing(this.pos, "unexpected operator");
            }
            noperators += 2;
            this.addfunc(tokenstack, operstack, TOP2);
            expected = (PRIMARY | LPAREN | FUNCTION | SIGN);
          }
        }
        else if (this.isNumber()) {
          if ((expected & PRIMARY) === 0) {
            this.error_parsing(this.pos, "unexpected number");
          }
          var token = new Token(TNUMBER, 0, 0, this.tokennumber);
          tokenstack.push(token);

expected = (OPERATOR | RPAREN | COMMA);
        }
        else if (this.isString()) {
          if ((expected & PRIMARY) === 0) {
            this.error_parsing(this.pos, "unexpected string");
          }
          var token = new Token(TNUMBER, 0, 0, this.tokennumber);
          tokenstack.push(token);

expected = (OPERATOR | RPAREN | COMMA);
        }
        else if (this.isLeftParenth()) {
          if ((expected & LPAREN) === 0) {
            this.error_parsing(this.pos, "unexpected \"(\"");
          }

if (expected & CALL) {
            noperators += 2;
            this.tokenprio = -2;
            this.tokenindex = -1;
            this.addfunc(tokenstack, operstack, TFUNCALL);
          }

expected = (PRIMARY | LPAREN | FUNCTION | SIGN);
        }
        else if (this.isRightParenth()) {
          if ((expected & RPAREN) === 0) {
            this.error_parsing(this.pos, "unexpected \")\"");
          }

expected = (OPERATOR | RPAREN | COMMA | LPAREN | CALL);
        }
        else if (this.isComma()) {
          if ((expected & COMMA) === 0) {
            this.error_parsing(this.pos, "unexpected \",\"");
          }
          this.addfunc(tokenstack, operstack, TOP2);
          noperators += 2;
          expected = (PRIMARY | LPAREN | FUNCTION | SIGN);
        }
        else if (this.isConst()) {
          if ((expected & PRIMARY) === 0) {
            this.error_parsing(this.pos, "unexpected constant");
          }
          var consttoken = new Token(TNUMBER, 0, 0, this.tokennumber);
          tokenstack.push(consttoken);
          expected = (OPERATOR | RPAREN | COMMA);
        }
        else if (this.isOp2()) {
          if ((expected & FUNCTION) === 0) {
            this.error_parsing(this.pos, "unexpected function");
          }
          this.addfunc(tokenstack, operstack, TOP2);
          noperators += 2;
          expected = (LPAREN);
        }
        else if (this.isOp1()) {
          if ((expected & FUNCTION) === 0) {
            this.error_parsing(this.pos, "unexpected function");
          }
          this.addfunc(tokenstack, operstack, TOP1);
          noperators++;
          expected = (LPAREN);
        }
        else if (this.isVar()) {
          if ((expected & PRIMARY) === 0) {
            this.error_parsing(this.pos, "unexpected variable");
          }
          var vartoken = new Token(TVAR, this.tokenindex, 0, 0);
          tokenstack.push(vartoken);

expected = (OPERATOR | RPAREN | COMMA | LPAREN | CALL);
        }
        else if (this.isWhite()) {
        }
        else {
          if (this.errormsg === "") {
            this.error_parsing(this.pos, "unknown character");
          }
          else {
            this.error_parsing(this.pos, this.errormsg);
          }
        }
      }
      if (this.tmpprio < 0 || this.tmpprio >= 10) {
        this.error_parsing(this.pos, "unmatched \"()\"");
      }
      while (operstack.length > 0) {
        var tmp = operstack.pop();
        tokenstack.push(tmp);
      }
      if (noperators + 1 !== tokenstack.length) {
        //print(noperators + 1);
        //print(tokenstack);
        this.error_parsing(this.pos, "parity");
      }

return new Expression(tokenstack, object(this.ops1), object(this.ops2), object(this.functions));
    },

evaluate: function (expr, variables) {
      return this.parse(expr).evaluate(variables);
    },

error_parsing: function (column, msg) {
      // PAU 2
      alert('Eingabefehler !'); 
      this.success = false;
      this.errormsg = "parse error [column " + (column) + "]: " + msg;
      throw new Error(this.errormsg);
      return;
    },

// \/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

addfunc: function (tokenstack, operstack, type_) {
      var operator = new Token(type_, this.tokenindex, this.tokenprio + this.tmpprio, 0);
      while (operstack.length > 0) {
        if (operator.prio_ <= operstack[operstack.length - 1].prio_) {
          tokenstack.push(operstack.pop());
        }
        else {
          break;
        }
      }
      operstack.push(operator);
    },

isNumber: function () {
      var r = false;
      var str = "";
      while (this.pos < this.expression.length) {
        var code = this.expression.charCodeAt(this.pos);
        if ((code >= 48 && code <= 57) || code === 46) {
          str += this.expression.charAt(this.pos);
          this.pos++;
          this.tokennumber = parseFloat(str);
          r = true;
        }
        else {
          break;
        }
      }
      return r;
    },

// Ported from the yajjl JSON parser at http://code.google.com/p/yajjl/
    unescape: function(v, pos) {
      var buffer = [];
      var escaping = false;

for (var i = 0; i < v.length; i++) {
        var c = v.charAt(i);
  
        if (escaping) {
          switch (c) {
          case "'":
            buffer.push("'");
            break;
          case '\\':
            buffer.push('\\');
            break;
          case '/':
            buffer.push('/');
            break;
          case 'b':
            buffer.push('\b');
            break;
          case 'f':
            buffer.push('\f');
            break;
          case 'n':
            buffer.push('\n');
            break;
          case 'r':
            buffer.push('\r');
            break;
          case 't':
            buffer.push('\t');
            break;
          case 'u':
            // interpret the following 4 characters as the hex of the unicode code point
            var codePoint = parseInt(v.substring(i + 1, i + 5), 16);
            buffer.push(String.fromCharCode(codePoint));
            i += 4;
            break;
          default:
            throw this.error_parsing(pos + i, "Illegal escape sequence: '\\" + c + "'");
          }
          escaping = false;
        } else {
          if (c == '\\') {
            escaping = true;
          } else {
            buffer.push(c);
          }
        }
      }
  
      return buffer.join('');
    },

isString: function () {
      var r = false;
      var str = "";
      var startpos = this.pos;
      if (this.pos < this.expression.length && this.expression.charAt(this.pos) == "'") {
        this.pos++;
        while (this.pos < this.expression.length) {
          var code = this.expression.charAt(this.pos);
          if (code != "'" || str.slice(-1) == "\\") {
            str += this.expression.charAt(this.pos);
            this.pos++;
          }
          else {
            this.pos++;
            this.tokennumber = this.unescape(str, startpos);
            r = true;
            break;
          }
        }
      }
      return r;
    },

isConst: function () {
      var str;
      for (var i in this.consts) {
        if (true) {
          var L = i.length;
          str = this.expression.substr(this.pos, L);
          if (i === str) {
            this.tokennumber = this.consts[i];
            this.pos += L;
            return true;
          }
        }
      }
      return false;
    },

isOperator: function () {
      var code = this.expression.charCodeAt(this.pos);
      if (code === 43) { // +
        this.tokenprio = 0;
        this.tokenindex = "+";
      }
      else if (code === 45) { // -
        this.tokenprio = 0;
        this.tokenindex = "-";
      }
      else if (code === 124) { // |
        if (this.expression.charCodeAt(this.pos + 1) === 124) {
          this.pos++;
          this.tokenprio = 0;
          this.tokenindex = "||";
        }
        else {
          return false;
        }
      }
      else if (code === 42) { // *
        this.tokenprio = 1;
        this.tokenindex = "*";
      }
      else if (code === 47) { // /
        this.tokenprio = 2;
        this.tokenindex = "/";
      }
      else if (code === 37) { // %
        this.tokenprio = 2;
        this.tokenindex = "%";
      }
      else if (code === 94) { // ^
        this.tokenprio = 3;
        this.tokenindex = "^";
      }
      else {
        return false;
      }
      this.pos++;
      return true;
    },

isSign: function () {
      var code = this.expression.charCodeAt(this.pos - 1);
      if (code === 45 || code === 43) { // -
        return true;
      }
      return false;
    },

isPositiveSign: function () {
      var code = this.expression.charCodeAt(this.pos - 1);
      if (code === 43) { // -
        return true;
      }
      return false;
    },

isNegativeSign: function () {
      var code = this.expression.charCodeAt(this.pos - 1);
      if (code === 45) { // -
        return true;
      }
      return false;
    },

isLeftParenth: function () {
      var code = this.expression.charCodeAt(this.pos);
      if (code === 40) { // (
        this.pos++;
        this.tmpprio += 10;
        return true;
      }
      return false;
    },

isRightParenth: function () {
      var code = this.expression.charCodeAt(this.pos);
      if (code === 41) { // )
        this.pos++;
        this.tmpprio -= 10;
        return true;
      }
      return false;
    },

isComma: function () {
      var code = this.expression.charCodeAt(this.pos);
      if (code === 44) { // ,
        this.pos++;
        this.tokenprio = -1;
        this.tokenindex = ",";
        return true;
      }
      return false;
    },

isWhite: function () {
      var code = this.expression.charCodeAt(this.pos);
      if (code === 32 || code === 9 || code === 10 || code === 13) {
        this.pos++;
        return true;
      }
      return false;
    },

isOp1: function () {
      var str = "";
      for (var i = this.pos; i < this.expression.length; i++) {
        var c = this.expression.charAt(i);
        if (c.toUpperCase() === c.toLowerCase()) {
          if (i === this.pos || c < '0' || c > '9') {
            break;
          }
        }
        str += c;
      }
      if (str.length > 0 && (str in this.ops1)) {
        this.tokenindex = str;
        this.tokenprio = 5;
        this.pos += str.length;
        return true;
      }
      return false;
    },

isOp2: function () {
      var str = "";
      for (var i = this.pos; i < this.expression.length; i++) {
        var c = this.expression.charAt(i);
        if (c.toUpperCase() === c.toLowerCase()) {
          if (i === this.pos || c < '0' || c > '9') {
            break;
          }
        }
        str += c;
      }
      if (str.length > 0 && (str in this.ops2)) {
        this.tokenindex = str;
        this.tokenprio = 5;
        this.pos += str.length;
        return true;
      }
      return false;
    },

isVar: function () {
      var str = "";
      for (var i = this.pos; i < this.expression.length; i++) {
        var c = this.expression.charAt(i);
        if (c.toUpperCase() === c.toLowerCase()) {
          if (i === this.pos || c < '0' || c > '9') {
            break;
          }
        }
        str += c;
      }
      if (str.length > 0) {
        this.tokenindex = str;
        this.tokenprio = 4;
        this.pos += str.length;
        return true;
      }
      return false;
    },

isComment: function () {
      var code = this.expression.charCodeAt(this.pos - 1);
      if (code === 47 && this.expression.charCodeAt(this.pos) === 42) {
        this.pos = this.expression.indexOf("*/", this.pos) + 2;
        if (this.pos === 1) {
          this.pos = this.expression.length;
        }
        return true;
      }
      return false;
    }
  };

scope.Parser = Parser;
  return Parser
})(typeof exports === 'undefined' ? {} : exports);

// -------------------------------------------------------------------------
// HP, Ende von "parser.js"
// -------------------------------------------------------------------------
// HP0

var hide = true;

function Calcul() {
  var s,t,x,y,z;

a = 1 * document.MyForm.ein1.value.trim();
  b = 1 * document.MyForm.ein2.value.trim();
  c = 1 * document.MyForm.ein3.value.trim();
  d = 1 * document.MyForm.ein4.value.trim();
  e = 1 * document.MyForm.ein5.value.trim();
  setValues('a',a);
  setValues('b',b);
  setValues('c',c);
  setValues('d',d);
  setValues('e',e);
// alert(a + ' / ' + b + ' / ' + c + ' / ' + d + ' / ' + e);

z = document.MyForm.aus.value;
  x = z.includes('yes');
  if (x) { return; }
  x = z.includes('no');
  if (x) { return; }

s = document.MyForm.ein.value.trim();
  if (s == '') {document.MyForm.ein.value = '0'; }
  y = formel(s);
  // alert(s + ' / ' + y);

t = 1 * document.MyForm.aus.value.trim();
  // alert(y + ' / ' + t);

if (y != t) { document.MyForm.aus.value = t + ' [no] => ' + y; }
  else { document.MyForm.aus.value = y + ' [yes]'; }
}

function Clear() {
  document.MyForm.ein.value = '';
  document.MyForm.aus.value = '';
}

function ClearAll(){
  document.MyForm.ein.value = '';
  document.MyForm.aus.value = '';
  document.MyForm.ein1.value = '';
  document.MyForm.ein2.value = '';
  document.MyForm.ein3.value = '';
  document.MyForm.ein4.value = '';
  document.MyForm.ein5.value = '';
}

function Var1(){
  ClearAll();
  let x = Math.floor(10 * Math.random());
  let y = Math.floor(10 * Math.random());
  let z = Math.floor(10 * Math.random());
  let u = Math.floor(10 * Math.random());
  a = x.toString();
  b = y.toString();
  c = z.toString();
  d = z.toString();
  document.MyForm.ein1.value = a;
  document.MyForm.ein2.value = b;
  document.MyForm.ein3.value = c;
  document.MyForm.ein4.value = d;
  document.MyForm.ein.value = '2*a - 4*b + 3*c - d';
}

function Var2(){
  ClearAll();
  let x = Math.floor(10 * Math.random());
  let y = Math.floor(10 * Math.random());
  let z = Math.floor(10 * Math.random());
  a = x.toString();
  b = y.toString();
  c = z.toString();
  document.MyForm.ein1.value = a;
  document.MyForm.ein2.value = b;
  document.MyForm.ein3.value = c;
  document.MyForm.ein.value = 'a*(b - c)';
  document.MyForm.aus.focus();
}

function Var3(){
  ClearAll();
  let x = Math.floor(10 * Math.random());
  let y = Math.floor(10 * Math.random());
  a = x.toString();
  b = y.toString();
  document.MyForm.ein1.value = a;
  document.MyForm.ein2.value = b;
  document.MyForm.ein.value = '(a + b) * (a - b)';
}

function Var4(){
  ClearAll();
  let arr = [1,2,3,4,5,6,7,8,9,10];
  let len = arr.length;
  n = Math.floor(len * Math.random());
  x = arr[n];
  a = x.toString();
  // alert(n + ' : ' + a);
  document.MyForm.ein1.value = a;
  document.MyForm.ein.value = 'a^2 + 3';
}

function Var5(){
  ClearAll();
  let arr = [1,4,9,16,25,36,49,64,81,100];
  let len = arr.length;
  n = Math.floor(len * Math.random());
  x = arr[n];
  a = x.toString();
  // alert(n + ' : ' + a);
  document.MyForm.ein1.value = a;
  document.MyForm.ein.value = '3 * sqrt(a)';
}

function Var6(){
  ClearAll();
  let arr = [1,2,3,4,5,6,7,8,9,10];
  let len = arr.length;
  n = Math.floor(len * Math.random());
  x = arr[n];
  a = x.toString();
  // alert(n + ' : ' + a);
  document.MyForm.ein1.value = a;
  document.MyForm.ein.value = 'sqrt(a^2)';
}

function Var7(){
  ClearAll();
  let arr = [1,2,3,4,5,6,7,8,9,10];
  let len = arr.length;
  n = Math.floor(len * Math.random());
  x = arr[n];
  a = x.toString();
  n = Math.floor(len * Math.random());
  x = arr[n];
  b = x.toString();
  // alert(n + ' : ' + a);
  document.MyForm.ein1.value = a;
  document.MyForm.ein2.value = b;
  document.MyForm.ein.value = '(a - b)^2';
}

function Var8(){
  ClearAll();
  let arr = [2,4,6,8,10];
  let len = arr.length;
  n = Math.floor(len * Math.random());
  x = arr[n];
  a = x.toString();
  // alert(n + ' : ' + a);
  document.MyForm.ein1.value = a;
  document.MyForm.ein.value = '(a/2)^2 - a';
}

function Var9(){
  ClearAll();
  let arr = [2,4,6,8,10];
  let len = arr.length;
  n = Math.floor(len * Math.random());
  x = arr[n];
  a = x.toString();
  n = Math.floor(len * Math.random());
  x = arr[n];
  b = x.toString();
  // alert(n + ' : ' + a);
  document.MyForm.ein1.value = a;
  document.MyForm.ein2.value = b;
  document.MyForm.ein.value = '(a/2)^2 - (b/2)^2';
}

</script>
</head>

<body id="body">
<form name="MyForm">
<h2>Rechnen mit Variablen</h2> 
Eingabe von fünf Variablen oder<br>
[A1], [A2], [A3], ........... [A8], [A9].<br>
Dann den Term ausrechnen und<br>
in das Result-Feld schreiben und<br>
zuletzt mit [Test] überprüfen. Die<br>
Results sind auf 16 Stellen gerundet.<br>
Leere Results sind immer Null und <br>
"NaN" bedeutet "not a number".<br>
<br>
a: <input type="text" name="ein1" value="" size="8" class="cd1"><br>
b: <input type="text" name="ein2" value="" size="8" class="cd1"><br> 
c: <input type="text" name="ein3" value="" size="8" class="cd1"><br>
d: <input type="text" name="ein4" value="" size="8" class="cd1"><br>
e: <input type="text" name="ein5" value="" size="8" class="cd1"><br>
<br>
<input type="button" name="btn" value="A1" class="cd2" onclick="Var1()"> 
<input type="button" name="btn" value="A2" class="cd2" onclick="Var2()"> 
<input type="button" name="btn" value="A3" class="cd2" onclick="Var3()"> 
<input type="button" name="btn" value="A4" class="cd2" onclick="Var4()"> 
<input type="button" name="btn" value="A5" class="cd2" onclick="Var5()"> 
<input type="button" name="btn" value="A6" class="cd2" onclick="Var6()"> 
<input type="button" name="btn" value="A7" class="cd2" onclick="Var7()"> 
<input type="button" name="btn" value="A8" class="cd2" onclick="Var8()"> 
<input type="button" name="btn" value="A9" class="cd2" onclick="Var9()"> 
<br><br>
Term:   <input type="text" name="ein" value="" size="30" class="cd1"><br>
Result: <input type="text" name="aus" value=" " size="30" class="cd1"><br>
<br>
<input type="button" name="btn" value="Test" class="cd2" onclick="Calcul()">  
<input type="button" name="btn" value="Clear(Term,Res)" class="cd2" onclick="Clear()">  
<input type="button" name="btn" value="ClearAll" class="cd2" onclick="ClearAll()">  
<input type="button" name="btn" value="Info e/a" class="cd2" onclick="Info()"><br>
<br>
<div id='inf'> 
<font color = "black">
--------------------------------------------------------------<br>
Der universelle Mathematik-Parser erlaubt die<br>
Eingabe von 26 numerischen Variablen (a,b,...z)<br>
und einem String s als Term. Dieser wird mt<br>
"[Test]" ausgewertet und das entsprechende<br>
Resultat wird angezeigt. Im Programm hier<br>
werden nur die 5 Variablen a,b c d,e verwendet.<br>
Alle Variable müssen klein geschrieben werden,<br>
ausgenommen die zwei Konstanten PI und E. <br>
<br>
<font color = "red">
Folgende Operatoren stehen zur Verfügung:<br>
</font>
(, ), +, -, *, /, ^, sqrt, % = Rest, fac = Faktorielle,<br>
round, rd2, rd4, floor, abs, exp, log, lg, deg, rad, sin,<br>
cos, tan, asin, acos, atan, atan2(y,x) = Steigungs-<br>
winkel, random(x) = Zufallszahlen in [0,x), PI, E.<br>
("Infinity" = Unendlich, "NaN" = Not a Number).<br>
<br>
Beispiele;
<br>
a % b, sin(rad(x)), deg(asin(x)), deg(atan2(a,b)),<br>
sqrt(x), log(x), exp(x). Grundsätzlich werden<br>
Winkelfunktionen in Radianten berechnet.<br>
"deg(x)" wandelt Radianten in Grade um.<br>
"rad(x)" wandelt Grade in Radianten um.<br>
<br>
<font color = "red">Beispiel 1:</font><br>
Eingabe der Variablen a = 3 und b = 4. <br>
Formeleingabe "sqrt(a^2 + b^2)" und "[Test]".<br>
<font color = "red">Beispiel 2:</font><br>
Eingabe der Variablen a = 90. <br>
Formeleingabe "sin(rad(a))" und "[Test]".<br>
--------------------------------------------------------------<br>
© Herbert Paukert
</font>
<br>
</div>
<script>
  var smallWidth = 800;
  var scrWidth = window.screen.width;
  var smallScr = false;
  if (scrWidth <= smallWidth) { smallScr = true; }

if (smallScr) { smart(); }

if (!smallScr) { document.addEventListener("contextmenu", (e) => {e.preventDefault()}); }

</script>
</form>
</body>
</html>

<!DOCTYPE html>
<html lang="de">
<head>
<title>gleichungen2.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="Lineare 2x2-Systeme">

function closeChild() {
// Hilfetext schließen 
   if (!childWindow || childWindow.closed) { return; }
   if (child) { childWindow.document.close(); childWindow.close(); }
}

function info() {
// Hilfetext anzeigen 
     if (child) { closeChild(); child = false; return; }
     child = true;
     childWindow = window.open('','childWindow','top=20, left=600, width=560, height=720, srollbars=yes, menubar=no, toolbar=no');
     childWindow.document.open();
     childWindow.document.write('<html><head><meta name="viewport" content="width=device-width, initial-scale=0.9"></head>');
     childWindow.document.write('<html><head></head><body style="id: base; background-color:#FFFFE8; font-family:Calibri,Arial; font-size:15px; text-size-adjust:none; margin-left:30px; margin-bottom:30px;">');
     childWindow.document.write('<br><input type="button" value="Print" onclick="print();"><br><br>')
     childWindow.document.write('<b>Lineares Gleichungssystem in 2 Variablen</b><br><br>');
     childWindow.document.write('<b>Musteraufgabe:</b><br>');
     childWindow.document.write('Gleichung ( I) 1 * X + 2 * Y = 3<br>');
     childWindow.document.write('Gleichung (II) 3 * X + 2 * Y = 1<br><br>');
     childWindow.document.write('<b><i>Die Einsetzungsmethode in 6 Lösungsschritten:</i></b><br><br>');
     childWindow.document.write('<b><i>1. Lösungschritt: X aus (I) explizit darstellen.</i></b><br>');
     childWindow.document.write('(I) 1 * X + 2 * Y = 3<br>');
     childWindow.document.write('(I) X = 3 - 2 * Y<br><br>');
     childWindow.document.write('<b><i>2. Lösungsschritt: X in (II) einsetzen.</i></b><br>');
     childWindow.document.write('(II) 3 * ( 3 - 2 * Y) + 2 * Y = 1<br><br>');
     childWindow.document.write('<b><i>3. Lösungsschritt: Gleichung (II) vereinfachen.</i></b><br>');
     childWindow.document.write('(II) 9 - 6 * Y + 2 * Y = 1<br>');  
     childWindow.document.write('(II) 9 - 4 * Y = 1<br>');
     childWindow.document.write('(II)-4 * Y = - 8<br>');
     childWindow.document.write('(II)<b> Y = 2</b><br><br>');
     childWindow.document.write('<b><i>4. Lösungsschritt: Y in (I) zurück einsetzen.</i></b><br>');
     childWindow.document.write('(I) 1 * X + 2 * 2 = 3<br>');
     childWindow.document.write('(I) X + 4 = 3<br>');
     childWindow.document.write('(I)<b> X = -1</b><br><br>');
     childWindow.document.write('<b><i>5. Die Lösungen  anschreiben.</i></b><br>');
     childWindow.document.write('Lösungen: X = -1, Y = 2<br><br>');
     childWindow.document.write('<b><i>6. Lösungsschritt: Die Probe durchführen.</i></b><br>');
     childWindow.document.write('(I) 1 * X + 2 * Y = 3, -1 + 4 = 3, 3 = 3<br>');
     childWindow.document.write('(II) 3 * X + 2 * Y = 1, -3 + 4 = 1, 1 = 1<br><br>');
     childWindow.document.write('</body></html>');
}

function myTrim(x) { return x.replace(/^\s+|\s+$/gm,'') }
function round2(x) { return Math.round(100*x)/100 }
function round4(x) { return Math.round(10000*x)/10000 }

n = 3;
// Erster Lösungsvektor
var L1xy = new Array(n);
L1xy[0] = 0;
L1xy[1] = 0;
L1xy[2] = 0;
L1xy[3] = 0;

// Zweiter Lösungsvektor
var L2xy = new Array(n);
L2xy[0] = 0;
L2xy[1] = 0;
L2xy[2] = 0;
L2xy[3] = 0;

// mehrdimensionale (n)x(n+1)-Matrix
var mat = new Array(n);
for (var i = 0; i <= n+1; i++) { mat[i]= new Array(n+1); }

var error = -999;

// die i-te zeile mit der m-ten zeile tauschen 
          if (i != m) {
             for (var j = i; j <= n+1; j++) {
                 s = a[i][j];
                 a[i][j] = a[m][j];
                 a[m][j] = s;
             }
         }
      }
  // elimination von x[i] aus der k-ten gleichung 
      for (var k = i+1; k <= n; k++) {
         if (a[i][i] == 0) { error = -999; x[0] = error; return error; }
         s = a[k][i] / a[i][i];
         for (var j = i+1; j <= n+1; j++) {
         a[k][j]= a[k][j]-a[i][j]*s;
         } 
      }
   }
  // eigentliche berechnung der lösungen    
   for (var i = n; i >= 1; i = i-1) {
   s = a[i][n+1];
   for (var j = i+1; j <= n; j++) { s = s - a[i][j]*x[j]; }
   if (a[i][i] == 0) { error = -999; x[0] = error; return error; }
   x[i]= s / a[i][i];
   }
   L1xy = x;
}

function matInit() { 
  for (var i = 0; i <= 3; i++) { L1xy[i] = 0; }  
  mat[1][1] = 1*document.MyForm.ein1.value;  
  mat[1][2] = 1*document.MyForm.ein2.value;
  mat[1][3] = 1*document.MyForm.ein3.value;
  mat[2][1] = 1*document.MyForm.ein4.value;
  mat[2][2] = 1*document.MyForm.ein5.value; 
  mat[2][3] = 1*document.MyForm.ein6.value;
}

var a1, a2;  // Antworten
var r1, r2;  // Lösungen
var z1, z2;  // Ausgaben
var erg;

function Pruef() {
matInit();
a1 = document.MyForm.aus1.value; 
a2 = document.MyForm.aus2.value;

erg = deta(mat,2);
erg = round2(erg);
document.MyForm.erg0.value = erg;
if ((erg == 0) || (erg == -999)) { 
   document.MyForm.erg0.value = '0';
   document.MyForm.erg1.value = '';
   document.MyForm.erg2.value = '';
   alert('System NICHT lösbar !');
   return;
}

linglei(mat,2,L1xy);
if (L1xy[0] == -999){ 
   document.MyForm.erg0.value = '0';
   document.MyForm.erg1.value = '';
   document.MyForm.erg2.value = '';
   alert('System NICHT lösbar !');
   return;
}
 
r1 = round2(L1xy[1]);
r2 = round2(L1xy[2]);

document.MyForm.aus1.value = '';
document.MyForm.aus2.value = '';
document.MyForm.erg1.value = '';
document.MyForm.erg2.value = '';
document.MyForm.erg0.value = '';
document.MyForm.rech.focus();
}

function Reset() {
document.MyForm.reset();
location.load();
}
</script>
</head>

<body id="body">
<form name="MyForm">
<h3>Lineare Gleichungssysteme<br>
mit zwei Variablen</h3>
Die Lösungen sind auf Papier zu ermitteln,<br>
auf zwei Dezimalstellen zu runden, und dann<br>
in die entsprechenden Felder zu schreiben.<br>
<br>
<font color = "darkblue">
<input type="text" name="ein1" value="1" size="3" class="cd1"> * X   +   
<input type="text" name="ein2" value="2" size="3" class="cd1"> * Y   =   
<input type="text" name="ein3" value="3" size="3" class="cd1"> <br>
<input type="text" name="ein4" value="3" size="3" class="cd1"> * X   +   
<input type="text" name="ein5" value="2" size="3" class="cd1"> * Y   =   
<input type="text" name="ein6" value="1" size="3" class="cd1"> <br>
<br>
Lösung X:  <input type=text" name="aus1" value="" size="6" class="cd1"><br> 
Lösung Y:  <input type=text" name="aus2" value="" size="6" class="cd1"> 
</font>
<br><br>
<input type="button" name="rech" value="Rechnung überprüfen" class="cd2" onclick="Pruef()"> <br>
<br>
Determinante: <input type=text" name="erg0" value="" size="15" class="cd1" readonly="true"><br>
<br>
Ergebnis X: <input type=text" name="erg1" value="" size="15" class="cd1" readonly="true"><br>
Ergebnis Y: <input type=text" name="erg2" value="" size="15" class="cd1" readonly="true"><br>
<br>
<input type="button" name="knopf" value="Rechnung wiederholen" class="cd2" onclick="Neu()"><br>
<br>
<input type = "button" value="Info e/a" onclick="info()" class="cd2"/>   
<input type="button" name="knopf" value="Reset" class="cd2" onclick="Reset()">
</form>
<script>
  var smallWidth = 800;
  var scrWidth = window.screen.width;
  var smallScr = false;
  if (scrWidth <= smallWidth) { smallScr = true; }

if (smallScr) { smart(); }

if (!smallScr) { document.addEventListener("contextmenu", (e) => {e.preventDefault()}); }

document.MyForm.rech.focus();
</script>

</body>
</html>

<!DOCTYPE html>
<html lang="de">
<head>
<title>gleichungen3.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="Lineare 3x3-Systeme">

n = 3;
// Erster Lösungsvektor
var L1xy = new Array(n);
L1xy[0] = 0;
L1xy[1] = 0;
L1xy[2] = 0;
L1xy[3] = 0;

// Zweiter Lösungsvektor
var L2xy = new Array(n);
L2xy[0] = 0;
L2xy[1] = 0;
L2xy[2] = 0;
L2xy[3] = 0;

// mehrdimensionale (n)x(n+1)-Matrix
var mat = new Array(n);
for (var i = 0; i <= n+1; i++) { mat[i]= new Array(n+1); }

var error = -999;

mat[2][1] = 1*document.MyForm.ein5.value;
  mat[2][2] = 1*document.MyForm.ein6.value; 
  mat[2][3] = 1*document.MyForm.ein7.value;
  mat[2][4] = 1*document.MyForm.ein8.value;

mat[3][1] = 1*document.MyForm.ein9.value;
  mat[3][2] = 1*document.MyForm.ein10.value; 
  mat[3][3] = 1*document.MyForm.ein11.value;
  mat[3][4] = 1*document.MyForm.ein12.value;
}

var a1, a2, a3;  // Antworten
var r1, r2, r3;  // Lösungen
var z1, z2, z3;  // Ausgaben
var erg;

function Pruef() {
matInit();

a1 = document.MyForm.aus1.value; 
a2 = document.MyForm.aus2.value; 
a3 = document.MyForm.aus3.value;

erg = deta(mat,3);
erg = round2(erg);
document.MyForm.erg0.value = erg;
if ((erg == 0) || (erg == -999)) { 
   document.MyForm.erg0.value = '0';
   document.MyForm.erg1.value = '';
   document.MyForm.erg2.value = '';
   document.MyForm.erg3.value = '';
   alert('System NICHT lösbar !');
   return;
}

linglei(mat,3,L1xy);
if (L1xy[0] == -999){ 
   document.MyForm.erg0.value = '0';
   document.MyForm.erg1.value = '';
   document.MyForm.erg2.value = '';
   document.MyForm.erg3.value = '';
   alert('System NICHT lösbar !');
   return;
}

r1 = round2(L1xy[1]);
r2 = round2(L1xy[2]);
r3 = round2(L1xy[3]);

if (myTrim(a1) == r1) { z1 = 'richtig' } else { z1 = 'falsch (' + r1 + ')' };
document.MyForm.erg1.value = z1;
if (myTrim(a2) == r2) { z2 = 'richtig' } else { z2 = 'falsch (' + r2 + ')' };
document.MyForm.erg2.value = z2;
if (myTrim(a3) == r3) { z3 = 'richtig' } else { z3 = 'falsch (' + r3 + ')' };
document.MyForm.erg3.value = z3;
document.MyForm.rech.focus();
}

function Neu() {
document.MyForm.ein1.value = Math.round(9 * Math.random());
document.MyForm.ein2.value = Math.round(9 * Math.random());
document.MyForm.ein3.value = Math.round(9 * Math.random());
document.MyForm.ein4.value = Math.round(9 * Math.random());
document.MyForm.ein5.value = Math.round(9 * Math.random());
document.MyForm.ein6.value = Math.round(9 * Math.random());
document.MyForm.ein7.value = Math.round(9 * Math.random());
document.MyForm.ein8.value = Math.round(9 * Math.random());
document.MyForm.ein9.value = Math.round(9 * Math.random());
document.MyForm.ein10.value = Math.round(9 * Math.random());
document.MyForm.ein11.value = Math.round(9 * Math.random());
document.MyForm.ein12.value = Math.round(9 * Math.random());
document.MyForm.aus1.value = '';
document.MyForm.aus2.value = '';
document.MyForm.aus3.value = '';
document.MyForm.erg0.value = '';
document.MyForm.erg1.value = '';
document.MyForm.erg2.value = '';
document.MyForm.erg3.value = '';
document.MyForm.rech.focus();
}

function Reset() {
document.MyForm.reset();
location.load();
}

</script>
</head>

<body id="body">
<form name="MyForm">
<h3>Lineare Gleichungssysteme<br>
mit drei Variablen</h3>
Die Lösungen sind auf Papier zu ermitteln,<br>
auf zwei Dezimalstellen zu runden, und dann<br>
in die entsprechenden Felder zu schreiben.<br>
<br>
<font color = "darkblue">
<input type="text" name="ein1" value="1" size="3" class="cd1"> * X   +   
<input type="text" name="ein2" value="2" size="3" class="cd1"> * Y   +   
<input type="text" name="ein3" value="2" size="3" class="cd1"> * Z   =   
<input type="text" name="ein4" value="3" size="3" class="cd1"> <br>
<input type="text" name="ein5" value="3" size="3" class="cd1"> * X   +   
<input type="text" name="ein6" value="0" size="3" class="cd1"> * Y   +   
<input type="text" name="ein7" value="2" size="3" class="cd1"> * Z   =   
<input type="text" name="ein8" value="1" size="3" class="cd1"> <br>
<input type="text" name="ein9" value="0" size="3" class="cd1"> * X   +   
<input type="text" name="ein10" value="1" size="3" class="cd1"> * Y   +   
<input type="text" name="ein11" value="2" size="3" class="cd1"> * Z   =   
<input type="text" name="ein12" value="0" size="3" class="cd1"> <br>
<br>
Lösung X:  <input type=text" name="aus1" value="" size="8" class="cd1"><br>
Lösung Y:  <input type=text" name="aus2" value="" size="8" class="cd1"><br>
Lösung Z:  <input type=text" name="aus3" value="" size="8" class="cd1"> <br>
</font>
<br>
<input type="button" name="rech" value="Rechnung überprüfen" class="cd2" onclick="Pruef()"> <br>
<br>
Determinante:  <input type=text" name="erg0" value="" size="12" class="cd1" readonly="true"><br>
Ergebnis X:  <input type=text" name="erg1" value="" size="15" class="cd1" readonly="true"><br>
Ergebnis Y:  <input type=text" name="erg2" value="" size="15" class="cd1" readonly="true"><br>
Ergebnis Z:  <input type=text" name="erg3" value="" size="15" class="cd1" readonly="true"><br>
<br>
<input type="button" name="knopf" value="Rechnung wiederholen" class="cd2" onclick="Neu()"><br>
<br>
<input type="button" name="knopf" value="Reset" class="cd2" onclick="Reset()">
</form>
<script>
  var smallWidth = 800;
  var scrWidth = window.screen.width;
  var smallScr = false;
  if (scrWidth <= smallWidth) { smallScr = true; }

if (smallScr) { smart(); }

if (!smallScr) { document.addEventListener("contextmenu", (e) => {e.preventDefault()}); }

document.MyForm.rech.focus();
</script>
</body>
</html>

<!DOCTYPE html>
<html lang="de">
<head>
<title>gerade1.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="Gerade in der Ebene">

var fSign = 1;      // Funktions-Vorzeichen
  var xMin = -kw;     // Startpunkt der Funktion
  var xMax = kw;      // Endpunkt der Funktion
  var xStep = 1/100;  // Schrittweite der Funktion
  var fCol = 'red';   // Farbe der Funktion
  var fText = ' ';    // Name der Funktion

var P1 = new TPoint;
  var A = new TPoint;
  var B = new TPoint;
   
  function round2(x) { return Math.round(100*x)/100 }

function TPoint(tx,ty) {
    // Konstruktor fuer das Punkt-Objekt (zweidimensional)
    this.x = tx;
    this.y = ty;
    this.len = function() {
       z = Math.sqrt(this.x*this.x + this.y*this.y); 
       return z.toFixed(2);
     }
  }

function w2p(W,kw,kb) {
    // WeltzuBild-Transformation von Weltpunkt W auf Bildpunkt P
    P = new TPoint;
    P.x = round2((W.x + kw) * kb / (2*kw));
    P.y = round2(kb - (W.y + kw) * kb / (2*kw));
    return P;
  }

function p2w(P,kw,kb) {
    // BildzuWelt-Transformation von Bildpunkt P auf Weltpunkt W
    // Inverse Transformation zu "w2p(W,kw,kb)"
    W = new TPoint;
    W.x = round2(P.x*2*kw/kb - kw);
    W.y = round2((kb - P.y)*2*kw/kb - kw);
    return W;
  }

function changeKS(x) {
    // Aenderung der Halbbreite kw des Welt-Koordinatensystems
    kw = x;
    xMin = -kw;
    xMax = kw;
    initCanvas();    
  }

function initCanvas() {
    // Canvas initialisieren
    canvas = document.getElementById('MyCanvas');
    ctx = canvas.getContext('2d');
    ctx.lineWidth = 2;
    ctx.fillStyle = "white";
    ctx.fillRect(0,0,kb,kb);
    ctx.strokeStyle = "black";
    ctx.strokeRect(0,0,kb,kb);
    drawCoord2(kw,kb); 
    document.MyForm.aus9.value = '';
  }

function drawWidth(f) {
    // Liniendicke
    var canvas = document.getElementById('MyCanvas');
    var ctx = canvas.getContext('2d');
    ctx.lineWidth = f; 
  }

function drawColor(f) {
    // Linienfarbe
    var canvas = document.getElementById('MyCanvas');

var ctx = canvas.getContext('2d');
    ctx.strokeStyle = f;
  }

function drawLine(R9,S9) {
    //  Strecke durch die Punkte R9 und S9 zeichnen
    var canvas = document.getElementById('MyCanvas');
    var ctx = canvas.getContext('2d');
    var U1 = new TPoint;
    var V1 = new TPoint;
    U1 = R9;
    V1 = S9;
    U1 = w2p(U1,kw,kb);
    V1 = w2p(V1,kw,kb);
    ctx.beginPath();
//  ctx.strokeStyle = "black"
    ctx.moveTo(U1.x,U1.y);
    ctx.lineTo(V1.x,V1.y);
    ctx.stroke();
    ctx.closePath();
  }

function drawPoint(tex,P) {
    // Punkt P zeichnen und mit tex beschriften
    var Q = new TPoint;
    Q = w2p(P,kw,kb);
    var r = 3;
    ctx.font = 'bold 14px Arial';
    ctx.fillStyle = "black";
    ctx.beginPath();
    ctx.arc(Q.x,Q.y,r,0,2*Math.PI);
    ctx.fill();
    drawPosText(P.x,P.y,tex)
  }

function drawPosText(x,y,tex) {
  // Text positioniert ausgeben
    ctx.font = 'bold 13pt Arial';
    var P = new TPoint;
    P.x = x;
    P.y = y;
    P = w2p(P,kw,kb);
    ctx.fillStyle = "black";
    ctx.fillText(tex,P.x+5,P.y+10);
  }

function drawWidth(f) {
    // Liniendicke
    var canvas = document.getElementById('MyCanvas');
    var ctx = canvas.getContext('2d');
    ctx.lineWidth = f; 
  }

function drawColor(f) {
    // Linienfarbe
    var canvas = document.getElementById('MyCanvas');
    var ctx = canvas.getContext('2d');
    ctx.strokeStyle = f;
  }

function drawRect(x1,y1,x2,y2,farbe) {
    // Rechteck (Schriftbereich) in der Grafik lÃ¶schen
    var W1 = new TPoint;
    var W2 = new TPoint;
    var P1 = new TPoint;
    var P2 = new TPoint;
    W1.x = x1;
    W1.y = y1;
    W2.x = x2;
    W2.y = y2;
    P1 = w2p(W1,kw,kb);
    P2 = w2p(W2,kw,kb);
    ctx.fillStyle = farbe;
    ctx.fillRect(P1.x,P1.y,P2.x,P2.y);
  }

function fun(x) {
    // Funktion festlegen
    fSign = 1;
    y = k*x + d;
    return y;
  }

function drawCoord2(kw,kb) {
    // Koordinatensystem zeichnen (2-dimensional)
    var g,h;
    ctx.strokeStyle = "black";
    ctx.strokeRect(0,0,kb,kb);     
    ctx.font = '10pt Arial';
    ctx.beginPath();
    g = kb / 2; 
    ctx.lineWidth = 1;
    ctx.strokeStyle = "blue";
    ctx.moveTo(0,g);
    ctx.lineTo(2*g,g);
    ctx.moveTo(g,0);
    ctx.lineTo(g,2*g);
    ctx.stroke();
    h = g / kw;
    ctx.fillStyle = "blue";
    ctx.fillText('0',g+2,g+10);
    ctx.fillText('1',g+h,g+10);
    ctx.fillText(-kw,5,g+10);
    ctx.fillText(kw,2*g-20,g+10);
    ctx.fillText(kw,g+5,15);
    ctx.fillText(-kw,g+5,2*g-10);
    ctx.strokeStyle = "black";
  }

function showPos(ev) {
    // Angeklickte Koordinaten anzeigen
    var P = new TPoint;
    var cRect = document.getElementById("dc").getBoundingClientRect();
    var cTop  = cRect.top;
    var cLeft = cRect.left;
    P.x = (ev.clientX - cLeft);
    P.y = (ev.clientY - cTop);
    var W = new TPoint;
    W = p2w(P,kw,kb);
    var info = round2(W.x) + '  /  ' + round2(W.y);
    document.MyForm.aus9.value = info;
  }

function Reset() {
    // Formular initialisieren
    document.MyForm.reset();
    kw = 10;
    xMin = -kw;
    xMax = kw;
    fNum = 0;
    initCanvas(); 
    window.scroll(0,0);
  }

// ----------------------------------------------------------------------------

var neu = false;
var fall = 1;
var k,d;
var a1,a2,b1,b2;

function Pruef() {
let info = 'Fall 1: g(a,b,c)\nFall 2: g(A,B)\n(1) oder (2) wählen';
let s = '1';
fall = prompt(info,s);
let wahl = ((fall == '1') || (fall == '2'));
if (!wahl) { alert('Falsche Eingabe !'); return; }

if (fall == '1') {
  let a = document.MyForm.ein1.value.trim();
  let b = document.MyForm.ein2.value.trim();
  if (a == '') { k = 1; document.MyForm.ein1.value = k; }
  else { k = 1 * document.MyForm.ein1.value.trim(); }
  if (b == '') { d = -2; document.MyForm.ein2.value = d; }
  else { d = 1 * document.MyForm.ein2.value.trim(); }

a1 = 0;
  a2 = d;
  b1 = -d/k;
  b2 = 0;

/*
  alert(k + ' / ' + d);
  alert('A('+a1+'/'+a2+')');
  alert('B('+b1+'/'+b2+')');
*/

document.MyForm.aus1.value = round2(a1); 
  document.MyForm.aus2.value = round2(a2);
  document.MyForm.aus3.value = round2(b1);
  document.MyForm.aus4.value = round2(b2);
}

if (fall == '2') {
  a1 =  document.MyForm.aus1.value.trim();
  a2 =  document.MyForm.aus2.value.trim();
  if (a1 == '') { a1 = 0; document.MyForm.aus1.value = a1; }
  else { a1 = 1 * document.MyForm.aus1.value.trim(); }
  if (a2 == '') { a2 = -3; document.MyForm.aus2.value = a2; }
  else { a2 = 1 * document.MyForm.aus2.value.trim(); }

b1 =  document.MyForm.aus3.value.trim();
  b2 =  document.MyForm.aus4.value.trim();
  if (b1 == '') { b1 = 4; document.MyForm.aus3.value = b1; }
  else { b1 = 1 * document.MyForm.aus3.value.trim(); }
  if (b2 == '') { b2 = 0; document.MyForm.aus4.value = b2; }
  else { b2 = 1 * document.MyForm.aus4.value.trim(); }

document.MyForm.aus1.value = a1; 
  document.MyForm.aus2.value = a2;
  document.MyForm.aus3.value = b1;
  document.MyForm.aus4.value = b2;

k = (a2-b2)/(a1-b1);
  d = a2 - k*a1;
  k = round2(k);
  d = round2(d);

/*
  alert(k + ' / ' + d);
  alert('A('+a1+'/'+a2+')');
  alert('B('+b1+'/'+b2+')');
*/

document.MyForm.ein1.value = k;
  document.MyForm.ein2.value = d;
}

A.x = 1 * document.MyForm.aus1.value;
A.y = 1 * document.MyForm.aus2.value;
B.x = 1 * document.MyForm.aus3.value; 
B.y = 1 * document.MyForm.aus4.value;

kw1 = Amax10(A.x,A.y,B.x,B.y);
kw1 = Math.abs(kw1) + 5;
if (kw1 > 10) { kw = Math.round(kw1); }
else { kw = 10; }
changeKS(kw)

alert('Weiter mit [Funktion]');

document.MyForm.rech.focus();
if (neu == true) { neu = false; return; }
}

</script>
</head>

<div id='dc'>
     <canvas id='MyCanvas' width='500' height='500' onmousedown = "showPos(event)">   
     Your browser does not support HTML5 Canvas.
  </canvas>
</div>

<form name="MyForm">
<h2>Gerade in der Ebene</h2>
<div id="ein">
Fall 1:<br> 
Die Gleichung der Geraden g: Y = k*X + d.<br>
Die Zahl "k" gibt die Geradensteigung an.<br>
P[0/d] ist der Schnittpunkt mit der Y-Achse.<br>
</div>
<br>
<div id = "aus">
Fall 2:<br>
Zwei Punkte A und B auf der Geraden g.<br>
Die Punkte liegen im Definitionsbereich,<br>
der immer automatisch ermittelt wird.<br>
</div>
<br>
Gerade g: 
Y = <input type="text" name="ein1" value="1" size="5" class="cd1"> * X  + 
<input type="text" name="ein2" value="-2" size="5" class="cd1">
<br><br>
Punkt A( <input type="text" name="aus1" value="0" size="5" class="cd1"> / 
<input type="text" name="aus2" value="-2" size="5" class="cd1"> ) <br>
Punkt B( <input type="text" name="aus3" value="2" size="5" class="cd1"> / 
<input type="text" name="aus4" value="0" size="5" class="cd1"> ) <br>
<br>
<input type="button" name="rech" value="Rechnung durchführen" class="cd2" onclick="Pruef()">
<br>
<input type="button" name="knopf1" value="Rechnung wiederholen" class="cd2" onclick=Neu()>
<br>
<input type="button" value="Funktion" class="cd2" onClick="plotFun()">
<br>
<input type="button" value="ClearCanvas" class="cd2" onClick="initCanvas()"> 
<br>
<input type="button" value="ResetForm" class="cd2" onClick="Reset()"> 
<br><br>
<div id="vier">
Ein Klick in die Grafik zeigt die Punkt-Koordinaten an:<br>
<input type="text" id="aus9" name="aus9" value=" " size="15" class="cd1"><br>
</div>
</form>

if (smallScr) { smart(); }

if (!smallScr) { document.addEventListener("contextmenu", (e) => {e.preventDefault()}); }
</script>

</body>
</html>

<!DOCTYPE html>
<html lang="de">
<head>
<title>gerade2.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="Schnitt von Geraden">

var wahl = 1;       // Auswahlparameter für die Funktion
  var S = new TPoint; // Schnittpunkt

function round2(x) { return Math.round(100*x)/100 }

function changeKS(x) {
    // Aenderung der Halbbreite kw des Welt-Koordinatensystems
    kw = x;
    xMin = -kw;
    xMax = kw;
    initCanvas();    
  }

function drawWidth(f) {
    // Liniendicke
    var canvas = document.getElementById('MyCanvas');
    var ctx = canvas.getContext('2d');
    ctx.lineWidth = f; 
  }

function drawColor(f) {
    // Linienfarbe
    var canvas = document.getElementById('MyCanvas');

var ctx = canvas.getContext('2d');
    ctx.strokeStyle = f;
  }

function drawWidth(f) {
    // Liniendicke
    var canvas = document.getElementById('MyCanvas');
    var ctx = canvas.getContext('2d');
    ctx.lineWidth = f; 
  }

function drawColor(f) {
    // Linienfarbe
    var canvas = document.getElementById('MyCanvas');
    var ctx = canvas.getContext('2d');
    ctx.strokeStyle = f;
  }

function fun(x) {
  // Funktion g festlegen
    fSign = 1;
    if (wahl == 1) { y = k1*x + d1; }
    if (wahl == 2) { y = k2*x + d2; }
    return y;
  }

function Reset() {
    // Formular initialisieren
    document.MyForm.reset();
    kw = 10;
    xMin = -kw;
    xMax = kw;
    fNum = 0;
    initCanvas(); 
    window.scroll(0,0);
  }

// ----------------------------------------------------------------------------

var neu = false;
var k1,d1,k2,d2;
var s1,s2;

// alert(k1 + ' / ' + d1);

// alert(k2 + ' / ' + d2);

s1 = (d2-d1) / (k1-k2);
  s2 = k1*s1 + d1;
  s1 = round2(s1);
  s2 = round2(s2); 
  document.MyForm.aus1.value = s1;
  document.MyForm.aus2.value = s2;

S.x = s1;
  S.y = s2;
  // alert(S.x + ' / ' + S.y);

if (k1 != k2) {
     kw1 = Amax10(S.x,S.y);
     kw1 = Math.abs(kw1) + 5;
     if (kw1 > 10) { kw = Math.round(kw1); }
     else { kw = 10; }
     changeKS(kw);
     // document.MyForm.aus1.value = S.x;
     // document.MyForm.aus2.value = S.y;
  }

alert('Weiter mit [Funktion]');

document.MyForm.rech.focus();
if (neu == true) { neu = false; return; }
}

</script>
</head>

<div id='dc'>
     <canvas id='MyCanvas' width='500' height='500' onmousedown = "showPos(event)">   
     Your browser does not support HTML5 Canvas.
  </canvas>
</div>

<form name="MyForm">
<h2>Schnitt von Geraden</h2>
<div id="eins">
Die Gleichung einer Geraden ist Y = k*X + d.<br>
Die Zahl "k" gibt die Geradensteigung an.<br>
P[0/d] ist der Schnittpunkt mit der Y-Achse.<br>
</div>
<div id = "zwei">
In der Ebene liegen zwei Gerade g und h.<br>
Es gibt drei Lagemöglichkeiten der Geraden:<br>
(1) Sie sind identisch (k1 = k2 und d1 = d2).<br>
(2) Sie sind parallel (k1 = k2 und d1 <> d2).<br>
(3) Sie schneiden sich (k1 <> k2 und d1 <> d2)<br>
      und haben dann einen Schnittpunkt S(x/y).<br>
</div>
g: 
Y = <input type="text" name="ein1" value="1" size="5" class="cd1"> * X  + 
<input type="text" name="ein2" value="-2" size="5" class="cd1">  (rot)
<br>
h: 
Y = <input type="text" name="ein3" value="-1" size="5" class="cd1"> * X  + 
<input type="text" name="ein4" value="5" size="5" class="cd1">  (grün)
<br>
Schnittpunkt S( <input type="text" name="aus1" value=" " size="5" class="cd1" readonly> / 
<input type="text" name="aus2" value=" " size="5" class="cd1" readonly> )
<br><br>
<div id="drei">
<input type="button" name="rech" value="Rechnung durchführen" class="cd2" onclick="Pruef()">
<br>
<input type="button" name="knopf1" value="Rechnung wiederholen" class="cd2" onclick=Neu()>
<br>
<input type="button" value="Funktion" class="cd2" onClick="plotFun()">
<br>
<input type="button" value="ClearCanvas" class="cd2" onClick="initCanvas()"> 
<br>
<input type="button" value="ResetForm" class="cd2" onClick="Reset()"> 
</div>
<br>
<div id="vier">
Ein Klick in die Grafik zeigt die Punkt-Koordinaten an:<br>
<input type="text" name="aus9" value=" " size="15" class="cd1"><br>
</div>
</form>

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</html>

<!DOCTYPE html>
<html lang="de">
<head>
<title>textglei1.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="Textgleichungen">

function closeChild() {
// Hilfetext schließen 
   if (!childWindow || childWindow.closed) { return; }
   if (child) { childWindow.document.close(); childWindow.close(); }
}

function info() {
// Hilfetext anzeigen 
     if (child) { closeChild(); child = false; return; }
     child = true;
     childWindow = window.open('','childWindow','top=20, left=700, width=580, height=720, srollbars=yes, menubar=no, toolbar=no');
     childWindow.document.open();
     childWindow.document.write('<html><head><meta name="viewport" content="width=device-width, initial-scale=0.80"></head>');
     childWindow.document.write('<html><head></head><body style="background-color:#FFFFE8; font-family:Calibri,Arial; font-size:15px; text-size-adjust:none; margin-left:30px; margin-bottom:30px;">');
     childWindow.document.write('<br><input type="button" value="Print" onclick="print();"><br><br>');
     childWindow.document.write('<b>Textaufgaben</b> (© Herbert Paukert)<br><br>');
     childWindow.document.write('<b>Musteraufgabe:</b><br>');
     childWindow.document.write('In einem Stall befinden sich Hasen und Hühner.<br>');
     childWindow.document.write('Die Tiere haben zusammen 35 Köpfe und 94 Füße.<br>');
     childWindow.document.write('Wieviele Hasen und Hühner befinden sich im Stall ?<br><br>');
     childWindow.document.write('<b>Lösung in sechs Schritten:</b><br><br>');
     childWindow.document.write('<b><i>1. Schritt: Die Variablen definieren.</i></b><br>');
     childWindow.document.write('X = Anzahl der Hasen, Y = Anzahl der Hühner.<br><br>');
     childWindow.document.write('<b><i>2. Schritt: Eine Tabelle anlegen.</i></b><br>');
     childWindow.document.write('Köpfe: Hasenköpfe = X, Hühnerköpfe  = Y.<br>');
     childWindow.document.write('Füße : Hasenfüße = 4 * X, Hühnerfüße = 2 * Y.<br><br>');
     childWindow.document.write('<b><i>3. Schritt: Gleichungen aufstellen.</i></b><br>');
     childWindow.document.write(' (I)  X + Y = 35<br>');
     childWindow.document.write('(II) 4*X + 2*Y = 94<br><br>');
     childWindow.document.write('<b><i>4. Schritt: Die Gleichungen lösen.</i></b><br>');
     childWindow.document.write('Umformung von (I)... X + Y = 35, Y = 35 - X<br>');
     childWindow.document.write('Einsetzen von Y in (II)... 4*X + 2*(35 - X) = 94, 70 + 2*X = 94<br>');
     childWindow.document.write('Vereinfachen von (II)... 70 + 2*X = 94, 2*X = 24, <b><u>X = 12</u></b><br>');
     childWindow.document.write('Einsetzen von X in (I)... 12 + Y = 35, <b><u>Y = 23</u></b><br><br>');
     childWindow.document.write('<b><i>5. Schritt: Die Antwort formulieren.</i></b><br>');
     childWindow.document.write('Im Stall befinden sich 12 Hasen und 23 Hühner.<br><br>');
     childWindow.document.write('<b><i>6. Schritt: Die Probe durchführen.</i></b><br>');
     childWindow.document.write('(I) X + Y = 35, 12 + 23 = 35, 35 = 35<br>');
     childWindow.document.write('(II) 4*X + 2*Y = 94, 4*12 + 2*23 = 48 + 46 = 94, 94 = 94<br><br>');
     childWindow.document.write('</body></html>');
}

function myTrim(x) { return x.replace(/^\s+|\s+$/gm,''); }

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<!DOCTYPE html>
<html lang="de">
<head>
<title>textglei2.html</title>
<meta charset="ISO-8859-1">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="Paukert Herbert">
<meta name="description" content="Textgleichungen">

function closeChild() {
// Hilfetext schließen 
   if (!childWindow || childWindow.closed) { return; }
   if (child) { childWindow.document.close(); childWindow.close(); }
}

function info() {
// Hilfetext anzeigen 
     if (child) { closeChild(); child = false; return; }
     child = true;
     childWindow = window.open('','childWindow','top=20, left=700, width=580, height=720, srollbars=yes, menubar=no, toolbar=no');
     childWindow.document.open();
     childWindow.document.write('<html><head><meta name="viewport" content="width=device-width, initial-scale=0.80"></head>');
     childWindow.document.write('<html><head></head><body style="background-color:#FFFFE8; font-family:Calibri,Arial; font-size:15px; text-size-adjust:none; margin-left:30px; margin-bottom:30px;">');
     childWindow.document.write('<br><input type="button" value="Print" onclick="print();"><br><br>');
     childWindow.document.write('<b>Textaufgaben</b> (© Herbert Paukert)<br><br>');
     childWindow.document.write('<b>Musteraufgabe:</b><br>');
     childWindow.document.write('In einem Stall befinden sich Hasen und Hühner.<br>');
     childWindow.document.write('Die Tiere haben zusammen 35 Köpfe und 94 Füße.<br>');
     childWindow.document.write('Wieviele Hasen und Hühner befinden sich im Stall ?<br><br>');
     childWindow.document.write('<b>Lösung in sechs Schritten:</b><br><br>');
     childWindow.document.write('<b><i>1. Schritt: Die Variablen definieren.</i></b><br>');
     childWindow.document.write('X = Anzahl der Hasen, Y = Anzahl der Hühner.<br><br>');
     childWindow.document.write('<b><i>2. Schritt: Eine Tabelle anlegen.</i></b><br>');
     childWindow.document.write('Köpfe: Hasenköpfe = X, Hühnerköpfe = Y.<br>');
     childWindow.document.write('Füße : Hasenfüße = 4 * X, Hühnerfüße = 2 * Y.<br><br>');
     childWindow.document.write('<b><i>3. Schritt: Gleichungen aufstellen.</i></b><br>');
     childWindow.document.write(' (I)  X + Y = 35<br>');
     childWindow.document.write('(II) 4*X + 2*Y = 94<br><br>');
     childWindow.document.write('<b><i>4. Schritt: Die Gleichungen lösen.</i></b><br>');
     childWindow.document.write('Umformung von (I)... X + Y = 35, Y = 35 - X<br>');
     childWindow.document.write('Einsetzen von Y in (II)... 4*X + 2*(35 - X) = 94, 70 + 2*X = 94<br>');
     childWindow.document.write('Vereinfachen von (II)... 70 + 2*X = 94, 2*X = 24, <b><u>X = 12</u></b><br>');
     childWindow.document.write('Einsetzen von X in (I)... 12 + Y = 35, <b><u>Y = 23</u></b><br><br>');
     childWindow.document.write('<b><i>5. Schritt: Die Antwort formulieren.</i></b><br>');
     childWindow.document.write('Im Stall befinden sich 12 Hasen und 23 Hühner.<br><br>');
     childWindow.document.write('<b><i>6. Schritt: Die Probe durchführen.</i></b><br>');
     childWindow.document.write('(I) X + Y = 35, 12 + 23 = 35, 35 = 35<br>');
     childWindow.document.write('(II) 4*X + 2*Y = 94, 4*12 + 2*23 = 48 + 46 = 94, 94 = 94<br><br>');
     childWindow.document.write('</body></html>');
}

function myTrim(x) { return x.replace(/^\s+|\s+$/gm,''); }

function pruef()
{
  var  num = 0; 
  var  antwo = new Array(11);
 
  antwo[0] = "2.4";
  antwo[1] = "3.2";
  antwo[2] = "3";
  antwo[3] = "2";
  antwo[4] = "7";
  antwo[5] = "6";
  antwo[6] = "36";
  antwo[7] = "45";
  antwo[8] = "24";
  antwo[9] = "28";
  antwo[10] = "21";

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MATHEMATIK-Lernprogramme Projekt "Gleichungen"

MATHEMATIK-Lernprogramme
Projekt "Gleichungen"