// Numbas version: finer_feedback_settings
{"name": "Euklidischer Algorithmus", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Euklidischer Algorithmus", "tags": [], "metadata": {"description": "<p>Aufgabe zum einfachen und erweiterten euklidischen Algorithmus (mit \"sch&ouml;nen\" Zahlen)</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "<p>&nbsp;In dieser Aufgabe geht es um den einfachen und den erweiterten Euklidischen Algorithmus.</p>", "advice": "<p>a) $\\operatorname{ggT}(\\var{a},\\var{b})=\\var{ergebnis[0]}$</p>\n<div id=\"ausg\">Rechenweg:<br/>{app}</div>\n<div>&nbsp;</div>\n<div>b)&nbsp;Durch R&uuml;ckeinsetzung in die Zeilen oben ermittelt man $r=\\var{ergebnis[1]},s=\\var{ergebnis[2]}$</div>\n<div><br/>Eine ausf&uuml;hrliche Rechenanleitung finden Sie zB <a href=\"https://www.arndt-bruenner.de/mathe/scripts/erweitertereuklid.htm\" target=\"_blank\" rel=\"noopener noreferrer\">hier</a>.</div>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "chosen[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "chosen[1]", "description": "", "templateType": "anything"}, "ergebnis": {"name": "ergebnis", "group": "Ungrouped variables", "definition": "euclid_gcd(a,b)", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[['a',a],['b',b]]", "description": "", "templateType": "anything"}, "app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet('https://www.geogebra.org/m/mzkxnpvm',defs)", "description": "", "templateType": "anything"}, "choice": {"name": "choice", "group": "Ungrouped variables", "definition": "[[3641,1243],[4303,1441],[4303,1469],[5627,1921],[6289,2147],[3707,1243],[4381,1469],[5729,1921],[6403,2147],[3817,1639],[3817,1963],[4511,1937],[5899,2533],[6593,2831],[3839,1243]]", "description": "", "templateType": "anything"}, "chosen": {"name": "chosen", "group": "Ungrouped variables", "definition": "random(choice)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "ergebnis", "defs", "app", "choice", "chosen"], "variable_groups": [], "functions": {"euclid_gcd": {"parameters": [["a", "number"], ["b", "number"]], "type": "anything", "language": "javascript", "definition": "  a = +a;\n  b = +b;\n  if (a !== a || b !== b) {\n    return [NaN, NaN, NaN];\n  }\n  \n  if (a === Infinity || a === -Infinity || b === Infinity || b === -Infinity) {\n    return [Infinity, Infinity, Infinity];\n  }\n  // Checks if a or b are decimals\n  if ((a % 1 !== 0) || (b % 1 !== 0)) {\n    return false;\n  }\n  var signX = (a < 0) ? -1 : 1,\n    signY = (b < 0) ? -1 : 1,\n    x = 0,\n    y = 1,\n    u = 1,\n    v = 0,\n    q, r, m, n;\n  a = Math.abs(a);\n  b = Math.abs(b);\n\n  while (a !== 0) {\n    q = Math.floor(b / a);\n    r = b % a;\n    m = x - u * q;\n    n = y - v * q;\n    b = a;\n    a = r;\n    x = u;\n    y = v;\n    u = m;\n    v = n;\n  }\n  return [b, signX * x, signY * y];"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Ermitteln Sie mittels Euklidischem Algorithmus: $\\operatorname{ggT}(\\var{a},\\var{b})=$[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "ggT", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ergebnis[0]", "maxValue": "ergebnis[0]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Ermitteln Sie mittels erweitertem Euklidischem Algorithmus Zahlen $r,s\\in\\mathbb{Z}$, f&uuml;r die gilt:</p>\n<p style=\"text-align: center;\">$r\\cdot \\var{a}+s\\cdot \\var{b}=\\operatorname{ggT}(\\var{a},\\var{b})$</p>\n<p>$r=$[[0]] , $s=$[[1]]</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 1265px; width: 0px; top: 35px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 1250px; width: 50px; top: 20px; height: 20px; font-size: 10px; color: black;\"></span></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "r", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ergebnis[1]", "maxValue": "ergebnis[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "s", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ergebnis[2]", "maxValue": "ergebnis[2]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}]}], "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}