// Numbas version: exam_results_page_options
{"name": "Lois's copy of Conjugate of permutations", "extensions": ["permutations"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Lois's copy of Conjugate of permutations", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Note that in this question cycles are indicated with commas between each element. So (1, 2, 3) denotes the cycle (1 2 3) and no gaps are left between cycles. You should omit cycles of length 1 in your answers.</p>", "advice": "<p>These answers omit cycles of length 1.</p>\n<p>a)</p>\n<p>$\\var{conjugate1}$</p>\n<h4>b)</h4>\n<p>$\\var{conjugate2}$</p>\n<p></p>", "rulesets": {}, "extensions": ["permutations"], "variables": {"sigma2": {"name": "sigma2", "group": "Ungrouped variables", "definition": "perm(deal(random(5..11)))", "description": "", "templateType": "anything"}, "conjugate2": {"name": "conjugate2", "group": "Ungrouped variables", "definition": "tau2*sigma2*inverse(tau2)", "description": "", "templateType": "anything"}, "tau2": {"name": "tau2", "group": "Ungrouped variables", "definition": "perm(deal(random(5..11)))", "description": "", "templateType": "anything"}, "conjugate1": {"name": "conjugate1", "group": "Ungrouped variables", "definition": "tau1*sigma1*inverse(tau1)", "description": "", "templateType": "anything"}, "sigma1": {"name": "sigma1", "group": "Ungrouped variables", "definition": "perm(randomcycle(7))", "description": "", "templateType": "anything"}, "tau1": {"name": "tau1", "group": "Ungrouped variables", "definition": "perm(deal(random(5..11)))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["sigma2", "conjugate2", "tau2", "conjugate1", "sigma1", "tau1"], "variable_groups": [], "functions": {"randomcycle": {"parameters": [["n", "number"]], "type": "list", "language": "javascript", "definition": "var off = Numbas.math.randomint(n);\nvar d = Numbas.math.deal(n);\nwhile(d[off]==off) {\n  d = Numbas.math.deal(n);\n}\nvar out = [];\nfor(var i = 0;i<n;i++) {\n  out[i]=i;\n}\nvar old = off;\nvar i = off;\nwhile((i=d[i])!=off) {\n  out[old]=i;\n  old = i;\n}\nout[old] = i;\nreturn out;"}, "primepowerfactors": {"parameters": [["n", "number"]], "type": "list", "language": "javascript", "definition": "var factors = Numbas.math.factorise(n);\nvar out = [];\nfor(var i=0;i<factors.length;i++) {\n  if(factors[i]) {\n    out.push(Math.pow(Numbas.math.primes[i],factors[i]));\n  }\n}\nreturn out;"}, "showsum": {"parameters": [["l", "list"]], "type": "string", "language": "javascript", "definition": "var t = 0;\nvar out = '';\nfor(var i=0;i<l.length;i++) {\n  if(i>0) {\n    out += ' + ';\n  }\n  out += l[i]\n  t += l[i];\n}\nout += ' = '+t;\nreturn out;"}, "orderpossible": {"parameters": [["n", "number"], ["s_n", "number"]], "type": "boolean", "language": "javascript", "definition": "var factors = Numbas.math.factorise(n);\nvar t = 0;\nfor(var i=0;i<factors.length;i++) {\n  if(factors[i]) {\n    t += Math.pow(Numbas.math.primes[i],factors[i]);\n  }\n}\nreturn t<=s_n;"}, "showlist": {"parameters": [["l", "list"]], "type": "string", "language": "javascript", "definition": "var out = '';\nfor(var i=0;i<l.length;i++) {\n  if(i==l.length-1 && l.length>1) {\n    out += ' and ';\n  } else if(i>0) {\n    out += ', ';\n  }\n  out += '$'+l[i]+'$';\n}\nreturn out;"}, "permfrompartition": {"parameters": [["cycle_sizes", "list"]], "type": "list", "language": "javascript", "definition": "var to = [];\nvar offset = 0;\nfor(var i=0; i<cycle_sizes.length; i++) {\n  var o_offset = offset;\n  for(var j=0;j<cycle_sizes[i]-1;j++) {\n    to[offset] = offset+1;\n    offset += 1;\n  }\n  to[offset] = o_offset;\n  o_offset = offset;\n  offset += 1;\n}\nreturn to;"}, "permwithorder": {"parameters": [["n", "number"]], "type": "list", "language": "javascript", "definition": "var factors = Numbas.math.factorise(n);\nvar off = 0;\nvar out = [];\nfor(var i=0;i<factors.length;i++) {\n  if(factors[i]>0) {\n    var cycle_length = Math.pow(Numbas.math.primes[i],factors[i]);\n    for(var j=0;j<cycle_length-1;j++) {\n      out[off+j]=off+j+1;\n    }\n    out[off+cycle_length-1]=off;\n    off = off+cycle_length;\n  }\n}\nreturn out;"}, "sum": {"parameters": [["l", "list"]], "type": "number", "language": "javascript", "definition": "var t = 0;\nfor(var i=0;i<l.length;i++) {\n  t = Numbas.math.add(t,l[i]);\n}\nreturn t;"}, "tracemap": {"parameters": [["n", "number"], ["perms", "list"]], "type": "string", "language": "javascript", "definition": "n -= 1;\nvar l = perms.length;\nvar out = ''+(n+1);\nfor(var i=l-1;i>=0;i--) {\n  n = perms[i].map(n);\n  out += ' \\\\to '+(n+1);\n}\nreturn out;"}, "randompartition": {"parameters": [["n", "number"]], "type": "list", "language": "javascript", "definition": "var l = [];\nwhile(n) {\n  var t = Numbas.math.randomint(n)+1;\n  l.push(t);\n  n -= t;\n}\nreturn l;"}, "show_factorisation": {"parameters": [["n", "number"]], "type": "string", "language": "javascript", "definition": "var factors = Numbas.math.factorise(n);\nvar out = '';\nfor(var i=0;i<factors.length;i++) {\n  if(factors[i]) {\n    if(out.length) {\n      out += ' \\\\cdot ';\n    }\n    out += Numbas.math.primes[i];\n    if(factors[i]>1) {\n      out += '^{'+factors[i]+'}';\n    }\n  }\n}\nreturn out;"}}, "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>If $\\sigma = \\var{sigma1}$ and $\\tau = \\var{tau1}$, write down the permutation $\\tau \\circ \\sigma &nbsp;\\circ \\tau^{-1}$.</p>\n<p>$\\tau &nbsp;\\circ \\sigma \\circ \\tau^{-1}$ = [[0]]</p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"mark": {"script": "var Permutation = Numbas.extensions.permutations.Permutation;\ntry {\n  var p = Permutation.fromString(this.studentAnswer);\n} catch(e) {\n  this.setCredit(0,\"Invalid notation\");\n  return;\n}\nif(!Permutation.is_disjoint(this.studentAnswer)) {\n  this.setCredit(0,\"Your 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"marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If &nbsp;$\\sigma = \\var{sigma2}$ and $\\tau = \\var{tau2}$, write down the permutation $\\tau \\circ \\sigma \\circ \\tau^{-1}$.</p>\n<p>$\\tau \\circ \\sigma \\circ \\tau^{-1}$ = [[0]]</p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"mark": {"script": "var Permutation = Numbas.extensions.permutations.Permutation;\ntry {\n  var p = Permutation.fromString(this.studentAnswer);\n} catch(e) {\n  this.setCredit(0,\"Invalid notation\");\n  return;\n}\nif(!Permutation.is_disjoint(this.studentAnswer)) {\n  this.setCredit(0,\"Your cycles are not disjoint\");\n  return;\n}\nvar unwrapValue = Numbas.jme.unwrapValue;\nvar prod = unwrapValue(question.scope.variables.conjugate2);\nif(p.equal(prod)) {\n  this.setCredit(1,\"Correct!\");\n} else {\n  this.setCredit(0,\"Wrong\");\n}", "order": "instead"}, "validate": {"script": "var Permutation = Numbas.extensions.permutations.Permutation;\ntry{\n  Permutation.parse(this.studentAnswer);\n} catch(e) {\n  this.giveWarning(\"Invalid notation\");\n  return false;\n}\nreturn true;", "order": "instead"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "", "displayAnswer": "{show(conjugate2)}", "matchMode": "regex"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}