// Numbas version: exam_results_page_options
{"name": "Write a permutation as a product of disjoint cycles", "extensions": ["permutations"], "custom_part_types": [{"source": {"pk": 68, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/68/edit"}, "name": "Write a permutation in cycle notation", "short_name": "write-a-permutation-in-cycle-notation", "description": "<p>The student must write a permutation in cycle notation. You can optionally require the cycles to be disjoint and/or all of length 2.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "let(ans,\n  if(settings[\"must_be_transpositions\"],\n    as_transpositions(settings[\"correct_answer\"]),\n    show(settings[\"correct_answer\"])\n  ),\n  if(ans=\"\",settings[\"identity_name\"],ans)\n)", "hint": {"static": false, "value": "if(settings[\"show_hint\"],\n  if(settings[\"must_be_disjoint\"],\n    if(settings[\"must_be_transpositions\"],\n      \"Write a permutation in cycle notation as a product of disjoint transpositions.\",\n      \"Write a permutation in cycle notation as a product of disjoint cycles.\"\n    ),\n    if(settings[\"must_be_transpositions\"],\n      \"Write a permutation in cycle notation as a product of transpositions.\",\n      \"Write a permutation in cycle notation.\"\n    )\n  ),\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(student_permutation);\napply(is_correct);\napply(is_disjoint);\napply(is_transpositions)\n\ninterpreted_answer:\nstudent_permutation\n\nis_correct:\ncorrectif(student_permutation=settings[\"correct_answer\"])\n\nis_disjoint:\nif(is_disjoint(studentAnswer),\n  true\n,\n  assert(not settings[\"must_be_disjoint\"],\n    set_credit(0,\"You have not written your answer as a product of disjoint cycles.\"),\n  );\n  false\n)\n\nstudent_permutation:\ntry(\n  if(studentAnswer=settings[\"identity_name\"],\n    permutation(\"\"), \n    permutation(studentAnswer)\n  ),\n  message,\n    warn(\"Your answer is not valid cycle notation: \"+message);\n    fail(\"Your answer is not valid cycle notation: \"+message)\n)\n\nis_transpositions:\nif(is_transpositions(studentAnswer),\n  true\n,\n  assert(not settings[\"must_be_transpositions\"],\n    set_credit(0,\"You have not written your answer as a product of transpositions.\")\n  );\n  false\n)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "apply(student_permutation);\napply(is_correct);\napply(is_disjoint);\napply(is_transpositions)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_permutation"}, {"name": "is_correct", "description": "", "definition": "correctif(student_permutation=settings[\"correct_answer\"])"}, {"name": "is_disjoint", "description": "", "definition": "if(is_disjoint(studentAnswer),\n  true\n,\n  assert(not settings[\"must_be_disjoint\"],\n    set_credit(0,\"You have not written your answer as a product of disjoint cycles.\"),\n  );\n  false\n)"}, {"name": "student_permutation", "description": "", "definition": "try(\n  if(studentAnswer=settings[\"identity_name\"],\n    permutation(\"\"), \n    permutation(studentAnswer)\n  ),\n  message,\n    warn(\"Your answer is not valid cycle notation: \"+message);\n    fail(\"Your answer is not valid cycle notation: \"+message)\n)"}, {"name": "is_transpositions", "description": "", "definition": "if(is_transpositions(studentAnswer),\n  true\n,\n  assert(not settings[\"must_be_transpositions\"],\n    set_credit(0,\"You have not written your answer as a product of transpositions.\")\n  );\n  false\n)"}], "settings": [{"name": "correct_answer", "label": "Correct answer", "help_url": "", "hint": "", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "show_hint", "label": "Show answer input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "must_be_disjoint", "label": "Must the cycles be disjoint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "must_be_transpositions", "label": "Must the cycles be transpositions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "identity_name", "label": "Name of the identity permutation", "help_url": "", "hint": "The student should write this string for the identity permutation.", "input_type": "string", "default_value": "e", "subvars": true}], "public_availability": "always", "published": true, "extensions": ["permutations"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Write a permutation as a product of disjoint cycles", "tags": ["checked2015", "groups", "permutations"], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "<p>Each set of brackets represents a <em>cycle</em>, with each number being mapped to the one on its right, and the last number in the sequence mapped to the first.</p>\n<p>Follow each number through the cycles, starting with the rightmost cycle and reading leftwards. For example, here's how $1$ is mapped to $\\var{prod[1]}$:</p>\n<p>\\[ \\var{latex(tracemap(1,perms))} \\]</p>\n<p>Then repeat this for $\\var{prod[1]}$, until you get back to $1$. This is a single cycle. If any number is not included in this cycle, repeat this process starting at that number to get another, disjoint, cycle. Some numbers are mapped to themselves - these are trivial cycles and you don't need to write them down. Once you've covered every number, you should have the following:</p>\n<p>\\[ \\var{prod} \\]</p>\n", "rulesets": {}, "extensions": ["permutations"], "variables": {"prod": {"name": "prod", "group": "Ungrouped variables", "definition": "compose(perms[0],perms[1],perms[2],perms[3])", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(4..9)", "description": "", "templateType": "anything"}, "perms": {"name": "perms", "group": "Ungrouped variables", "definition": "repeat(perm(randomcycle(n)),4)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["perms", "prod", "n"], "variable_groups": [], "functions": {"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;"}, "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;"}, "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;"}, "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;"}, "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;"}, "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;"}, "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;"}, "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;"}, "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;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "write-a-permutation-in-cycle-notation", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Write as a product of disjoint cycles</p>\n<p>\\[\\var{perms[0]} \\var{perms[1]} \\var{perms[2]} \\var{perms[3]} \\]</p>", "settings": {"correct_answer": "prod", "must_be_disjoint": true, "must_be_transpositions": false}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}