// Numbas version: exam_results_page_options
{"name": "Permutations: two-line form", "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. 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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": "Permutations: two-line form", "tags": ["permutations"], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>\\[ \\pi = \\var{twoline(ppi)} \\]</p>", "advice": "<p>Each number on the top row is mapped to the number directly beneath it. 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"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) 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"unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Write $\\pi$ and $\\pi^{-1}$ as a product of disjoint cycles.</p>\n<p>$\\pi = $ [[0]]</p>\n<p>$\\pi^{-1} = $ [[1]]</p>", "gaps": [{"type": "write-a-permutation-in-cycle-notation", "useCustomName": true, "customName": "$\\pi$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [{"variables": [{"name": "ppi_num_even_cycles", "value": "1"}, {"name": "ppi_num_cycles", "value": "1"}, {"name": "ppi", "value": "perm(\"(1,6,7,5,4,2)\")"}, {"name": "ppi_cycle_lengths", "value": "[ 6 ]"}], "answer": {"empty": false, "valid": true, "value": "(1,6,7,5,4,2)"}, "notes": [{"name": "mark", "expected": {"value": "nothing", "messages": ["Your answer is correct.\n\nYou were awarded 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