// Numbas version: exam_results_page_options
{"name": "Lois's copy of Write a permutation as a product of transpositions", "extensions": ["permutations"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["pi1", "pi2"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "advice": "<h4></h4>\n<p>Possible solutions are shown below -- but remember that these are not unique.</p>\n<p>a) \\[ \\var{as_transpositions(pi1)} \\]</p>\n<h4></h4>\n<p>b) &nbsp;Recall that you can just write each cycle in turn as a product of transpositions. \\[ \\var{as_transpositions(pi2)} \\]</p>", "preamble": {"css": "", "js": ""}, "extensions": ["permutations"], "statement": "<p>For this question you need to enter a transposition using commas between the terms in it. Do not leave spaces between each transposition in a product (composition).</p>", "tags": [], "rulesets": {}, "parts": [{"showCorrectAnswer": true, "marks": 0, "type": "gapfill", "gaps": [{"showCorrectAnswer": true, "marks": 1, "displayAnswer": "{as_transpositions(pi1)}", "type": "patternmatch", "answer": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "matchMode": "regex", "scripts": {"validate": {"order": "instead", "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;"}, "mark": {"order": "instead", "script": "this.setCredit(0);\nvar 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_transpositions(this.studentAnswer)) {\n  this.setCredit(0,\"Your answer is not a product of transpositions\");\n  return;\n}\nvar unwrapValue = Numbas.jme.unwrapValue;\nvar p_totranspose = unwrapValue(question.scope.variables.pi1);\nif(p.equal(p_totranspose)) {\n  this.setCredit(1,\"Correct!\");\n} else {\n  this.setCredit(0,\"Wrong\");\n}"}}}], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "prompt": "<p>Write the permutation $\\pi_1 = \\var{pi1}$ as a product (composition) of transpositions.</p>\n<p>$\\pi_1 = $ [[0]]</p>"}, {"showCorrectAnswer": true, "marks": 0, "type": "gapfill", "gaps": [{"showCorrectAnswer": true, "marks": 1, "displayAnswer": "{as_transpositions(pi2)}", "type": "patternmatch", "answer": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "matchMode": "regex", "scripts": {"validate": {"order": "instead", "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;"}, "mark": {"order": "instead", "script": "this.setCredit(0);\nvar 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_transpositions(this.studentAnswer)) {\n  this.setCredit(0,\"Your answer is not a product of transpositions\");\n  return;\n}\nvar unwrapValue = Numbas.jme.unwrapValue;\nvar p_totranspose = unwrapValue(question.scope.variables.pi2);\nif(p.equal(p_totranspose)) {\n  this.setCredit(1,\"Correct!\");\n} else {\n  this.setCredit(0,\"Wrong\");\n}"}}}], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "prompt": "<p>Write the permutation $\\pi_2 = \\var{pi2}$ as a product (composition) of transpositions.</p>\n<p>$\\pi_2 = $ [[0]]</p>"}], "functions": {"sum": {"language": "javascript", "type": "number", "parameters": [["l", "list"]], "definition": "var t = 0;\nfor(var i=0;i<l.length;i++) {\n  t = Numbas.math.add(t,l[i]);\n}\nreturn t;"}, "permwithorder": {"language": "javascript", "type": "list", "parameters": [["n", "number"]], "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;"}, "show_factorisation": {"language": "javascript", "type": "string", "parameters": [["n", "number"]], "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;"}, "tracemap": {"language": "javascript", "type": "string", "parameters": [["n", "number"], ["perms", "list"]], "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;"}, "randomcycle": {"language": "javascript", "type": "list", "parameters": [["n", "number"]], "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;"}, "randompartition": {"language": "javascript", "type": "list", "parameters": [["n", "number"]], "definition": "var l = [];\nwhile(n) {\n  var t = Numbas.math.randomint(n)+1;\n  l.push(t);\n  n -= t;\n}\nreturn l;"}, "showsum": {"language": "javascript", "type": "string", "parameters": [["l", "list"]], "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;"}, "primepowerfactors": {"language": "javascript", "type": "list", "parameters": [["n", "number"]], "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": {"language": "javascript", "type": "string", "parameters": [["l", "list"]], "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": {"language": "javascript", "type": "list", "parameters": [["cycle_sizes", "list"]], "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;"}, "orderpossible": {"language": "javascript", "type": "boolean", "parameters": [["n", "number"], ["s_n", "number"]], "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;"}}, "name": "Lois's copy of Write a permutation as a product of transpositions", "variable_groups": [], "variables": {"pi1": {"templateType": "anything", "name": "pi1", "group": "Ungrouped variables", "description": "", "definition": "perm(randomcycle(random(5..9)))"}, "pi2": {"templateType": "anything", "name": "pi2", "group": "Ungrouped variables", "description": "", "definition": "perm(deal(random(11..17)))"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "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/"}]}