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{"name": "Demo automatically generate latex for matrix/vector calculation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Demo automatically generate latex for matrix/vector calculation", "tags": ["automatically generated latex", "demo", "latex", "latex for matrix"], "metadata": {"description": "<p>Demo of automatically generating latex strings to out put vectors/matrices of variable size and that are calculated by some formula.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Let \\(A=\\var{A}\\), \\(u=\\var{u}\\). \\(m=\\var{m}\\) and \\(n=\\var{n}\\) give the variable size of \\(A\\).</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "matrix(repeat(repeat(random(-3..3),n),m))", "description": "", "templateType": "anything"}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "vector(repeat(random(-3..3),n))", "description": "", "templateType": "anything"}, "rawunresolvedAu": {"name": "rawunresolvedAu", "group": "Ungrouped variables", "definition": "map(if({A[k][l]<0,'({A[k][l]})','{A[k][l]}')+'\\\\cdot'+if(u[l]<0,'({u[l]})','{u[l]}')+symbols(m,n)[k][l],[k,l],product(0..m-1,0..n-1))", "description": "<p>collects the terms \\(a_{ij}\\cdot v_j\\) for the matrix times vector multiplication, with plus symbols or new line concatenated ready to put into latex code for the calulcation steps of the matrix.</p>\n<p>All the \"if\" things are to put brackets round negative numbers. not using simplify because i prefer \\(\\cdot\\) to \\(\\times\\).</p>\n<p>Without the need for brackets, it could just be&nbsp; map('{A[k][l]}\\\\cdot{va[l]}'+symbols(2,2)[k][l],[k,l],product(0..1,0..1))</p>\n<p>The \"symbols\" is a function giving the correct addition or new line symbols for the size of the matrix that is being used.</p>", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..3)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "unresolvedAu": {"name": "unresolvedAu", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(rawunresolvedAu) +'\\\\end{'+'pmatrix}')", "description": "<p>for the solution, the calculation steps written out unresolved.</p>", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "map('x_{k}',k,1..n)", "description": "<p>general vector x.&nbsp; ['x_1','x_2','x_3'] As list because vector can only take numbers as entries.</p>", "templateType": "anything"}, "latexAx": {"name": "latexAx", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(halfrawAx) +'\\\\end{'+'pmatrix}')", "description": "<p>Ax as needed for latex string. I've done '\\\\end{'+'pmatrix}' instead of '\\\\end{pmatrix}' because the latter kept giving me errors about pmatrix not being a variable. It doesn't seem to be a problem for the begin bit, but this way at least is a work-around.</p>", "templateType": "anything"}, "rawAx": {"name": "rawAx", "group": "Ungrouped variables", "definition": "map('{A[k][l]}*'+x[{l}]+symbols2(m,n)[k][l],[k,l],product(0..m-1,0..n-1))", "description": "", "templateType": "anything"}, "halfrawAx": {"name": "halfrawAx", "group": "Ungrouped variables", "definition": "map(string(simplify(expression(concatstrings(rawAx[(n*k)..(n*k+n)])),\"all\"))+symbols3(m)[k],k,0..m-1)", "description": "", "templateType": "anything"}, "halfrawx": {"name": "halfrawx", "group": "Ungrouped variables", "definition": "map(x[k]+symbols3(n)[k],k,0..n-1)", "description": "", "templateType": "anything"}, "latexx": {"name": "latexx", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(halfrawx) +'\\\\end{'+'pmatrix}')", "description": "<p>I've done '\\\\end{'+'pmatrix}' instead of '\\\\end{pmatrix}' because the latter kept giving me errors about pmatrix not being a variable. It doesn't seem to be a problem for the begin bit, but this way at least is a work-around.</p>", "templateType": "anything"}, "rawgeneralA": {"name": "rawgeneralA", "group": "Ungrouped variables", "definition": "map('a_{'+'{k}'+'{l}}'+symbols4(m,n)[k-1][l-1],[k,l],product(1..m,1..n))", "description": "", "templateType": "anything"}, "generalA": {"name": "generalA", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(rawgeneralA) +'\\\\end{'+'pmatrix}')", "description": "", "templateType": "anything"}, "rawunresolvedA1": {"name": "rawunresolvedA1", "group": "Ungrouped variables", "definition": "map('{k}+{l}'+symbols4(m,n)[k-1][l-1],[k,l],product(1..m,1..n))", "description": "", "templateType": "anything"}, "latexA1": {"name": "latexA1", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(rawunresolvedA1) +'\\\\end{'+'pmatrix}')", "description": "", "templateType": "anything"}, "rawA1": {"name": "rawA1", "group": "Ungrouped variables", "definition": "map(k+l,[k,l],product(1..m,1..n))", "description": "", "templateType": "anything"}, "A1": {"name": "A1", "group": "Ungrouped variables", "definition": "matrix(map(rawA1[k..k+n],k,list(vector(0..m-1)*n)))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["A", "u", "m", "n", "rawunresolvedAu", "unresolvedAu", "x", "rawAx", "halfrawAx", "latexAx", "halfrawx", "latexx", "rawgeneralA", "generalA", "rawunresolvedA1", "latexA1", "rawA1", "A1"], "variable_groups": [], "functions": {"concatstrings": {"parameters": [["input", "list"]], "type": "string", "language": "javascript", "definition": "var output = '';\nvar i;\nfor (i = 0; i < input.length; i++) {\n  output += input[i];\n} \nreturn output;"}, "symbols": {"parameters": [["m", "number"], ["n", "number"]], "type": "list", "language": "jme", "definition": "repeat(repeat('+',n-1)+['\\\\\\\\'],m-1)+[repeat('+',n-1)+['']]"}, "symbols2": {"parameters": [["m", "number"], ["n", "number"]], "type": "list", "language": "jme", "definition": "repeat(repeat('+',n-1)+[''],m-1)+[repeat('+',n-1)+['']]"}, "symbols3": {"parameters": [["m", "number"]], "type": "list", "language": "jme", "definition": "repeat('\\\\\\\\',m-1)+['']"}, "symbols4": {"parameters": [["m", "number"], ["n", "number"]], "type": "list", "language": "jme", "definition": "repeat(repeat('&',n-1)+['\\\\\\\\'],m-1)+[repeat('&',n-1)+['']]"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "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>To demonstrate matrix times vector:</p>\n<p>&nbsp;\\(\\var{A}\\var{u}=\\var{unresolvedAu}=\\var{A*u}\\)</p>\n<p>(Note: I prefer \\(\\cdot\\) to \\(\\times\\) for multiplication, and didn't need any other simplification rules than brackets, so I did it this way rather than use the inbuilt simplify function.)</p>\n<p>For a general vector:</p>\n<p>\\(\\var{A}\\var{latexx} = \\var{latexAx}\\)</p>\n<p></p>"}, {"type": "information", "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>A general matrix of random size: \\(\\var{generalA}\\)</p>\n<p>With some unresolved calculations: \\(\\var{latexA1}\\)</p>\n<p>And the same thing resolved: \\(\\var{A1}\\).</p>\n<p>You can see more complex things in the question called \"Find matrix from entry formula ( WBQ 1.23 randomized size and formula)\", which is in Chapter 1 Vectors and Matrices in Linear Algebra Y1.</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}]}], "contributors": [{"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}