2b:["$","title",null,{"children":"Canonicalization with Math.js | Tom Larkworthy | Observable"}] 30:T464,md`# Canonicalization with Math.js I want to get expressions like ${tex`(x_2 - x_1) * 4 \gt x_1 + 1`}, into _a) into a specialized canonical form for linear programming:- ${tex`-5 x_1 + 4 x_2 \geq 1`} in general ${tex`c_1x_1 + ... + c_nx_n \geq c_0`} Math.js has the power, but does not ship with enough rewrite rules by default. So this notebook is about adding the require rules to create a canonicalization routine. There is a fuzzer to help stress test these routines https://observablehq.com/@tomlarkworthy/expression-fuzzer Updated 2026-09-08 for math.js 15. The library is vendored as [@tomlarkworthy/mathjs](https://observablehq.com/@tomlarkworthy/mathjs) rather than pulled in with \`require\`, which the 2026 Observable standard library no longer provides. Improvements from [@jwoLondon's fork](https://observablehq.com/@jwolondon/canonicalization-with-math-js) are folded in: \`step2\` iterates to a fixpoint instead of a fixed number of passes, the operator swap clones rather than mutating the caller's AST, \`isCanonical\` decides by trial extraction, and \`extractLHS\` descends through parentheses. `31:Td0a,constantsToRHSFn = { const isOperatorNode = math.isOperatorNode; const isConstantNode = math.isConstantNode; const isNegativeConstantNode = (node) => isOperatorNode(node) && node.fn == "unaryMinus" && isConstantNode(node.args[0]); const isSymbolNode = math.isSymbolNode; const isParenthesisNode = math.isParenthesisNode; const isZero = math.isZero; const OperatorNode = math.OperatorNode; const ConstantNode = math.ConstantNode; const ParenthesisNode = math.ParenthesisNode; const SymbolNode = math.SymbolNode; let prunedLHS = (node, pruned) => { const pruneNode = (node) => isConstantNode(node) ? node : new ConstantNode(-node.args[0].value); if (isConstantNode(node) || isNegativeConstantNode(node)) { if (node.value !== 0) { pruned.push(pruneNode(node)); } return new ConstantNode(0); } else if (isParenthesisNode(node)) { return node; } else if (isOperatorNode(node) && node.isBinary()) { if (node.fn == "add") { if ( isConstantNode(node.args[0]) || isNegativeConstantNode(node.args[0]) ) { pruned.push(pruneNode(node.args[0])); return prunedLHS(node.args[1], pruned); } else if ( isConstantNode(node.args[1]) || isNegativeConstantNode(node.args[1]) ) { pruned.push(pruneNode(node.args[1])); return prunedLHS(node.args[0], pruned); } return new OperatorNode(node.op, node.fn, [ prunedLHS(node.args[0], pruned), prunedLHS(node.args[1], pruned) ]); } else if (node.fn == "subtract") { if ( isConstantNode(node.args[0]) || isNegativeConstantNode(node.args[0]) ) { pruned.push(pruneNode(node.args[0])); return new OperatorNode("-", "unaryMinus", [ prunedLHS(node.args[1], pruned) ]); } else if ( isConstantNode(node.args[1]) || isNegativeConstantNode(node.args[1]) ) { pruned.push(new ConstantNode(-pruneNode(node.args[1]).value)); return prunedLHS(node.args[0], pruned); } return new OperatorNode(node.op, node.fn, [ prunedLHS(node.args[0], pruned), prunedLHS(node.args[1], pruned) ]); } return node; } else if (isOperatorNode(node) && node.isUnary()) { return new OperatorNode(node.op, node.fn, [node.args[0]]); } else if (isSymbolNode(node)) { return node; } debugger; throw new Error(`Should not happen: ${node}`); }; let appendRHS = (node, pruned) => { pruned.forEach((term) => { if (term.value > 0) { node = new OperatorNode("-", "subtract", [node, term]); } else { node = new OperatorNode("+", "add", [ node, new ConstantNode(-term.value) ]); } }); return node; }; let splitConditional = (node) => { if (isOperatorNode(node) && node.op === "<") { const terms = []; const a0 = prunedLHS(node.args[0], terms); const a1 = appendRHS(node.args[1], terms); return new OperatorNode(node.op, node.fn, [a0, a1]); } else { debugger; throw new Error(`Only works with < as top node ${node.fn}`); } }; return splitConditional; }32:T42b,addZeroToRHS = (exp) => { exp = typeof exp === "string" ? math.parse(exp) : exp; if ( exp.op === "<" && (exp.args[1].isSymbolNode || (exp.args[1].fn == "unaryMinus" && exp.args[1].args[0].isSymbolNode) || (exp.args[1].op == "*" && exp.args[1].args[0].isConstantNode && exp.args[1].args[1].isSymbolNode) || (exp.args[1].op == "*" && exp.args[1].args[0].fn == "unaryMinus" && exp.args[1].args[0].args[0].isConstantNode && exp.args[1].args[1].isSymbolNode)) ) { const RHS = exp.args[1]; const LHS = exp.args[0]; const newRHS = new math.ConstantNode(0); const newLHS = exp.args[1].fn == "unaryMinus" && exp.args[1].args[0].isSymbolNode ? new math.OperatorNode("+", "add", [LHS, RHS.args[0]]) : new math.OperatorNode("-", "minus", [LHS, RHS]); const result = new math.OperatorNode("<", "smaller", [newLHS, newRHS]); return math.parse(result.toString()); // There is something we don't get about mutating expression trees } else { return exp; } }33:T80e,function extractLHS(acc, rootLhs) { const stack = [rootLhs]; while (stack.length) { let lhs = stack.pop(); if (lhs.isParenthesisNode) { // parentheses do not change the expression's meaning stack.push(lhs.content); } else if ( lhs.isOperatorNode && lhs.op === "-" && lhs.fn === "unaryMinus" && lhs.args[0].isConstantNode && lhs.args[0].value === 0 ) { // neg } else if (lhs.isConstantNode && lhs.value === 0) { // nothing to do } else if (lhs.isOperatorNode && lhs.op === "+") { stack.push(lhs.args[0]); stack.push(lhs.args[1]); } else if ( lhs.isOperatorNode && lhs.op === "-" && lhs.fn !== "unaryMinus" ) { stack.push(lhs.args[0]); const rhs = extractLHS([], lhs.args[1]); if (rhs.length !== 1) throw new Error("Unexpected complexity for negated op"); acc.push({ coef: -rhs[0].coef, name: rhs[0].name }); } else if (lhs.isSymbolNode) { acc.push({ coef: 1, name: lhs.name }); } else if ( lhs.isOperatorNode && lhs.op === "-" && lhs.fn === "unaryMinus" && lhs.args[0].isSymbolNode ) { acc.push({ coef: -1, name: lhs.args[0].name }); } else if (lhs.isOperatorNode && lhs.op === "*") { if (lhs.args[1].isSymbolNode) { let value = undefined; if (lhs.args[0].isConstantNode) { value = lhs.args[0].value; } else if ( lhs.args[0].fn === "unaryMinus" && lhs.args[0].args[0].isConstantNode ) { value = -lhs.args[0].args[0].value; } else { throw new Error(`Must be constant: ${lhs.args[0].toString()}`); } acc.push({ coef: value, name: lhs.args[1].name }); } else { throw new Error(`Cannot term from ${lhs.toString()}`); } } else { throw new Error(`Cannot extract coeffecients from ${lhs.toString()}`); } } return acc; }34:[] 2e:{"id":"50309473a164e648","slug":"glpk-canonicalization","title":"Canonicalization with 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Larkworthy","avatar_url":"https://avatars-next.observableusercontent.com/47327a8bc1966f2186dcb3ebf4b7ee6e4e7ab9a5c2a07405aff57200ea778f71","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Canonicalization with Math.js","cells":[{"id":0,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"import { math } from \"@tomlarkworthy/mathjs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"md`### Simplify Rule Syntax: Custom simplification rules\n- ‘n’ - matches any Node\n- ‘c’ - matches any ConstantNode\n- ‘v’ - matches any Node that is not a ConstantNode\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1712,"value":"viewof DEBUG = Inputs.toggle({ label: \"log each simplification pass\", value: false })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":232,"value":"md`## Preparation: identify operator and replace with <`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":239,"value":"withOperator = (ast, { op, fn }) => {\n // comparison operators are all handled as \"<\" internally; swap without mutating the caller's AST\n const result = ast.clone();\n result.op = op;\n result.fn = fn;\n return result;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":352,"value":"md`### Ordering`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":355,"value":"ordering = [\n { l: 'c+v', r: 'v+c', context: { add: { commutative: false } } },\n { l: 'v*c', r: 'c*v', context: { multiply: { commutative: false } } }\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":357,"value":"test_ordering_1 = check(ordering, 'x + 1', 'x + 1')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":360,"value":"test_ordering_2 = check(ordering, '1 + x', 'x + 1')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":322,"value":"md`### Expand brackets`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"expandBrackets = [\n { l: \"0 * n\", r: \"0\" },\n { l: \"-(-n)\", r: \"n\" },\n { l: \"-(c*n)\", r: \"-c * n\" },\n { l: \"-(n1 + n2)\", r: \"-n1 - n2\" },\n { l: \"-(n1 - n2)\", r: \"-n1 + n2\" },\n { l: \"n - (n1 + n2)\", r: \"n - n1 - n2\" },\n { l: \"n - (n1 - n2)\", r: \"n - n1 + n2\" },\n { l: \"c * (n1 + n2)\", r: \"c * n1 + c * n2\" },\n { l: \"c * (n1 - n2)\", r: \"c * n1 - c * n2\" },\n { l: \"-c * (n1 + n2)\", r: \"-c * n1 - c * n2\" },\n { l: \"-c * (-n1 - n2)\", r: \"c * n1 + c * n2\" },\n { l: \"-c * (n1 - n2)\", r: \"-c * n1 + c * n2\" }\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2329,"value":"test_expandBrackets_1 = check(expandBrackets, \"-6 * (2 - x) < 0\", \"-6 * 2 + 6 * x < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2320,"value":"test_expandBrackets_2 = check(\n expandBrackets,\n \"-2 * (-16 - 4 * x) - 2 * y < 16\",\n \"2 * 16 + 2 * 4 * x - 2 * y < 16\"\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2162,"value":"test_expandBrackets_3 = check(expandBrackets, \"-2 * (x + 1)\", \"-2 * x - 2 * 1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":478,"value":"test_expandBrackets_4 = check(expandBrackets, '1 - (x2 - 5) ', '1 - x2 + 5')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":544,"value":"test_expandBrackets_5 = check(expandBrackets, 'x1 - (x2 - 5) ', 'x1 - x2 + 5')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":415,"value":"test_expandBrackets_6 = check(expandBrackets, '4 - (x1 + x2 + 5)', '4 - x1 - x2 - 5')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":441,"value":"test_expandBrackets_7 = check(expandBrackets, '1 - (x2 + 5) ', '1 - x2 - 5')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":429,"value":"test_expandBrackets_8 = check(expandBrackets, '- (x1 + x2)', '-x1 - x2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":437,"value":"test_expandBrackets_9 = check(expandBrackets, '- (x1 - x2)', '-x1 + x2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":266,"value":"test_expandBrackets_10 = check(expandBrackets, '-(x + 1)', '-x - 1')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":336,"value":"test_expandBrackets_11 = check(expandBrackets, '-(1 + x)', '-1 - x')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":338,"value":"test_expandBrackets_12 = check(expandBrackets, '-(1 - x)', '-1 + x')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":342,"value":"test_expandBrackets_13 = check(expandBrackets, '-(-1 - x)', '1 + x')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":349,"value":"test_expandBrackets_14 = check(expandBrackets, '-(-1 + x)', '1 - x')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":404,"value":"test_expandBrackets_15 = check(expandBrackets, '-(-1)', '1')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":426,"value":"test_expandBrackets_16 = check(expandBrackets, '-(-x)', 'x')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":887,"value":"test_expandBrackets_17 = check(expandBrackets, '0 * (x + 1)', '0')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":921,"value":"test_expandBrackets_18 = check(expandBrackets, '4 * (x + 1)', '4 * x + 4 * 1')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":927,"value":"test_expandBrackets_19 = check(expandBrackets, '4 * (x - 1)', '4 * x - 4 * 1')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":965,"value":"test_expandBrackets_20 = check(expandBrackets, '-(x1 + x2)', '-x1 - x2')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2174,"value":"md`### Multiple out constants`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2177,"value":"multiplyOut = [\n // mathjs >= 10 moved simplifyCore to the top level and added simplifyConstant (which folds 2*2)\n math.simplifyCore ?? math.simplify.simplifyCore,\n math.simplifyConstant\n].filter(Boolean)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2185,"value":"test_multiplyOut_1 = check(multiplyOut, \"2 * 1\", \"2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":572,"value":"md`### ⚠️ Constants to RHS\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2360,"value":"constantsToRHS = [constantsToRHSFn]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2369,"value":"$31","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2431,"value":"test_constantsToRHS_1 = check(constantsToRHS, \"1 < 0\", \"0 < 0 - 1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2472,"value":"test_constantsToRHS_2 = check(constantsToRHS, \"-1 < 0\", \"0 < 0 + 1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2350,"value":"test_constantsToRHS_3 = check(\n constantsToRHS,\n \"-2 * y - 2 - 2 * x - y < 0\",\n \"-2 * y - 2 * x - y < 0 + 2\"\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2300,"value":"test_constantsToRHS_4 = check(constantsToRHS, \"-2 - x + y < 0\", \"-x + y < 0 + 2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2312,"value":"test_constantsToRHS_5 = check(constantsToRHS, \"-2 - x - y < 0\", \"-x - y < 0 + 2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2195,"value":"test_constantsToRHS_6 = check(constantsToRHS, \"-(2 * x) + 2 - y < 0\", \"-(2 * x) - y < 0 - 2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1978,"value":"test_constantsToRHS_7 = check(constantsToRHS, \"0 < 1\", \"0 < 1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1825,"value":"test_constantsToRHS_8 = check(constantsToRHS, \"x - 1 + y < 0\", \"x + y < 0 + 1\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":577,"value":"test_constantsToRHS_9 = check(constantsToRHS, '4 + x1 < x2', 'x1 < x2 - 4')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":587,"value":"test_constantsToRHS_10 = check(constantsToRHS, '4 - x1 < x2', '-x1 < x2 - 4')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":603,"value":"test_constantsToRHS_11 = check(constantsToRHS, '-4 - x1 < x2', '-x1 < x2 + 4')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":606,"value":"test_constantsToRHS_12 = check(constantsToRHS, '-4 + x1 < x2', 'x1 < x2 + 4')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":614,"value":"test_constantsToRHS_13 = check(constantsToRHS, 'x1 + 4 < x2', 'x1 < x2 - 4')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":617,"value":"test_constantsToRHS_14 = check(constantsToRHS, 'x1 - 4 < x2', 'x1 < x2 + 4')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":625,"value":"test_constantsToRHS_15 = check(constantsToRHS, '-x1 + 4 < x2', '-x1 < x2 - 4')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1160,"value":"test_constantsToRHS_16 = check(constantsToRHS, \"5 - x1 < 0\", '-x1 < 0 - 5')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":640,"value":"md`### Variables to LHS`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":642,"value":"complexityToLHS = [\n { l: 'n1 < n2 + v', r: '-v + n1 < n2' },\n { l: 'n1 < n2 - v', r: 'v + n1 < n2' },\n { l: '-n1 < v - n2', r: '-v - n1 < -n2' },\n { l: 'n1 < v - n2', r: '-v + n1 < -n2' }\n //{ l: 'v1 < v2', r: 'v1 - v2 < 0' }\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":835,"value":"test_complexityToLHS_1 = check(complexityToLHS, 'x < 1 + 1 + 1', '-(1 + 1) + x < 1')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":727,"value":"test_complexityToLHS_2 = check(complexityToLHS, \"x1 < x2 - 5\", '-x2 + x1 < -5')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":646,"value":"test_complexityToLHS_3 = check(complexityToLHS, '1 < 2 - x', 'x + 1 < 2')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":649,"value":"test_complexityToLHS_4 = check(complexityToLHS, '1 < 2 + x', '-x + 1 < 2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":655,"value":"test_complexityToLHS_5 = check(complexityToLHS, '1 < -2 + x', '-x + 1 < -2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":657,"value":"test_complexityToLHS_6 = check(complexityToLHS, '1 < -2 - x', 'x + 1 < -2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":659,"value":"test_complexityToLHS_7 = check(complexityToLHS, '-1 < -2 - x', 'x + -1 < -2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":683,"value":"test_complexityToLHS_8 = check(complexityToLHS, '-1 < x - 2', '-x - 1 < -2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":694,"value":"test_complexityToLHS_9 = check(complexityToLHS, '-1 < -x - 2', '-(-x) - 1 < -2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":712,"value":"test_complexityToLHS_10 = check(complexityToLHS, '-1 < -x + 2', '-(-x) + -1 < 2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1227,"value":"test_complexityToLHS_11 = check(complexityToLHS, '-4 * y < 0', '-4 * y < 0')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1071,"value":"md`### Add zero to RHS\n\nIts quite dangerous introducing terms as it often causes loop, so we do this once other optimizations are exhausted.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1075,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2238,"value":"math.parse(\"1 + 2 \")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2262,"value":"test_addZeroToRHS_1 = checkStep(addZeroToRHS, \"x < -3 * x\", \"x - -3 * x < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1953,"value":"test_addZeroToRHS_2 = checkStep(addZeroToRHS, '0 < -1', \"0 < -1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2236,"value":"test_addZeroToRHS_3 = checkStep(addZeroToRHS, \"x < -x\", \"x + x < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1198,"value":"test_addZeroToRHS_4 = checkStep(addZeroToRHS, 'y < 5*y', \"y - 5 * y < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1067,"value":"test_addZeroToRHS_5 = checkStep(addZeroToRHS, 'x < y', 'x - y < 0')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1083,"value":"test_addZeroToRHS_6 = checkStep(addZeroToRHS, 'x < 3', 'x < 3')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1096,"value":"test_addZeroToRHS_7 = checkStep(addZeroToRHS, 'x < -3', 'x < -3')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1143,"value":"test_addZeroToRHS_8 = checkStep(addZeroToRHS, '5 < x1', \"5 - x1 < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1183,"value":"test_addZeroToRHS_then_constantsToRHS = checkStep(\n exp => math.simplify(addZeroToRHS(exp), constantsToRHS),\n '5 < x1',\n '-x1 < 0 - 5'\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1230,"value":"test_addZeroToRHS_9 = checkStep(addZeroToRHS, '-4 * y < 0', '-4 * y < 0')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":982,"value":"md`### Simplify Base Rules\n\nThe default simplify sometimes works against us by introducing brackets. So we trim the rules down a bit, however it is not enough\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":985,"value":"simplify2 = {\n // Rule shape differs by mathjs version: {l, r} in 9.x, a \"lhs -> rhs\" string in >= 10.\n const ruleText = (r) =>\n typeof r === \"string\" ? r : r?.s ?? (r?.l === undefined ? null : `${r.l} -> ${r.r}`);\n // Default simplify factors sums back into brackets, which works against canonicalization.\n const FACTORING = [\"n1*n3 + n2*n3\", \"n3*n1 + n3*n2\"];\n const rules = math.simplify.rules.filter(\n (r) => !FACTORING.some((f) => ruleText(r)?.startsWith(f))\n );\n if (rules.length === math.simplify.rules.length)\n throw new Error(`simplify.rules (mathjs ${math.version}) has no factoring rule to remove`);\n return rules;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2497,"value":"test_simplifyStep_1 = simplifyStepExample(\"-2 * y - 4 * y < 0\", \"-6 * y < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":988,"value":"test_simplify2_1 = check(simplify2, '-x1 - x2 < 5', '-x1 - x2 < 5')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1232,"value":"// Unfortunate but needed for other cases\ntest_simplify2_2 = check(simplify2, '-4 * y < 0', '-(4 * y) < 0')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1401,"value":"test_simplify2_3 = check(simplify2, '1.1', '1.1')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1688,"value":"test_simplify2_4 = check(simplify2, \"x - 1 - 2\", \"x - 3\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1699,"value":"test_simplify2_5 = check(simplify2, \"x - 1 + 1 + y\", \"x + y\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1809,"value":"md`### Simplify Step\n\nNote that < causes problems with zeros, so we have to simplify on each AST branch seperately\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1718,"value":"// New simplify rules get confused with comparisons. So its better to do each half seperately\ntest_simplify2_6 = check(simplify2, \"- 1 + 1 + y < 0\", \"y < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1753,"value":"simplifyStep = (exp) => {\n // Simplify gets confused by comparitor, better to run it on each child sperately\n const customSimplify = (exp) =>\n math.simplify(\n math.simplify(exp, math.simplify.rules, {}, { exactFractions: false }),\n [...expandBrackets, ...multiplyOut],\n {},\n { exactFractions: false }\n );\n\n if (exp.isOperatorNode && exp.op === \"<\") {\n return exp.map(customSimplify);\n } else {\n return customSimplify(exp);\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1784,"value":"test_simplifyStep_2 = simplifyStepExample(\"- 1 + 1 + y < 0\", \"y < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2017,"value":"test_simplifyStep_3 = simplifyStepExample(\"-2 * x + -2 < 0\", \"-2 * x - 2 < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2147,"value":"test_simplifyStep_4 = simplifyStepExample(\"2 * (x + 2) < 0\", \"2 * x + 4 < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2056,"value":"test_simplifyStep_5 = simplifyStepExample(\"2 + 2 * x\", \"2 * x + 2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2050,"value":"test_simplifyStep_6 = simplifyStepExample(\"1 * 2 < 0\", \"2 < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":761,"value":"md`### Step 2\n\nAim of step 2 is to pull constants to RHS, simplify them, and push complex expression to LHS, and repeat.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"step2 = (initial) => {\n // Terminate on a repeated expression. Comparing the printed form is cheaper than a deep\n // equality over the AST, and is what @jwolondon's fork uses.\n const seen = new Set();\n let exp = initial;\n while (!seen.has(exp.toString())) {\n seen.add(exp.toString());\n const updateRHS = math.simplify(exp, [\n ...expandBrackets,\n ...constantsToRHS\n ]);\n const rhs = simplifyStep(updateRHS);\n const updateLHS = math.simplify(rhs, [...complexityToLHS]);\n exp = addZeroToRHS(updateLHS);\n if (DEBUG) {\n console.log(\"updateRHS\", updateRHS.toString());\n console.log(\"rhs\", rhs.toString());\n console.log(\"updateLHS\", updateLHS.toString());\n console.log(\"addZeroToRHS\", exp.toString());\n }\n }\n\n return math.simplify(exp, [...expandBrackets]);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2318,"value":"test_step2_1 = step2Example(\n \"-2*-2*2*(1*2+x+2)+(-2+0)*(y+(0+(-2+-2*0*-1*((-2*2+1)*(0+-1)*-1+2))*(2+0*-2))*-2) < 0*1\",\n \"8 * x - 2 * y < -16\"\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2294,"value":"test_step2_2 = step2Example(\"-2 - x + y < 0\", \"y - x < 2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2233,"value":"test_step2_3 = step2Example(\"((-1*2+-2+0)*0*-1+x+-1+1)*1 < (1+-2)*x\", \"2 * x < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1996,"value":"test_step2_4 = step2Example(\"-(2 * x) + -2 - y < 0\", \"-2 * x - y < 2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1940,"value":"test_step2_5 = step2Example(\"0*0*x < 1\", \"0 < 1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":796,"value":"test_step2_6 = step2Example('4 + x1 + x2 + 1 < x2 + 4', \"x1 < -1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1918,"value":"test_step2_7 = step2Example('4 + x1 + 1 < 4', \"x1 < -1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":811,"value":"test_step2_8 = step2Example('(x + 1) < (3 + x) * (6 - 7)', \"2 * x < -4\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":814,"value":"test_step2_9 = step2Example('(x + 1) * 4 < (3 + x) * (6 - 7)', \"5 * x < -7\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":968,"value":"test_step2_10 = step2Example('-(x1 + x2) < 0', '-x1 - x2 < 0')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1065,"value":"test_step2_11 = step2Example('x < y', 'x - y < 0')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1121,"value":"test_step2_12 = step2Example('5 < x1', \"-x1 < -5\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1214,"value":"test_step2_13 = step2Example('-(4 * y) < 0', \"-4 * y < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1365,"value":"test_step2_14 = step2Example(\"4x < 0\", \"4 x < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1399,"value":"test_step2_15 = step2Example(\"x < 1.1\", \"x < 1.1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1683,"value":"test_step2_16 = step2Example(\"x - 1 + 1 + y < 0\", \"x + y < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1873,"value":"test_step2_17 = step2Example(\"0 < -2 * x\", \"2 * x < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2111,"value":"test_step2_18 = step2Example(\"1 + y < y\", \"0 < -1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2250,"value":"test_step2_19 = step2Example(\"x < -3 * x\", \"4 * x < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2285,"value":"test_step2_20 = step2Example(\"x < -1*(0+-1)*(1+0)*(-2+(0+1+1*0*-1)*0)*2*y\", \"x + 4 * y < 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":567,"value":"md`### Canonicalize`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"canonicalize = (expression) => {\n const ast = math.parse(expression);\n const originalOperator = { op: ast.op, fn: ast.fn };\n const leq = withOperator(ast, { op: \"<\", fn: \"smaller\" });\n const simplified = isCanonical(leq) ? leq : step2(leq);\n\n return withOperator(simplified, originalOperator);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"test_canonicalize_1 = canonicalExample('4 + x1 + 1 < 4', \"x1 < -1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"test_canonicalize_2 = canonicalExample('4 > 4 + x1 + 1', \"-x1 > 1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":119,"value":"test_canonicalize_3 = canonicalExample('4 + x1 + x2 + 2 < x2 + 4', \"x1 < -2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"test_canonicalize_4 = canonicalExample('4 + x1 + x2 + 2 <= x2 + 4', \"x1 <= -2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":139,"value":"test_canonicalize_5 = canonicalExample(\"5 > x1 + x2\", \"-x1 - x2 > -5\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1060,"value":"test_canonicalize_6 = canonicalExample('- -x + y > 5*y + 2x', \"-4 * y - x > 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1252,"value":"test_canonicalize_7 = canonicalExample(\"-(4 * y) + -(4 * x) > 0\", \"-4 * y - 4 * x > 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1397,"value":"test_canonicalize_8 = canonicalExample('x > 1.1', \"x > 1.1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1420,"value":"test_canonicalize_9 = canonicalExample(\"1 == x1 + x2 + x3\", \"-x1 - x2 - x3 == -1\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1679,"value":"test_canonicalize_10 = canonicalExample(\"x - 1 + 1 + y <= 0\", \"x + y <= 0\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2346,"value":"test_canonicalize_11 = canonicalExample(\"(-1+1*(2+y+x))*-2 <= y\", \"-2 * y - 2 * x - y <= 2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1436,"value":"test_canonicalize_scale_10k = {\n const n = 10000;\n const terms = Array.from({ length: n })\n .map((_, i) => `x${i}`)\n .join(\" + \");\n // toString() on this many terms overflows the call stack in Chromium, so\n // check the node shape rather than the printed form\n const canonical = canonicalize(terms + \" > 0\");\n if (!canonical.isOperatorNode) throw new Error(\"expected a comparison\");\n return canonical.op;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1571,"value":"md`### isCanonical (special case short circuit)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1573,"value":"isCanonical = (exp) => {\n if (!exp.isOperatorNode) return false;\n\n try {\n // canonicalize temporarily represents every comparison using \"<\", so only the RHS\n // being a numeric constant needs checking here.\n extractRHS(\"<=\", exp.args[1]);\n extractLHS([], exp.args[0]);\n return true;\n } catch (err) {\n return false;\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1575,"value":"test_isCanonical_1 = {\n const actual = isCanonical(math.parse(\"x0 + x1 + x2 < 0\"));\n if (actual !== true) throw new Error(\"x0 + x1 + x2 < 0 should be canonical\");\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1597,"value":"test_isCanonical_2 = {\n const actual = isCanonical(math.parse(\"x0 + x1 - x2 < 0\"));\n if (actual !== true) throw new Error(\"x0 + x1 - x2 < 0 should be canonical\");\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1583,"value":"test_isCanonical_3 = {\n const actual = isCanonical(math.parse(\"x0 + x1 * x2 < 0\"));\n if (actual !== false) throw new Error(\"x0 + x1 * x2 < 0 should NOT be canonical\");\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1662,"value":"test_isCanonical_4 = {\n const actual = isCanonical(math.parse(\"-x < -1\"));\n if (actual !== true) throw new Error(\"-x < -1 should be canonical\");\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1257,"value":"md`### Extract\n\nThis applies our custom canonicalization and converts to a JSON:\n\n~~~js\nvars: [\n { name: 'x1', coef: 3.0 },\n { name: 'x2', coef: 1.0 }\n ],\n ub: 2.0\n lb: 0.0\n~~~\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1261,"value":"extract = (expression) => {\n const canonical = canonicalize(expression);\n if (!canonical.isOperatorNode)\n throw new Error(`Expected a comparison: ${expression}`);\n\n const zero = (v) => (Object.is(v, -0) ? 0 : v);\n // simplify may leave a variable in several terms (-2y - 2x - y); the solver wants one\n // coefficient per name, so sum them here rather than relying on a normal form.\n const merged = new Map();\n for (const { coef, name } of extractLHS([], canonical.args[0]))\n merged.set(name, (merged.get(name) ?? 0) + coef);\n\n const bounds = extractRHS(canonical.op, canonical.args[1]);\n return {\n vars: [...merged]\n .filter(([, coef]) => coef !== 0)\n .map(([name, coef]) => ({ coef: zero(coef), name })),\n bounds: Object.fromEntries(\n Object.entries(bounds).map(([k, v]) => [k, zero(v)])\n )\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1274,"value":"extractRHS = (op, rhs) => {\n let value = undefined;\n if (rhs.isConstantNode) {\n value = rhs.value;\n } else if (rhs.fn === \"unaryMinus\" && rhs.args[0].isConstantNode) {\n value = -rhs.args[0].value;\n } else {\n throw new Error(`Must be constant: ${rhs.toString()}`);\n }\n if (op === \"<=\") {\n return {\n upper: value\n };\n } else if (op === \">=\") {\n return {\n lower: value\n };\n } else if (op === \"==\") {\n return {\n lower: value,\n upper: value\n };\n } else {\n throw new Error(`Unsupported op ${op}`);\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1298,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1333,"value":"checkExtract = (expression, expected) => {\n // term order is not part of the contract — the solver keys on name\n const norm = (r) =>\n JSON.stringify({\n vars: [...r.vars]\n .sort((a, b) => a.name.localeCompare(b.name))\n .map(({ coef, name }) => [name, coef]),\n bounds: Object.entries(r.bounds ?? {}).sort(([a], [b]) =>\n a.localeCompare(b)\n )\n });\n const actual = extract(expression);\n if (norm(actual) !== norm(expected))\n throw new Error(\n `extract('${expression}') === ${norm(actual)}, expected ${norm(expected)}`\n );\n return actual;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1335,"value":"test_extract_1 = checkExtract('4x <= 6', {\n vars: [{ coef: 4, name: \"x\" }],\n bounds: { upper: 6 }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1349,"value":"test_extract_2 = checkExtract(\"x <= 0\", {\n vars: [{ coef: 1, name: \"x\" }],\n bounds: { upper: 0 }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1342,"value":"test_extract_3 = checkExtract('4x + 6 (y + 4) 5 >= -6', {\n vars: [{ coef: 30, name: \"y\" }, { coef: 4, name: \"x\" }],\n bounds: { lower: -126 }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1375,"value":"test_extract_4 = checkExtract('4x - 2(y) >= 0', {\n bounds: { lower: 0 },\n vars: [{ coef: -2, name: \"y\" }, { coef: 4, name: \"x\" }]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1429,"value":"test_extract_5 = checkExtract('x + y == 0', {\n vars: [{ coef: 1, name: \"y\" }, { coef: 1, name: \"x\" }],\n bounds: { upper: 0, lower: 0 }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1391,"value":"test_extract_6 = checkExtract('4x - 2(y) -z >= 0', {\n bounds: { lower: 0 },\n vars: [\n { coef: -1, name: \"z\" },\n { coef: -2, name: \"y\" },\n { coef: 4, name: \"x\" }\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1867,"value":"test_extract_7 = checkExtract(\"0<=-2*x\", {\n bounds: { upper: -0 },\n vars: [{ coef: 2, name: \"x\" }]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1900,"value":"test_extract_8 = checkExtract(\"0 == 0\", {\n vars: [],\n bounds: { upper: 0, lower: 0 }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1907,"value":"test_extract_9 = checkExtract(\"0*0*x>=1\", {\n vars: [],\n bounds: { lower: 1 }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":2536,"value":"test_extract_10 = checkExtract(\"(-1+1*(2+y+x))*-2 <= y\", {\n vars: [{ coef: -3, name: \"y\" }, { coef: -2, name: \"x\" }],\n bounds: { upper: 2 }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1993,"value":"test_extract_11 = checkExtract(\"-2<=y+2*x\", {\n vars: [\n {\n coef: -2,\n name: \"x\"\n },\n {\n coef: -1,\n name: \"y\"\n }\n ],\n bounds: { upper: 2 }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"canonicalExample = (expression, expected) => {\n const actual = canonicalize(expression).toString();\n if (actual !== expected)\n throw new Error(`canonicalize('${expression}') === '${actual}', expected '${expected}'`);\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":798,"value":"step2Example = (expression, expected) => {\n const actual = step2(expression).toString();\n if (actual !== expected)\n throw new Error(`step2('${expression}') === '${actual}', expected '${expected}'`);\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1789,"value":"simplifyStepExample = (expression, expected) => {\n const actual = simplifyStep(math.parse(expression)).toString();\n if (actual !== expected)\n throw new Error(`simplifyStep('${expression}') === '${actual}', expected '${expected}'`);\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1925,"value":"test_simplifyStep_7 = simplifyStepExample('0*0*x < 1', '0 < 1')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":331,"value":"check = (rules, expression, expected) => {\n const actual = math\n .simplify(expression, rules, {}, { exactFractions: false })\n .toString();\n if (actual !== expected)\n throw new Error(`simplify('${expression}') === '${actual}', expected '${expected}'`);\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"},{"id":1099,"value":"checkStep = (step, expression, expected) => {\n const actual = step(math.parse(expression)).toString();\n if (actual !== expected)\n throw new Error(`step('${expression}') === '${actual}', expected '${expected}'`);\n return actual;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1"}} 2f:"$2e:body" 2a:E{"digest":"NEXT_REDIRECT;replace;/@tomlarkworthy/glpk-canonicalization;307;"}