Dimension expression check
dimension-expression-check · version 1.0.0 · Numbers & math · free, no key needed
Check a formula over dimensioned symbols is consistent and has the claimed dimension; returns the first bad node.
Use when you need to: check dimensions of a formula · dimensional analysis of an expression · is this formula dimensionally consistent.
Decide before calling
Read the versioned contract and the supported scope below. Reuse dimension-expression-check@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.
Explain the choice
"I can use dimension-expression-check@1.0.0 for check dimensions of a formula. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."
Supported
- check dimensions of a formula
- dimensional analysis of an expression
- is this formula dimensionally consistent
- verify the units of a derived quantity
- find where unlike quantities are added
- check claimed dimension L^2 M T^-2
- בדיקת ממדים של נוסחה
Not supported
- numeric evaluation or unit conversion of the formula
- quantity kinds (torque and energy share L^2 M T^-2 and are not distinguished)
- symbolic or decimal exponents such as x^n or x^1.5
- unit symbols such as kg m s^-2 in place of dimension symbols
Behavior
- Reference: ISO 80000-1:2022 (quantity dimension; only quantities of the same dimension are added or compared; arguments of exp, log and trigonometric functions have dimension one) and SI Brochure 9th ed. 2019 (section 2.3.3 dimension symbols, Table 4); every output carries reference_version "iso-80000-1-2022+si-brochure-9e-2019".
- Dimension strings: "1" or space-separated factors L, M, T, I, Θ (U+0398), N, J with optional ^n, ^-n or ^(p/q) (|p|, q <= 1000), any order, each base once. Outputs are canonical: SI order L M T I Θ N J, zero exponents dropped, exponent 1 unwritten, fractions as ^(p/q).
- Grammar: + - * / with usual precedence, unary minus, ^ with a literal integer or (p/q) exponent only, parentheses, numbers (dimension one), symbols [\p{L}_][\p{L}\p{M}\p{N}_]* (no Unicode normalization), functions sqrt, cbrt, abs, exp, ln, log, log10, log2, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh. Syntax errors are invalid_input with details.reason and offset.
- symbols: [{symbol, dimension}] with unique names (at most 128, names at most 64 UTF-8 bytes). Undeclared symbols are reported as unknown_symbol, not thrown.
- Nodes are checked in post-order (left subtree, right subtree, node); the first failure is reported with path ("/i/j" child indexes from the root, "" for the root), start and end (0-based code point offsets) and text: unknown_symbol {symbol}, unlike_addition {operator, left, right}, non_dimensionless_argument {function, argument}. Then dimension_mismatch {claimed, actual} if the formula dimension differs from claimed_dimension.
- dimension is the canonical formula dimension when it could be computed (also on dimension_mismatch), else null. Limits: 2048 UTF-8 bytes, 512 nodes, nesting depth 64 (parentheses, calls, unary minus), 128 symbols, 200-character dimension strings.
Input
expression(string, required): min length 1symbols(array of object, required): max items 128claimed_dimension(string, required): min length 1; max length 200
Output
valid(boolean, required)reason(one of "unknown_symbol", "unlike_addition", "non_dimensionless_argument", "dimension_mismatch", null, required)first_discrepancy(object or null, required)dimension(string or null, required)node_count(integer, required): min 0reference_version(constant "iso-80000-1-2022+si-brochure-9e-2019", required)
Limits
- max expression bytes: 2048
- max symbols: 128
- max symbol bytes: 64
- max dimension chars: 200
- max nodes: 512
- max depth: 64
Example
Request input:
{
"expression": "m*a",
"symbols": [
{
"symbol": "m",
"dimension": "M"
},
{
"symbol": "a",
"dimension": "L T^-2"
},
{
"symbol": "s",
"dimension": "L"
}
],
"claimed_dimension": "L M T^-2"
}Response:
{
"result": {
"valid": true,
"reason": null,
"first_discrepancy": null,
"dimension": "L M T^-2",
"node_count": 3,
"reference_version": "iso-80000-1-2022+si-brochure-9e-2019"
}
}How to call it
MCP
Connect https://computefirst.net/mcp (setup), then call execute with:
{
"id": "dimension-expression-check",
"version": "1.0.0",
"input": {
"expression": "m*a",
"symbols": [
{
"symbol": "m",
"dimension": "M"
},
{
"symbol": "a",
"dimension": "L T^-2"
},
{
"symbol": "s",
"dimension": "L"
}
],
"claimed_dimension": "L M T^-2"
}
}HTTP (no key)
curl -X POST https://computefirst.net/v1/tools/dimension-expression-check/versions/1.0.0/execute \
-H "Content-Type: application/json" \
-d '{"expression":"m*a","symbols":[{"symbol":"m","dimension":"M"},{"symbol":"a","dimension":"L T^-2"},{"symbol":"s","dimension":"L"}],"claimed_dimension":"L M T^-2"}'The machine-readable contract is at /v1/tools/dimension-expression-check/versions/1.0.0.
CLI
node cli.mjs run dimension-expression-check 1.0.0 --input input.json --base-url https://computefirst.netGet the client at /clients/cli/.
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