CVP verified calculation capability
Solve ax + b = rhs, ax + b ○ rhs, |ax + b| = rhs, |ax + b| ○ rhs, (ax + b)/(cx + d) = rhs, or (ax + b)/(cx + d) ○ rhs. a = 0 is identity/inconsistent or ℝ/∅. Discovery /linear-inequality, /absolute-value, /absolute-value-inequality, /rational-equation, /rational-inequality. Not the quadratic formula, not a system, not CAS.
Math · Algebra Capability ID math.algebra.linear_equation version 1.5.1 CVP VERIFIED CURRENT Core
Solution
x = (rhs − b) / aa = 0 and b = rhs → every xa = 0 and b ≠ rhs → no solutionModes: solve · linear · ax+b · equation · eq · equality · inequality · ineq · linear inequality · linear-inequality · linear ineq · linear-ineq · abs · absolute · absolute value · absolute-value · absolutevalue · modulus · abs inequality · abs-inequality · abs ineq · abs-ineq · absolute inequality · absolute-inequality · absolute value inequality · absolute-value-inequality · rational · rational equation · rational-equation · rational eq · rational-eq · fractional equation · fractional-equation · rational inequality · rational-inequality · rational ineq · rational-ineq · fractional inequality · fractional-inequality
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
a | — | — | input / output |
b | — | — | input / output |
c | — | — | input / output |
d | — | — | input / output |
rhs | — | — | input / output |
op | — | — | input / output |
relation | — | — | input |
inequality | — | — | input |
x | — | — | output |
x2 | — | — | output |
lo | — | — | output |
hi | — | — | output |
bound | — | — | output |
pole | — | — | output |
n | — | — | output |
sense | — | — | output |
op_symbol | — | — | output |
sense_symbol | — | — | output |
solutions | — | — | output |
interval | — | — | output |
ranges | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | ax + b ○ rhs solved as a linear (in)equality; pole excluded on rationals |
valid_domain | finite reals; mode-specific (equation / inequality / abs / rational) |
singularity_policy | identity / inconsistent when a = 0; rational pole x = −d/c excluded |
branch_policy | not applicable — real principal value only |
tolerance | not applicable — closed form; capability Evidence owns comparison, no global default |
convergence | not applicable — non-iterative |
conditioning | not applicable — not a matrix κ product |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | deterministic algorithm + Capability@Version |
independent_oracle | cvp:math.algebra.linear_equation O2 / Evidence published cases |
golden_vectors | Evidence golden + boundary + property (and published_reference_case when listed) |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
a=2 b=3 rhs=11 → x=4
CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all six published modes. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.
Human page, REST, and MCP share the same engine and calculation_version.
Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json
and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/linear-equation' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"a":2,"b":3,"rhs":11},"calculation_version":"1.5.1"}'{
"inputs": {
"a": 2,
"b": 3,
"rhs": 11
},
"calculation_version": "1.5.1"
}POST /api/v1/calc/linear-equation. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Declared calculation modes for this capability.
solveinequalityabsabs_inequalityrationalrational_inequalityHuman-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior
Inspect, then execute. Same engine as REST and the human calculator.
curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: inspect_capability' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.algebra.linear_equation"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: execute_calculation' \
-d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.algebra.linear_equation","inputs":{"a":2,"b":3,"rhs":11},"calculation_version":"1.5.1"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.5.1) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.