Chebotarev Density Calculator
Chebotarev theorem conditional conjugacy class density|C|/|G|for independently certifiedfiniteGaloisextension/classunramifiedprimes; not certify extension/group or approximate finite prime count.
Description
A Chebotarev class-density calculation depends on an independently certified finite Galois-extension context.
A Chebotarev class-density calculation depends on an independently certified finite Galois-extension context.1
This tool divides supplied conjugacy-class size by group order without certifying the extension or counting finite primes.
When to use Chebotarev Density Calculator
Use this tool to calculate supplied conjugacy-class size by group order without certifying the extension or counting finite primes.
How to use Chebotarev Density Calculator and how it works
- Prepare actualCertifiedFrobeniusConjugacyClassSize, actualCertifiedFiniteGaloisGroupOrder, with the units, conventions and assumptions below.
- Enter the required fields and run Chebotarev Density Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualCertifiedFrobeniusConjugacyClassSize | Actual Certified Frobenius Conjugacy Class Size. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
| actualCertifiedFiniteGaloisGroupOrder | Actual Certified Finite Galois Group Order. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
Require positive integer class size and group order, each at most 1,000,000, with class size no greater than and dividing the group order. Return their ratio as a number. The tool does not construct an extension, identify a conjugacy class or verify the hypotheses of the Chebotarev theorem.
density=classSize/groupOrder Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Conditional dimensionless conjugacy-class density. | number |
{
"input": {
"actualCertifiedFrobeniusConjugacyClassSize": 2,
"actualCertifiedFiniteGaloisGroupOrder": 4
},
"output": {
"result": {
"value": 0.5
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Dirichlet Approximation Calculator for a complementary operation: A finite rational-approximation search compares nearby fractions within a chosen denominator budget.
Use Composite Density Approximation for a complementary operation: A complement of the prime-density heuristic is an asymptotic illustration rather than a measured composite fraction.
References
-
Chebotarev Density Calculator — tool.io
Similar or alternative tools
- Dirichlet Approximation Calculator
A finite rational-approximation search compares nearby fractions within a chosen denominator budget.
- Composite Density Approximation
A complement of the prime-density heuristic is an asymptotic illustration rather than a measured composite fraction.