computer-algebra-oracles
Skill4 starsChanged 20 days agoMITView on GitHub
Route exact algebra, finite-field, coding-theory, polynomial-system, group-theory and number-theory questions through SageMath, Magma, OSCAR, Singular, GAP/GUAVA, PARI/GP or Hecke, with replayable evidence and an independent check.
In this repository34 other files it gives its agents.
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The file
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We split this skill into the rules it gives an agent
14 rules. About 0 are common, 14 are distinctive, and 0 are very specific to this project.
≈0
Common · estimate
Many files like this have a rule of this kind.
≈14
Distinctive · estimate
This author's own choices. Worth a look.
0
Very specific
Tied to their project's names, files or tools. Probably skip.
- Common
- Distinctive
- Very specific
- Distinctive: line 8
Use an exact computer-algebra system to expose structure, compute a witness, or falsify a claim.
- Distinctive: line 12
Read references/routing.md when more than one system is plausible or a specialist feature is required.
- Distinctive: line 14
Start with SageMath for broad interactive exploration and cross-domain glue.
- Distinctive: line 15
Prefer OSCAR for integrated exact algebra and geometry, and Singular for ideals, Groebner bases, elimination, and polynomial systems.
- Distinctive: line 16
Prefer GAP/GUAVA for finite groups, automorphisms, equivalence, and coding-theory constructions.
- Distinctive: line 17
Prefer PARI/GP or Hecke for algebraic-number-theory computations.
- Distinctive: line 18
Use Magma when a named Magma algorithm, database, or independent implementation supplies a concrete advantage and a licensed route is …
- Distinctive: line 20
Do not infer mathematical independence merely because two front ends have different names.
- Distinctive: line 26
Use exact literals and exact types.
- Distinctive: line 28
Check load-bearing results through a semantically equivalent route with a genuinely distinct implementation or translate them into the …
- Distinctive: line 31
Read references/receipts.md before handing a result to another lane or treating a computation as exhaustive.
- Distinctive: line 35
Stop and repair the model if the mathematical object in the program is not demonstrably equivalent to the stated object.
- Distinctive: line 36
Stop calling a route independent when its decisive computation shares the same backend or generated artifact.
- Distinctive: line 37
Stop before using an online calculator, licensed installation, paid service, or external upload unless that action is authorized.
≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.
Files
Computer algebra oracles
Use an exact computer-algebra system to expose structure, compute a witness, or falsify a claim. Produce a replayable mathematical receipt; do not silently promote oracle output into a proof.
Route by structure
Read references/routing.md when more than one system is plausible or a specialist feature is required.
- Start with SageMath for broad interactive exploration and cross-domain glue.
- Prefer OSCAR for integrated exact algebra and geometry, and Singular for ideals, Groebner bases, elimination, and polynomial systems.
- Prefer GAP/GUAVA for finite groups, automorphisms, equivalence, and coding-theory constructions.
- Prefer PARI/GP or Hecke for algebraic-number-theory computations.
- Use Magma when a named Magma algorithm, database, or independent implementation supplies a concrete advantage and a licensed route is available.
Do not infer mathematical independence merely because two front ends have different names. Record shared backends such as FLINT, Singular, GAP, or PARI.
Execution contract
- State the ring, field, characteristic, coefficient domain, variable order, quotient, and normalization conventions before computing.
- Probe capability with a small representative calculation. Binary presence or a successful import is not a workload check.
- Use exact literals and exact types. Any floating-point approximation must be explicitly bounded and cannot certify an exact claim by itself.
- Save minimal executable input, tool and package versions, seed when used, and output sufficient to replay the claim.
- Check load-bearing results through a semantically equivalent route with a genuinely distinct implementation or translate them into the target proof system.
- Report the narrowest status supported: explored, witnessed, falsified on the declared domain, independently reproduced, or formally proved.
Read references/receipts.md before handing a result to another lane or treating a computation as exhaustive.
Stop conditions
- Stop and repair the model if the mathematical object in the program is not demonstrably equivalent to the stated object.
- Stop calling a route independent when its decisive computation shares the same backend or generated artifact.
- Stop before using an online calculator, licensed installation, paid service, or external upload unless that action is authorized.
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