| name | sage-compute |
| description | Quick symbolic/exact computation via the Sage MCP -- factor, simplify, symbolic eigenvalues, exact integrals. Use when float answers are not good enough |
| argument-hint | <expression> | --code "<multiline sage>" | --eig "<matrix>" | --latex "<expr>" | --factor "<integer>" | --simplify "<expr>" |
| allowed-tools | ["Read","mcp__sage__sage_eval","mcp__sage__sage_simplify","mcp__sage__sage_latex","mcp__sage__sage_symbolic_eig","mcp__sage__sage_backend_info"] |
/sage-compute -- Exact Symbolic Computation via Sage
Requires: the sage MCP server (this discipline pack ships it at mcps/sage/). If the server is not configured, every tool below returns a clean "no backend available" error -- install/enable it first.
Front-end to the sage MCP server. Routes common patterns to the right tool with the right preamble, so you do not need to remember Sage syntax for one-off queries.
When to use this skill vs. raw Python
Use /sage-compute when the answer must be exact or symbolic:
- Factor a large integer into primes
- Eigenvalues of a small rational/integer matrix, returned as algebraic roots (not floats)
- Closed-form integral or sum
- Simplify a trigonometric/algebraic expression
- Render a symbolic expression to LaTeX
Use plain Python (numpy/torch) when a numerical answer is fine. Sage is slower and the round-trip to the remote backend adds latency.
Usage
/sage-compute factor(2^64 - 1)
/sage-compute --factor 18446744073709551615
/sage-compute --eig "[[1,2,3],[4,5,6],[7,8,0]]"
/sage-compute --latex "integrate(sin(x)^2, x)"
/sage-compute --simplify "sin(x)^2 + cos(x)^2"
/sage-compute --code "
R.<x> = QQ[]
p = x^4 - 10*x^2 + 1
print(p.factor())
print(p.roots(AA))
"
The first form (bare expression) is treated as a Sage expression and evaluated with a print(...) wrapper.
Execution steps
-
Parse $ARGUMENTS. Branch on flags:
--factor N -> sage_eval(code="print(factor(N))")--eig "<matrix>" -> sage_symbolic_eig(matrix="<matrix>")--latex "<expr>" -> sage_latex(expr="<expr>")--simplify "<expr>" -> sage_simplify(expr="<expr>")--code "<block>" -> sage_eval(code="<block>")- No flag (bare expression) ->
sage_eval(code="print(<expression>)")
-
Call the right MCP tool. All tools are on the sage server:
| Skill route | MCP tool | Required arg |
|---|
--factor, bare expr, --code | mcp__sage__sage_eval | code |
--simplify | mcp__sage__sage_simplify | expr |
--latex | mcp__sage__sage_latex | expr |
--eig | mcp__sage__sage_symbolic_eig | matrix (nested-list literal) |
| (health check) | mcp__sage__sage_backend_info | (none) |
-
Relay the result. The MCP tool already formats backend / success / stdout / stderr. Pass it through unchanged. If success is false, surface the stderr prominently; do not silently hide errors.
-
Verify the result if the caller will act on it. Substitution-chain discipline applies: a Sage output is an oracle, not a proof. Before citing a Sage answer in a working paper, run a cross-check in Python with sympy (or torch) on a small instance to confirm.
Backend transparency
The Sage MCP auto-selects a backend (report it with mcp__sage__sage_backend_info):
- Local Sage -- if a
sage binary is on PATH (or SAGE_BIN is set). Fastest, no network, highest trust.
- SageCell (remote) -- default fallback over the SageCell Jupyter WebSocket. No install required. Session-isolated: no state between calls.
Guard rails
- No persistent state in SageCell mode: each call starts a fresh kernel. If you need state (e.g. define a ring, then manipulate polynomials in it), put everything in ONE
--code block.
- Do not use Sage for floating-point throughput.
numpy.linalg / torch.linalg are faster and more appropriate -- Sage's value is symbolic correctness, not numerical speed.
- Bare expressions are wrapped in
print(...). If your expression already prints, use --code instead to avoid double-printing.
- Heavy, reproducible computations belong in
{{COMPUTATION_DIR}}/ with a pinned script (sympy/torch) -- the MCP is for interactive, small-case work during a session.
