sage-compute

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

1. 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>)")

2. 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)

3. 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.

4. 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.