| name | wolfram-hart |
| description | This skill should be used when the user makes a math or science computation request — even when the answer seems easy to recall. Trigger phrases include: "what is the integral of x²", "solve x³ - 6x² + 11x = 6", "factor this polynomial", "find the eigenvalues of this matrix", "plot sin(x) from 0 to 2π", "convert 60 mph to km/h", "what's the Fourier transform of e^(-x²)", "minimize f(x,y) subject to a constraint". Also invoke for matrix operations of any size, exact symbolic integrals, ODE solving, data regression, modular arithmetic, and any mention of Wolfram, Mathematica, or Wolfram Language. Recalled math can silently contain errors; the Wolfram Engine verifies (e.g., a 4×4 matrix where recalled det=6 but the true det=12). Exception: truly trivial one-step problems (e.g., "what is 2+2") do not warrant the overhead. |
| version | 1.1.0 |
Wolfram Engine
Execute exact computation through the Wolfram Engine, either locally installed
or via Wolfram Cloud. The full Wolfram Language is available: symbolic algebra,
calculus, differential equations, linear algebra, number theory, statistics,
optimization, plotting, data analysis, and image processing.
Autonomy Rules
Compute immediately. When a request falls within the trigger conditions above,
translate the problem to Wolfram Language and execute it without asking the user
for confirmation. Do not ask "would you like me to use Wolfram?" or "shall I
compute this?" Just run the code and present the result.
Compute, don't guess. Do not answer mathematical questions from memory.
The Wolfram Engine produces verified results; training data does not.
Batch related work into one call. Each invocation of wolframscript carries
a 2-3 second kernel startup cost. Combine related computations into a single
Module[...] rather than making multiple calls. For example, if the user asks
to "solve this equation and plot the roots," do both in a single script.
Retry once on failure. If a computation returns an unevaluated expression or
an error, consult ${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/references/wolfram-language-guide.md to verify syntax,
adjust the code, and try once more before reporting the problem.
Skip the pre-flight check unless something fails. Do not run
wolfram-check.sh as a routine first step. Only run it if wolfram-eval.sh
exits with code 1 (not installed) or the output starts with NOT_CONFIGURED,
so the user gets actionable setup instructions.
Workflow
0. Signal routing
Before anything else, output exactly this line so the user knows the request
was routed to the Wolfram Engine:
_ᴡ wolfram_
1. Translate
Convert the user's request to Wolfram Language. Consult
${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/references/wolfram-language-guide.md when unsure about syntax.
Five rules that prevent the most common mistakes:
- Function names are capitalized:
Sin, Solve, Integrate
- Arguments go in square brackets:
Sin[x], never Sin(x)
- Equations use
==: Solve[x^2 == 4, x]
- Ranges and lists use braces:
{x, 0, 10}, {1, 2, 3}
- Constants are capitalized:
Pi, E, I, Infinity
When a request is mathematically ambiguous (e.g., real vs. complex solutions,
degrees vs. radians), choose a reasonable interpretation and state the
assumption briefly when presenting the result.
Quick-reference mapping from natural language to Wolfram functions:
| User says | Function | Example |
|---|
| solve / find x | Solve | Solve[x^2 - 4 == 0, x] |
| solve numerically | NSolve / FindRoot | NSolve[x^5 - x + 1 == 0, x] |
| integrate | Integrate | Integrate[Sin[x]^2, x] |
| definite integral | Integrate[f, {x, a, b}] | Integrate[x^2, {x, 0, 1}] |
| derivative | D | D[x^3 Sin[x], x] |
| limit | Limit | Limit[Sin[x]/x, x -> 0] |
| series / Taylor | Series | Series[Exp[x], {x, 0, 5}] |
| simplify | Simplify / FullSimplify | FullSimplify[Sin[x]^2 + Cos[x]^2] |
| factor | Factor | Factor[x^2 - 5x + 6] |
| expand | Expand | Expand[(x+1)^5] |
| plot / graph | Plot | Plot[Sin[x], {x, 0, 2Pi}] |
| scatter plot | ListPlot | ListPlot[data, PlotStyle -> Red] |
| line plot (data) | ListLinePlot | ListLinePlot[Table[Sin[x], {x, 0, 10, 0.1}]] |
| bar chart | BarChart | BarChart[{3, 1, 4, 1, 5}, ChartLabels -> labels] |
| histogram | Histogram | Histogram[data, 20, "ProbabilityDensity"] |
| contour / heatmap | ContourPlot | ContourPlot[x^2+y^2, {x,-2,2}, {y,-2,2}] |
| 3D surface | Plot3D | Plot3D[x^2+y^2, {x,-2,2}, {y,-2,2}] |
| eigenvalues | Eigenvalues | Eigenvalues[{{1,2},{3,4}}] |
| ODE / diff eq | DSolve | DSolve[y'[x] == -y[x], y[x], x] |
| prime factors | FactorInteger | FactorInteger[360] |
| regression / fit | LinearModelFit | see ${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/references/patterns-visualization.md |
| convert units | UnitConvert | UnitConvert[Quantity[100,"Miles"],"Kilometers"] |
| Fourier transform | FourierTransform | FourierTransform[Exp[-x^2], x, w] |
| optimize / minimize | NMinimize / Minimize | NMinimize[x^4 - 3x^2 + x, x] |
| sum of series | Sum | Sum[1/n^2, {n, 1, Infinity}] |
2. Build
One-liner for simple expressions:
Integrate[Sin[x]^2, {x, 0, Pi}]
Module for multi-step work (use semicolons to suppress intermediate output):
Module[{f, roots, plot},
f[x_] := x^3 - 6 x^2 + 11 x - 6;
roots = Solve[f[x] == 0, x];
plot = Export["/tmp/cubic.png",
Plot[f[x], {x, -1, 5}, PlotTheme -> "Scientific", ImageSize -> 500,
Epilog -> {Red, PointSize[0.02], Point[{x, 0} /. roots]}]];
roots
]
Plots must be exported to a file. Graphics objects have no useful text
representation. Always wrap in Export["/tmp/wolfram_descriptive_name.png", ...]
and then use the Read tool to show the image to the user. Use a unique
descriptive filename per plot to avoid overwriting previous results in the
same session.
3. Execute
Before calling the script, output a single status line so the user knows
computation is starting (the kernel takes 2-3 seconds to start):
_Running Wolfram Engine…_
Run all code through the wrapper script:
bash ${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/scripts/wolfram-eval.sh '<code>' [timeout]
The default timeout is 30 seconds. Pass a higher value as the second argument
for heavy computations (numerical ODEs, large plots, optimization):
bash ${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/scripts/wolfram-eval.sh '<code>' 120
Evaluation mode. The script respects the WOLFRAM_MODE environment
variable: auto (default, tries local then cloud), local, or cloud.
No manual setup needed — auto mode works transparently. When the user has
set WOLFRAM_MODE=cloud, the -cloud flag is added to the wolframscript
invocation and no local Engine is required. If the local kernel is present
but unlicensed, auto mode incurs the full local timeout before falling back;
in that case, WOLFRAM_MODE=cloud avoids the extra wait.
Quoting. Use single quotes around the code argument. When the code contains
derivative apostrophes (y'[x]), switch to double quotes and escape the inner
double quotes with \":
bash .../wolfram-eval.sh 'Solve[x^2 == 4, x]'
bash .../wolfram-eval.sh "DSolve[y'[x] + y[x] == 0, y[x], x]"
When using double quotes, escape dollar signs (\$) for any Wolfram system
variable ($VersionNumber, $SystemID, $ProcessorCount).
Exit codes: 0 = success, 1 = not installed, 2 = execution error, 3 = timeout.
4. Interpret and Present
| Output kind | What to do |
|---|
| Number | Present directly with context. |
| Symbolic expression | Render as LaTeX with ToString[TeXForm[expr]] for clean display. Fall back to Wolfram notation only for deeply nested procedural output. |
| List / Association | Format as a markdown table or bullet list. |
| File path (from Export) | Use the Read tool to display the image inline. |
| Unevaluated (output = input) | The function name or arguments are wrong. Check spelling and brackets. |
| Error message in output | Read the :: message tag. Adjust code and retry once. |
Verify and state assumptions. Apply trust proportional to the computation type:
| Computation | Trust | Action |
|---|
| Arithmetic, constants | Full | Present directly. |
| Symbolic algebra, calculus | High | State domain assumptions (real vs. complex, branch choice) when they affect the result. E.g., Integrate[Exp[-a x^2], {x, -Infinity, Infinity}] silently assumes Re[a] > 0. |
| Numerical optimization, root-finding | Moderate | Sanity-check convergence; try a second starting point if feasible. |
Simplification (Simplify, FullSimplify) | Moderate | Verify equivalence — simplification can drop solutions or change domain. |
| Entity / knowledge-base queries | Low | Warn the user that data may be outdated or missing. |
For high-trust results that are load-bearing, verify by substitution:
sol = Solve[x^2 - 5x + 6 == 0, x];
Simplify[x^2 - 5x + 6 /. sol] (* expect {0, 0} *)
Output Formats
| Goal | Wrapper | Produces |
|---|
| LaTeX | ToString[TeXForm[expr]] | \frac{x^3}{3} |
| Machine-readable | ToString[expr, InputForm] | x^3/3 |
| CSV | ExportString[data, "CSV"] | 1,2,3\n4,5,6 |
| JSON | ExportString[assoc, "JSON"] | {"key":"value"} |
| Image file | Export["/tmp/f.png", plot] | file path on stdout |
Timeouts
| Computation | Timeout |
|---|
| Arithmetic, simple algebra | 30 s (default) |
| Symbolic solving, series | 30-60 s |
| Numerical ODE/PDE, optimization | 60-120 s |
| 3D plots, large datasets | 60 s |
Troubleshooting
Not installed (exit 1). The eval script prints setup instructions covering
both the cloud option (wolframscript binary + free account) and the local
Engine option. Relay them to the user.
Not configured (output starts with NOT_CONFIGURED). wolframscript was
found but neither local nor cloud worked. Run wolfram-check.sh and relay
its setup recommendations to the user.
Graphics prints -Graphics-. The code forgot to call Export. Wrap the
plot in Export["/tmp/name.png", ...].
Computation hangs. Add TimeConstrained[expr, 20, "TIMEOUT"] inside the
Wolfram code for an inner safety net on top of the script-level timeout.
Entity/knowledge-base queries are slow. They fetch data over the internet on
first use. Warn the user or fall back to an approximate answer.
Cloud evaluation is slow. Cold-start latency for cloud kernels is higher
than local. For repeated work, consider the local Engine option.
Reference Files
Detailed syntax and cookbook patterns, loaded on demand:
${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/references/wolfram-language-guide.md -- Complete function reference by domain: algebra, calculus, linear algebra, statistics, plotting, data, strings, and programming constructs.${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/references/output-formats.md -- How the Wolfram Engine formats different expression types, how to control the format, and how to detect errors in output.
Computation Patterns (load by domain)
15 copy-paste-ready patterns split by domain. Load only the file relevant to the current query:
| Domain | File | Patterns | Route when query mentions |
|---|
| Core workflow | references/patterns-core.md | #1 Quick calc, #2 Symbolic LaTeX, #3 Solve+format, #10 Data export, Anti-patterns | solve, simplify, expand, factor, algebra, LaTeX, CSV, JSON |
| Visualization | references/patterns-visualization.md | #4 2D plot, #5 3D surface, #6 Data analysis pipeline | plot, graph, chart, regression, fit, surface, 3D |
| Analysis | references/patterns-analysis.md | #7 Differential equations, #12 Optimization, #13 Fourier/Laplace | integral, derivative, ODE, calculus, series, optimize, transform |
| Discrete & structured | references/patterns-discrete.md | #8 Matrix ops, #9 Number theory, #14 Probability | matrix, eigenvalue, determinant, prime, factor integer, probability, statistics |
| Applied | references/patterns-applied.md | #11 Unit conversions, #15 Image processing | unit, convert, image |
Scripts
${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/scripts/wolfram-eval.sh -- The only interface to the engine. Always use this; never call wolframscript directly.${CLAUDE_PLUGIN_ROOT}/skills/wolfram-hart/scripts/wolfram-check.sh -- Checks both local and cloud mode status. Run when wolfram-eval.sh exits with code 1 or produces NOT_CONFIGURED output.
