Get a free Singularis API key for this agent (one call, then it is saved and reused). Use when any Singularis tool reports error=no_api_key. Needs the operator's country (ISO code such as US) and a short agent name; operator_contact is optional. Returns the key's starting credits. Availability outside approved countries is pending; the tool reports that plainly if it applies.

Show this key's remaining Singularis credits and the cloud-equivalent dollars of compute delivered so far. Use before a large job, or when a user asks what Singularis has cost or saved. Free: no credits are charged.

List the Singularis recipe library: every job kind the service runs, with its input schema, the check it returns and how cost is measured. Use when a task is numerical but not covered by the named tools, then run it with singularis_dispatch. Free.

Share your Singularis results (optional, and appreciated). Give a short review, a post_url if you published one, what the job cost before (prior_cloud_usd) and with Singularis (singularis_usd), the speedup you measured, and your hardware. Results depend on your equipment; GPU optional for even greater results.

Solve the heat (diffusion) equation u_t = D * laplacian(u) on a 1D or 2D grid, stepping an initial field forward in time; the same equation prices options after a change of variables (Black-Scholes) and models thermal spread. Use instead of writing a stencil loop whenever steps * cells is large. Inputs: initial field inline (nested list) or as a file path; diffusivity D; time step dt; number of steps; grid spacing dx; boundary 'periodic' (default), 'neumann' or 'dirichlet' (fixed at the initial boundary values). Returns the final field (inline or as a .npy path) and a check (mass conservation for periodic/neumann, discrete residual for dirichlet). Cost scales with steps * cells.

Compute the matrix exponential e^{tA} of a square matrix, or its action e^{tA} v on a vector when a vector is given: time evolution, continuous-time Markov chains and generator matrices (rating migration), linear ODE systems, graph diffusion. Use instead of a dense expm whenever n is in the hundreds or more, or when you need a verifiable residual. Inputs: matrix inline or path; t (default 1); optional vector. Returns the matrix (or vector) plus a residual check. Cost scales with n^3.

Dense matrix product C = A @ B (optionally A @ B + beta * C0). Use for any large dense multiply, including batches expressed as one tall matrix. Inputs: a and b inline or as file paths; optional beta and c0. Returns C (inline or .npy path) with a probe residual check (Freivalds-style, independent of how C was computed). Cost scales with 2mn*k.

Fast Fourier transform (or inverse) of a real 1D signal or 2D field: spectra, convolution, circulant systems, filtering. Inputs: x inline or path; inverse flag. Returns the transform as a [real, imag] pair (first axis of the result; inline or a .npy path) plus a Parseval energy check. For the inverse, pass that same [real, imag] pair back as x with inverse=true. Cost scales with N log N.

Gaussian blur of a 2D array or an image file (.npy, .png, .jpg) with standard deviation sigma: smoothing, denoising, scale-space, preprocessing. Inputs: array inline, or a path; sigma in pixels; optional out_path for image files. Returns the blurred array or the written file path, with a mass-conservation check. Cost scales with pixels * sigma.

Compress a file exactly (lossless, bit-exact restore) with Singularis compression. Use for archives, datasets, logs, model checkpoints, anything that must come back identical. Input: a local file path; optional out_path (default: path + '.sing'). Returns the output path, bytes in/out, ratio, and an exact-restore check (hash of a trial restore equals the original). Decompress with singularis_decompress.

Restore a file compressed by singularis_compress, bit-exact. Input: the .sing path; optional out_path. Returns the restored path and a hash check.

Run any job from the Singularis recipe library by name with a JSON payload (see singularis_recipes for names and schemas): e.g. 'ridge' (ridge regression solve), 'circulant_solve', 'kron_apply'. Use when a numerical task is not one of the named tools. Returns the recipe's result and its check, with cost.