Produce a structured summary of an academic paper from its PDF, in the workshop's literature/<bibkey>.md format. Use when the user has a new paper to add to the project's literature/ directory, asks "what does this paper say?", or asks for a structured intake of a PDF for the lab. Always pair with a verified BibTeX entry; never emit citations from memory.
Render slides or pages of Office documents (.pptx, .ppt, .odp, .docx, .doc, .odt, .xlsx) to PNG images for visual inspection, using LibreOffice headless plus poppler. Use this WHENEVER you need to actually SEE what a PowerPoint, slide deck, or Word/Excel document looks like — verifying a generated or edited .pptx, previewing specific slides, checking layout/overflow/branding, comparing before/after, or turning a deck into thumbnails. Reach for this instead of `qlmanage` (which only renders the first slide) any time the task involves eyeballing more than page one of an Office file.
Compute the dominant k singular values of a LARGE SPARSE matrix or a MATRIX-FREE linear operator (available only through matvec) using Lanczos (scipy.sparse.linalg.svds). Use when the object is sparse or is only available as an apply()/matvec — never densify it. For a small dense matrix, use the qr-iteration skill instead.
Compute the singular values of a DENSE matrix (a 2D numpy array) via unshifted QR iteration. Use when the matrix is small enough to hold and factor densely and you want its singular values. Not for sparse matrices or matrix-free operators — use the lanczos skill for those.
Verify that a candidate primal-dual point (x, y, z) satisfies the KKT conditions for a QP or NLP of the form min f(x) s.t. A x = b, x >= 0 Reports max residuals for stationarity, primal feasibility, dual feasibility, and complementarity. Use whenever a "candidate solution" is reported and you want to confirm it is a KKT point, or to inspect per-block residuals.
Verify that a proposed timestep dt satisfies the element-wise CFL condition dt < 2/sqrt(lambda_max) for the second-order wave equation u_tt = div(c^2 grad u) on a Firedrake mesh, where lambda_max is the largest eigenvalue of the generalized eigenproblem K_e v = lambda M_e v on each cell (M_e: local consistent mass, K_e: local c^2-weighted stiffness). Reports per-element violations with offending cell indices, their lambda_max, and the local time-step bound.