Image Processing

Solution explanations

Generated solutions briefly explain why the chosen method applies, then show the essential calculations and conclusion. Routine arithmetic may be omitted; necessary assumptions, cases, domain restrictions, and endpoint arguments must remain. \intertext{} introduces a method or explains a meaningful transition, rather than narrating every equation. Faithful transcription of a supplied solution still preserves the source's reasoning.

For domain and range problems, a bound alone is not enough: the solution must justify which values are attained. Piecewise functions require checking branch ranges and possible gaps; compositions require checking the inner expression's values and the outer function's domain and mapping properties.

Graphs

Keep useful graphs, with only the labels needed to read the function or support the answer. Prefer sparse ticks and open/filled endpoint markers. Avoid repeated coordinate labels, a legend for a single curve, and unnecessary grids or guide lines. Required problem data, discontinuities, and endpoint inclusion must be preserved. The same rules apply to inline plots, specialist graph generation, and TikZ review/repair.

The solution agent first states the diagram's learning purpose. Its context and values provide exact construction data; they are not a request to print every value. labels contains only indispensable visible text and may be empty. annotations contains necessary drawing actions. For a minimum, request either exact axis ticks or one coordinate label, not both. The diagram agent chooses placement without changing the supplied mathematics. The specification's field names and types are unchanged.

The dispatcher forwards the drawing actions and subject settings (including the plot window and grid preference) with the construction context. An empty label list remains an explicit preference. Generators without separate context arguments receive that information in the drawing description instead. Diagram assembly adds centering only once.

Fractions

New LaTeX uses \dfrac{a}{b} everywhere, including inline mathematics, graph labels, tables, and answer keys. PGF arithmetic such as 2/3 stays arithmetic.

All VBAgent-owned document preambles make legacy \frac and \tfrac calls render like \dfrac, without redefining \dfrac itself or rewriting stored source files. This also applies to previews, exports, practice sets, notes, revision sheets, and archive renders. Display fractions are taller, so labels and tables need sufficient space.

Custom export templates remain under the caller's control. Load amsmath and include DISPLAY_FRACTION_PREAMBLE from vbagent.utils.latex if the template should follow the same policy.

Cached scans, solutions, alternate solutions, and diagrams from an older style contract are regenerated when those stages are next requested. Existing saved documents and published content are not rewritten automatically.