…n — 3.1.0.dev1 (#305) ## UI quality-of-life batch (issues #293–#304) + solution group projection These rough edges surfaced while implementing the numerical real cellular decomposition algorithm in Python. The through-line goal: get from a polynomial system to the projection values of critical points **as `real_mp`, straight through numpy, without a code maze**. Per the "put reusable primitives in core" doctrine, anything with a C++ home landed in **core + bindings** (behind C++ tests); only presentation/interop sugar stayed pure-Python. ### C++ core + bindings - **#294** — `Slice::RandomReal`'s orthogonal path was silently using the *complex* conjugate-orthonormal matrix, so a "real" slice came out complex; now genuinely real. New `random_real` / `random_complex` / `random_vector` factories (continuous, seed-reproducible — the generic-direction tool, unlike the quantized orthonormal `random_matrix`). - **#304** — reusable `IsDistinct` / `IsSamePoint` infinity-norm util → `bertini.is_distinct_up_to` (accepts `real_mp` / `complex_mp` / `real_dbl` / `complex_dbl` points). - **#299** — `merge_multiplicities` (default **True**) on the solver's own `SolutionsWhere` + finite accessors — dedup where the multiplicity clustering lives. - **#302** — `metadata_for(point)`: returns the cluster **representative** by default (one record, carrying `.multiplicity`), or `coincident=True` for the list of every copy — return type never depends on the point's multiplicity. - **#297** — `System.functions()` / `copy_functions()`. - **#300** — `node.eval` accepts a point array or a `{Variable-or-name: value}` dict (not just kwargs), still returning `complex_mp` natively. - **Group projection** — `System.coordinates_of(point, group)` + a `group=` keyword on every solution getter and `to_dataframe`: project solutions onto one variable group (projective groups returned as-is). Reusable for the eventual C++ decomposition. ### Python layer - **#293** — `variables(['x','y','z'])`; `add_variable_group` accepts loose variables / a list / a single Variable / a VariableGroup; `Slice.random_*` gives a clear message (and unwraps a one-group sequence) instead of an opaque converter error. - **#296** — `sys.clone()` method. - **#295** — `bertini.sympy_bridge` exposed lazily + nodes auto-sympify (`_sympy_`), so `sympy.sympify(node)` / `sympy.Matrix(array)` / `sympy.det(J)` just work. - **#294 sugar** — `VariableGroup @ coeffs` → the linear-combination node. ### #298 / #301 (numpy interop) — note the overlap Adds mp-native elementwise helpers `bertini.real/imag/abs/conj/round/sum/norm/is_real` (the numpy↔eigenpy dtype boundary is unpatchable for identity-seeded reductions; documented in `known_gotchas`). **These likely overlap with the native ufunc coverage on `feature/numpy_compat`** — left for the maintainer to reconcile (the helpers still stand alone for `is_real` / dedup / norm). ### Deferred - **#303** (HomogeneousVariableGroup) — out of scope by decision. ## Verification - C++: `test_classes` + `test_nag_algorithms` green (new regression tests for every C++ change). - Python: **660 passed, 4 skipped** (the one initial failure was the intended #299 default change; that test was updated). - Acceptance artifact: a polished marimo notebook (in the sibling `curve_decomposition_in_python` repo, original left untouched) runs end-to-end — projection values arrive as `real_mp`, plus a 3D plot of the real critical points. ## Heads-up for review - **Version bump 3.0.0rc1 → 3.1.0.dev1** is included (this branch *is* the 3.1.0.dev1 work). Drop the first commit if you'd rather bump separately. - **The projective-nullvector reformulation does not track** — mathematically cleaner (only critical points survive) but the mhom homotopy fails every path for this bilinear structure. The notebook uses the working affine+patch formulation and documents the projective attempt as an open question for the start-system / endgame work. - **`int(real_mp)` segfaults** (pre-existing `real_mp` binding bug; `float`/`str` fine) — hit incidentally, out of scope here, worth a follow-up (`real_mp.__int__`). - `doclint` not run locally (no doxygen in this env); every new public C++ entity carries a matching Doxygen comment, so the CI gate should pass. Closes #293, #294, #295, #296, #297, #299, #300, #302, #304. (#298 and #301 addressed via helpers — see the overlap note above before closing.) 🤖 Generated with [Claude Code](https://claude.com/claude-code)

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sys.functions() should return a list of functions #297

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