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add algebraic-range draft
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‎packages/algebraic-range/.github/workflows/algebraic-range.yml‎

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name: algebraic-range
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on:
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push:
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paths:
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- ".github/workflows/algebraic-range.yml"
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pull_request:
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paths:
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- ".github/workflows/algebraic-range.yml"
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workflow_dispatch:
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defaults:
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run:
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working-directory: packages/algebraic-range
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jobs:
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test:
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runs-on: ${{ matrix.os }}
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strategy:
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fail-fast: false
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matrix:
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os: [ubuntu-latest, macos-latest, windows-latest]
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python-version: ["3.9", "3.10", "3.11", "3.12", "3.13"]
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steps:
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- uses: actions/checkout@v4
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- name: Set up Python ${{ matrix.python-version }}
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uses: actions/setup-python@v5
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with:
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python-version: ${{ matrix.python-version }}
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- name: Install dependencies
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run: |
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python -m pip install --upgrade pip
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pip install -e ".[dev]"
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- name: Run tests
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run: pytest -v

‎packages/algebraic-range/LICENSE‎

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MIT License
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Copyright (c) 2026 Daniele Gregori
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.

‎packages/algebraic-range/README.md‎

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# algebraic-range
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[![Tests](https://github.com/Daniele-Gregori/PyPI-packages/actions/workflows/algebraic-range.yml/badge.svg)](https://github.com/Daniele-Gregori/PyPI-packages/actions/workflows/algebraic-range.yml)
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[![PyPI version](https://img.shields.io/pypi/v/algebraic-range.svg)](https://pypi.org/project/algebraic-range/)
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[![Python](https://img.shields.io/pypi/pyversions/algebraic-range.svg)](https://pypi.org/project/algebraic-range/)
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[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
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Generate ranges of algebraic numbers.
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Python port of the **Wolfram** [resource function "AlgebraicRange"](https://resources.wolframcloud.com/FunctionRepository/resources/AlgebraicRange/) resource function.
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Requires [SymPy](https://www.sympy.org/) ≥ 1.12.
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## Overview
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`algebraic_range` creates ranges made of [algebraic numbers](https://en.wikipedia.org/wiki/Algebraic_number). This extends the basic concept of `range()` to include, besides rational numbers, also roots — always restricted to the real domain.
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The first two arguments represent the bounds of the range (minimum and maximum values), while the optional third and fourth arguments (by default equal to 1 and 0) regulate the upper and lower bounds of the steps (differences between successive elements).
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## Usage
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```python
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algebraic_range(x) # Sqrt[Range[1, x²]] for x ≥ 1
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algebraic_range(x, y) # Sqrt[Range[x², y²]] for 0 ≤ x ≤ y
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algebraic_range(x, y, s) # step upper bound s, 0 < s ≤ y
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algebraic_range(x, y, s, d) # step lower bound d, 0 ≤ d ≤ s
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```
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### Parameters
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| Parameter | Default | Description |
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|-----------|---------|-------------|
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| `r1` | *(required)* | Start of range (or single argument) |
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| `r2` | `None` | End of range |
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| `s` | `None` | Step upper bound (negative → descending) |
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| `d` | `0` | Step lower bound |
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| `root_order` | `2` | `int r` → orders 2..r; `[r]` → only order r; `[r1,r2,…]` → listed orders |
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| `step_method` | `"Outer"` | `"Outer"` or `"Root"` |
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| `farey_range` | `False` | Use Farey-sequence–based rational multipliers |
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| `formula_complexity_threshold` | `inf` | Discard elements above this complexity |
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| `algebraics_only` | `True` | Reject transcendental inputs |
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### Options
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#### `root_order`
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```python
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# Include square and cubic roots
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algebraic_range(2, root_order=3)
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# Only cubic roots
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algebraic_range(2, root_order=[3])
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# Cubic and fifth roots
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algebraic_range(1, Rational(3, 2), root_order=[3, 5])
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```
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#### `step_method`
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```python
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# "Root" method: Sqrt[Range[x², y², s²]]
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algebraic_range(0, 3, Rational(1, 3), step_method="Root")
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```
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The default `"Outer"` method uses the outer product construction. The `"Root"` method is generally a superset.
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#### `farey_range`
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```python
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algebraic_range(0, 3, Rational(1, 3), farey_range=True)
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```
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Generalises `FareyRange` by combining algebraic ranges over all Farey-sequence steps.
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#### `formula_complexity_threshold`
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```python
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# Only keep simple expressions
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algebraic_range(4, root_order=4, formula_complexity_threshold=8)
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```
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#### `algebraics_only`
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```python
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from sympy import sqrt, E
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# This raises NotAlgebraicError:
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# algebraic_range(0, 5, sqrt(E))
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# Allow transcendental step:
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algebraic_range(0, 5, sqrt(E), algebraics_only=False)
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```
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## Properties
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- **Extends `range()`**: `set(range(x, y+1))` ⊆ `set(algebraic_range(x, y))`
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- **Negative reflection**: `algebraic_range(-y, -x)` = `list(reversed([-v for v in algebraic_range(x, y)]))`
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- **All outputs are algebraic** (when `algebraics_only=True`) and real
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- **Sorted** in ascending order (or descending for negative step)
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- **No duplicates**
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## See also
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More details and examples can be found in the documentation for the original Wolfram Language resource function [`AlgebraicRange`](https://resources.wolframcloud.com/FunctionRepository/resources/AlgebraicRange/), contributed by the same author and vetted by the Wolfram Review Team.
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‎packages/algebraic-range/pyproject.toml‎

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[build-system]
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requires = ["setuptools>=68.0", "wheel"]
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build-backend = "setuptools.build_meta"
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[project]
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name = "algebraic-range"
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version = "0.8.0"
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description = "Generate ranges of algebraic numbers — a Python port of the Wolfram Language AlgebraicRange resource function."
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readme = "README.md"
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license = "MIT"
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requires-python = ">=3.9"
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authors = [
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{ name = "Daniele Gregori", email = "dangregori@gmail.com" },
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]
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maintainers = [
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{ name = "Daniele Gregori", email = "dangregori@gmail.com" },
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]
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keywords = [
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"algebra",
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"algebraic-numbers",
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"range",
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"roots",
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"symbolic-computation",
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"number-theory",
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]
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classifiers = [
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"Development Status :: 4 - Beta",
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"Intended Audience :: Science/Research",
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"Intended Audience :: Education",
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"Operating System :: OS Independent",
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"Programming Language :: Python :: 3",
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"Programming Language :: Python :: 3.9",
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"Programming Language :: Python :: 3.10",
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"Programming Language :: Python :: 3.11",
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"Programming Language :: Python :: 3.12",
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"Programming Language :: Python :: 3.13",
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"Topic :: Scientific/Engineering :: Mathematics",
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]
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dependencies = [
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"sympy>=1.12",
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]
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[project.optional-dependencies]
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dev = [
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"pytest>=7.0",
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]
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[project.urls]
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Homepage = "https://github.com/Daniele-Gregori/PyPI-packages/tree/main/packages/algebraic-range"
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Documentation = "https://resources.wolframcloud.com/FunctionRepository/resources/AlgebraicRange/"
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Repository = "https://github.com/Daniele-Gregori/PyPI-packages/tree/main/packages/algebraic-range"
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Issues = "https://github.com/Daniele-Gregori/PyPI-packages/issues"
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[tool.setuptools.packages.find]
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where = ["src"]
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[tool.pytest.ini_options]
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testpaths = ["tests"]

‎packages/algebraic-range/src/algebraic_range/__init__.py‎

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"""
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algebraic-range — Generate ranges of algebraic numbers.
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A Python port of the Wolfram Language ResourceFunction ``AlgebraicRange``.
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"""
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from algebraic_range.core import (
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algebraic_range,
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formula_complexity,
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AlgebraicRangeError,
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NotRealError,
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NotAlgebraicError,
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StepBoundError,
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__version__,
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)
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__all__ = [
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"algebraic_range",
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"formula_complexity",
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"AlgebraicRangeError",
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"NotRealError",
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"NotAlgebraicError",
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"StepBoundError",
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]

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