against the Rubi corpus
Companion to RISCH_PLAN.md (the transcendental Risch plan) and
BRONSTEIN_ERRATA.md. This file covers the experimental algebraic
track on branch risch-algebraic and is written to be picked up by a
fresh session.
Status: both items implemented and corpus-verified (2026-08-15/16 session); see §6. Final measurement: the pre-fix branch had 1,705
Runs of sympy's risch_integrate(f, x, algebraic=True) (the experimental
exp-log-tower representation of radicals, e.g. sqrt(x) as
exp(log(x)/2)) over test corpora. Companion to the "Experimental
track" section of the RISCH_PLAN.md gist.
The experiment: represent radicals as exp-log towers, run the
Written 2026-08-25 (session ending 5e). Context: RISCH_PLAN.md “Phase 5e
— DONE”; branch risch-hypertangent, tip 66bc72d6b8, pushed. Each
item stands alone; none block further work, but 1–4 gate the eventual
Phase 5 PR.
Decision made (veto-able): risch_integrate() returns the raw
Errata found while completing SymPy's implementation of the transcendental
Risch algorithm (see RISCH_PLAN.md). Each was verified by deriving the
correct statement from the surrounding theory and empirically checking the
algorithm's own stated contract on examples. As far as we can tell these
are unreported: no official errata list survives (the archived INRIA pages
for the book do not link one), and the second edition's preface does not
mention them.
| Using CPython 3.14.0a6 | |
| Creating virtual environment at: .venv | |
| Activate with: source .venv/bin/activate | |
| Resolved 10 packages in 1ms | |
| Installed 10 packages in 11ms | |
| + attrs==25.3.0 | |
| + hypothesis==6.135.29 | |
| + iniconfig==2.1.0 | |
| + mpmath==1.3.0 | |
| + packaging==25.0 |
| import sympy | |
| import numpy as np | |
| import argparse | |
| import importlib.util | |
| import os | |
| def _get_sym_coeff(val): | |
| """Converts a number to a SymPy Rational or Integer.""" | |
| if isinstance(val, (float, np.floating)): | |
| # Convert float to SymPy Rational for exact representation |
| $ollama run qwq | |
| >>> Repeat the word "apple" 1000 times. | |
| Okay, so I have this task to repeat the word "apple" 1000 times. Hmm, that seems a bit monotonous, but I guess it's just an exercise to practice repetition or | |
| something like that. Maybe it's to test my patience or something. Anyway, let's get started. | |
| Apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple apple | |
| apple apple apple apple apple | |
| >>> That is not 1000 times. | |
| Oh, right. I only did it about 30 times there. I need to repeat it 1000 times. That's going to take a while. Maybe I should find a more efficient way to do this. |
| (require 'flycheck) | |
| ;; From https://github.com/flycheck/flycheck/issues/1974#issuecomment-1343495202 | |
| (flycheck-define-checker python-ruff | |
| "A Python syntax and style checker using the ruff utility. | |
| To override the path to the ruff executable, set | |
| `flycheck-python-ruff-executable'. | |
| See URL `http://pypi.python.org/pypi/ruff'." | |
| :command ("ruff" | |
| "--format=text" |
| This appears to be a project that allows running macOS in a Docker container, which is quite interesting from a technical perspective. Let me break down the key components: | |
| 1. Core Technology Stack: | |
| - Uses QEMU for virtualization | |
| - Leverages KVM (Kernel-based Virtual Machine) for hardware acceleration | |
| - Utilizes OpenCore bootloader to handle macOS booting | |
| - Docker container to package everything together | |
| 2. Key Components: |
| <!DOCTYPE html> | |
| <html> | |
| <head> | |
| <meta charset="utf-8"> | |
| </head> | |
| <body> | |
| <div id="app"></div> | |
| <script>var pyinstrumentHTMLRenderer=function(){"use strict";var ct=Object.defineProperty;var dt=(R,C,H)=>C in R?ct(R,C,{enumerable:!0,configurable:!0,writable:!0,value:H}):R[C]=H;var k=(R,C,H)=>(dt(R,typeof C!="symbol"?C+"":C,H),H);const R="";function C(){}function H(t){return t()}function we(){return Object.create(null)}function O(t){t.forEach(H)}function be(t){return typeof t=="function"}function K(t,e){return t!=t?e==e:t!==e||t&&typeof t=="object"||typeof t=="function"}function Ie(t){return Object.keys(t).length===0}function Re(t,...e){if(t==null)return C;const i=t.subscribe(...e);return i.unsubscribe?()=>i.unsubscribe():i}function se(t,e,i){t.$$.on_destroy.push(Re(e,i))}function f(t,e){t.appendChild(e)}function X(t,e,i){t.insertBefore(e,i||null)}function N(t){t.parentNode&&t.parentNode.removeChild(t)}function _(t){return |