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DOC: Add polynomial evaluation examples and improve polyval docs #29578

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DOC: Add polynomial evaluation examples and improve polyval docs
olivvius Aug 17, 2025
ff9c06b
Fix: Remove whitespace from line 719 in polynomial.py
olivvius Aug 17, 2025
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DOC: Add polynomial evaluation examples and improve polyval docs 
- Add evaluation examples to polynomial quick reference table
- Enhance polyval docstring with clearer examples
- Add warning about domain/window scaling with fitted polynomials
- Show comparison between legacy and new polynomial APIs

Fixes #25587"
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olivvius committed Aug 17, 2025
commit 721904422a8b51a4729f502976403f76defd7dab
34 changes: 19 additions & 15 deletions doc/source/reference/routines.polynomials.rst
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Expand Up @@ -47,23 +47,27 @@ The `~numpy.polynomial.polynomial.Polynomial` class is imported for brevity::
from numpy.polynomial import Polynomial


+------------------------+------------------------------+---------------------------------------+
| **How to...** | Legacy (`numpy.poly1d`) | `numpy.polynomial` |
+------------------------+------------------------------+---------------------------------------+
| Create a | ``p = np.poly1d([1, 2, 3])`` | ``p = Polynomial([3, 2, 1])`` |
| polynomial object | | |
| from coefficients [1]_ | | |
+------------------------+------------------------------+---------------------------------------+
| Create a polynomial | ``r = np.poly([-1, 1])`` | ``p = Polynomial.fromroots([-1, 1])`` |
| object from roots | ``p = np.poly1d(r)`` | |
+------------------------+------------------------------+---------------------------------------+
| Fit a polynomial of | | |
| degree ``deg`` to data | ``np.polyfit(x, y, deg)`` | ``Polynomial.fit(x, y, deg)`` |
+------------------------+------------------------------+---------------------------------------+

+------------------------+----------------------------------------+---------------------------------------+
| **How to...** | Legacy (`numpy.poly1d`) | `numpy.polynomial` |
+------------------------+----------------------------------------+---------------------------------------+
| Create a | ``p = np.poly1d([1, 2, 3])`` | ``p = Polynomial([3, 2, 1])`` |
| polynomial object | | |
| from coefficients [1]_ | | |
+------------------------+----------------------------------------+---------------------------------------+
| Create a polynomial | ``r = np.poly([-1, 1])`` | ``p = Polynomial.fromroots([-1, 1])`` |
| object from roots | ``p = np.poly1d(r)`` | |
+------------------------+----------------------------------------+---------------------------------------+
| Fit a polynomial of | | |
| degree ``deg`` to data | ``np.polyfit(x, y, deg)`` | ``Polynomial.fit(x, y, deg)`` |
+------------------------+----------------------------------------+---------------------------------------+
| Evaluate a polynomial | ``p(2.0)`` or | ``p(2.0)`` or ``polyval(2.0, p.coef)``|
| at a point [2]_ | ``np.polyval([1, 2, 3], 2.0)`` | (use ``p.convert().coef`` after fit) |
+------------------------+----------------------------------------+---------------------------------------+

.. [1] Note the reversed ordering of the coefficients

.. [2] When evaluating polynomials created with ``fit()``, use ``p(x)`` or ``polyval(x, p.convert().coef)`` to handle domain/window scaling correctly.

Transition Guide
~~~~~~~~~~~~~~~~

Expand Down Expand Up @@ -187,4 +191,4 @@ Documentation for legacy polynomials
.. toctree::
:maxdepth: 2

routines.polynomials.poly1d
routines.polynomials.poly1d
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The trailing newline is missing

5 changes: 5 additions & 0 deletions numpy/polynomial/polynomial.py
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Expand Up @@ -716,6 +716,11 @@ def polyval(x, c, tensor=True):
Notes
-----
The evaluation uses Horner's method.

.. warning::
When using coefficients from polynomials created with ``Polynomial.fit()``,
use ``p(x)`` or ``polyval(x, p.convert().coef)`` to handle domain/window
scaling correctly, not ``polyval(x, p.coef)``.

Examples
--------
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