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@MattStephanson MattStephanson commented Aug 15, 2025

For the Taylor element at DefElement, all the high-order DOFs are shown as, e.g.,
$$\displaystyle l_{3}:v\mapsto v'(\tfrac{1}{2}).$$
That is, any DerivativePointEvaluation in one dimension is rendered as a first derivative, regardless of the actual order.

This PR simply falls back to the Leibniz notation branch, but I could further extend the Lagrange notation (up to three primes, $v^{(n)}$ for $n > 3$) if desired.

Output difference from running python -m pytest test\test_dof_descriptions.py -s --verbose:

$ diff -u before.log after.log
--- before.log  2025-08-14 20:12:52.331668100 -0700
+++ after.log   2025-08-14 20:14:54.667755700 -0700
@@ -243,18 +243,18 @@
 PASSED
 test/test_dof_descriptions.py::test_element[interval-Taylor-2-kwargs62] v\mapsto\displaystyle\int_{R}v
 v\mapsto v'(\tfrac{1}{2})
-v\mapsto v'(\tfrac{1}{2})
+v\mapsto\frac{\partial^{2}}{\partial x^{2}}v(\tfrac{1}{2})
 PASSED
 test/test_dof_descriptions.py::test_element[interval-Taylor-3-kwargs63] v\mapsto\displaystyle\int_{R}v
 v\mapsto v'(\tfrac{1}{2})
-v\mapsto v'(\tfrac{1}{2})
-v\mapsto v'(\tfrac{1}{2})
+v\mapsto\frac{\partial^{2}}{\partial x^{2}}v(\tfrac{1}{2})
+v\mapsto\frac{\partial^{3}}{\partial x^{3}}v(\tfrac{1}{2})
 PASSED
 test/test_dof_descriptions.py::test_element[interval-Taylor-4-kwargs64] v\mapsto\displaystyle\int_{R}v
 v\mapsto v'(\tfrac{1}{2})
-v\mapsto v'(\tfrac{1}{2})
-v\mapsto v'(\tfrac{1}{2})
-v\mapsto v'(\tfrac{1}{2})
+v\mapsto\frac{\partial^{2}}{\partial x^{2}}v(\tfrac{1}{2})
+v\mapsto\frac{\partial^{3}}{\partial x^{3}}v(\tfrac{1}{2})
+v\mapsto\frac{\partial^{4}}{\partial x^{4}}v(\tfrac{1}{2})
 PASSED
 test/test_dof_descriptions.py::test_element[interval-Wu-Xu-3-kwargs65] v\mapsto v(0)
 v\mapsto v'(0)
@@ -5611,4 +5611,4 @@
 v\mapsto v(\tfrac{1}{3},\tfrac{1}{3},\tfrac{1}{3})
 PASSED

-======================= 450 passed in 71.59s (0:01:11) ========================
+======================= 450 passed in 77.73s (0:01:17) ========================

@mscroggs mscroggs enabled auto-merge (squash) August 15, 2025 06:39
@mscroggs mscroggs merged commit 89a1465 into mscroggs:main Aug 15, 2025
12 checks passed
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