Update num-dual requirement from 0.11 to 0.13

[dependabot]

Updates the requirements on num-dual to permit the latest version.

Release notes

Sourced from num-dual's releases.

v0.13.4

Added

• Add partial3 in analogy to partial and partial2.

Changelog

Sourced from num-dual's changelog.

[0.13.4] - 2026-02-20

Added

• Add partial3 in analogy to partial and partial2.

[0.13.3] - 2026-02-20

Changed

• Extended implicit_differentiation_sp to also handle dynamic variable arrays using the Gradients trait. #102

[0.13.2] - 2026-01-13

Added

• Added support for computing Jacobians in Python for arbitrary input sizes and increased the maximum number of variables that uses static allocation to 16 (from 10). #99
• Added implicit_differentiation_sp for implicit differentiation of stationary points. #100

[0.13.1] - 2025-12-17

Fixed

• Fixed the calculation of eigenvectors of 2x2 matrices with zeros as elements. #98

[0.13.0] - 2025-12-04

Packaging

• Updated pyo3 and numpy dependencies to 0.27. #97
• Updated ndarray dependency to 0.17. #97

[0.12.1] - 2025-10-11

Added

• Added derivative functions for vector dual numbers (DualVec, Dual2Vec, HyperDualVec) analogous to the scalar dual numbers. #96

[0.12.0] - 2025-09-28

Added

• Added Real datatype which can be useful to calculate zeroth derivatives in certain generic cases. #95
• Added an interface for implicit differentiation of univariate, bivariate and multivariate functions. #95
• Added partial and partial2 functions to pass additional arguments to explicit derivatives. #95
• Added the Gradients trait that is used to generalize over static and dynamic array types. #95

Changed

• The methods in the linalg module are now based on datastructures from nalgebra. #95
• The ndarray dependency is now optional and includes the ScalarOperand trait as supertrait for DualNum if activated. #95
• The functions for explicit derivatives are more generic regarding the return types. This renders the try_ versions obsolete. #95

Packaging

• Updated pyo3 and numpy dependencies to 0.26.
• Updated criterion dev-dependency to 0.7.
• Updated Rust edition to 2024.
• updated nalgebra dependency to 0.34.

[0.11.2] - 2025-06-24

Changed

• Changed the implicit function interface to deal more straightforwardly with complex function arguments. #94

[0.11.1] - 2025-04-09

Added

... (truncated)

Commits

• 61365c1 Add partial3
• d804d12 Extend implicit_differentiation_sp to dynamic arrays (#102)
• 7ca41d8 release v0.13.2
• ea1df79 Add implicit differentiation of stationary points (#100)
• 9752b8b [feat] Add dynamic jacobian (#99)
• c7fc5a9 Update changelog
• 0ae22f3 Fix the calculation of eigenvectors of 2x2 matrices with zeros as elements. (...
• 7ae47c0 Update dependencies and release v0.13.0 (#97)
• 93a746a Add derivative functions for vector dual numbers (#96)
• 99223da Restructure crate into explicit and implicit derivatives (#95)
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