Implement all math (#34)

* Move the NaN-checks into the math functions, right outside the operations that might fail.

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* deltaphi

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* Refactor to allow rotateZ to return a vector or an array of vectors.

* cottheta

* Implemented 'cross' and tested it for Cartesian coordinates.

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* Implemented but have not tested coordinate transformation methods.

* Tested coordinate system transformation methods and 'cross'.

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* deltaeta.

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* deltaR2

* deltaR

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* rotateX

* rotateY

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* rotate_axis

* fixed flake8

* Implemented but HAVE NOT TESTED rotate_euler

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* rotate_euler has been tested (target value comes from ROOT)

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* rotate_nautical

* Generate methods for rotate_axis as they are generated for rotate_euler.

* Generate methods for cross as they are generated for rotate_axis.

* Comments and complain about mixing libraries.

* rotate_quaternion

* Added (but didn't test) generic transformations.

* Transformations don't have to be objects. Methods are fine.

* If we don't have Transformation objects, we don't need the vector/point distinction.

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* Update inheritance diagram.

* Forgot a couple of lines.

* One more line.

* cosdeltaphi

* The momentum classes on the diagram was wrong; fixed.

* Spatial.dot is working.

* Fix flake8.

* Follow ROOT's rules for sqrt of negative Lorentz metric.

* Conversions to other coordinate systems can be centralized.

* 'cosdeltaphi' and 'cosdeltaangle' are not distinct from 'dot'.

* 'deltaphi' should stay within -pi .. pi.

* deltaangle

* beta and gamma

* rapidity

* Et and Et2

* Mt and Mt2

* Implemented but HAVE NOT TESTED 'unit'. It should not change the coordinate system.

* Tested 'unit'.

* boost_p4

* boost_beta3

* boostZ_gamma

* boostZ_beta

* Preserve tau (mass) in boosts.

* boostX_beta and boostX_gamma

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* boostY_beta and boostY_gamma

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* Fix imports.

* Implemented but have not tested is_* methods.

* Momentum vectors present themselves with momentum coordinates.

* Better interface functions.

* to_beta3

* Merge vector.geometry into vector.methods because the distinction wasn't meaningful and the name was unclear.

* scale

* equal, not_equal, and isclose

* add and subtract

* Added the NumPy methods to catch ufuncs (and added equivalent stubs on VectorObject). There are no tests for this yet.

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: jpivarski

docs/api/inheritance.svg

@@ -4,6 +4,43 @@
 # or https://github.com/scikit-hep/vector for details.
 
 
+from .backends.numpy_ import (  # noqa: 401
+    MomentumNumpy2D,
+    MomentumNumpy3D,
+    MomentumNumpy4D,
+    VectorNumpy2D,
+    VectorNumpy3D,
+    VectorNumpy4D,
+    array,
+)
+from .backends.object_ import (  # noqa: 401
+    MomentumObject2D,
+    MomentumObject3D,
+    MomentumObject4D,
+    VectorObject2D,
+    VectorObject3D,
+    VectorObject4D,
+    obj,
+)
+from .methods import (  # noqa: 401
+    Azimuthal,
+    AzimuthalRhoPhi,
+    AzimuthalXY,
+    Coordinates,
+    Longitudinal,
+    LongitudinalEta,
+    LongitudinalTheta,
+    LongitudinalZ,
+    Momentum,
+    Temporal,
+    TemporalT,
+    TemporalTau,
+    Vector,
+    Vector2D,
+    Vector3D,
+    Vector4D,
+)
+
 # from .version import version as __version__
 
 # __all__ = ("__version__",)