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TNorm is a package for computing the Thurston norm unit ball of finite volume orientable hyperbolic 3-manifolds. Currently, tnorm must be installed in Sage, and Sage must have Regina and SnapPy installed. To instal TNorm:

$ sage -pip install tnorm

To run the tnorm graphical user interface app:

$ sage -python -m

To get started:

sage: W=tnorm.load('m130') sage: B=W.norm_ball sage: B.vertices [Vertex 0: represented by (1/2)* S_1,2 at (-1), mapped from surface with index 10, Vertex 1: represented by (1/2)* S_1,2 at (1), mapped from surface with index 0] sage:

In a future release, we plan to remove the dependence on Sage.

Support for hyperbolic 3-manifolds that are not multi-component links in rational homology 3-spheres has been added very recently, and has not been thoroughly tested yet. If you get any results that don't make sense, please email me at


  • add feature: determine fiberedness of a hyp 3-mfld (and hence knot genus of a knot)
  • remove Sage dependence.
  • better documentation throughout.
  • some optimization for speed is probably still possible.

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