I recently found a very useful open-source math software called Sage, which provides many useful functions lacking in Mathematica. Since I'm more used to the Mathematica language instead of the language (Python) used in Sage, the ability of calling Sage functions from Mathematica will be of great help. Any ideas on how to do that?

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    $\begingroup$ Since Sage is built on a huge library consisting of lots of open-source packages and some other standalone softwares, calling Sage functions from Mathematica will strengthen the power of Mathematica. $\endgroup$ – hxiao Oct 8 '14 at 14:07
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    $\begingroup$ Could you please provide 1-2 examples of Sage functions lacking in Mathematica ? This will also attract more interest to your question. $\endgroup$ – b.gates.you.know.what Oct 8 '14 at 14:24
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    $\begingroup$ Take a look at Sage functions in algebraic geometry, etc.: sagemath.org/doc/tutorial/tour_advanced.html $\endgroup$ – murray Oct 8 '14 at 14:32
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    $\begingroup$ @b.gatessucks For example, recently I need to repeatedly enumerate all vertices of a large number of polytopes. In Mma, we can use a very old and inefficient package VertexEnum.m. Even the author of the package suggested this package can only handle polytopes with dimensions no larger than 8. To my knowledge, we have no other method to do vertex enumeration in Mma, not to mention other operations on polytopes. $\endgroup$ – hxiao Oct 8 '14 at 15:34
  • $\begingroup$ @b.gatessucks However, in Sage we can define an object Polyhedron via LP (H-representation). Then the vertex enumeration is just to list all vertices of the polytope. According to my experience, the speed of vertex enumeration in Sage is much much faster than that in Mma. $\endgroup$ – hxiao Oct 8 '14 at 15:37

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