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| = Falt surfaces examples = | = Flat surfaces examples = |
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| The latter installs a modified version of Sage. For more on what this command does or how to reverse it, you can read this [[http://wiki.sagemath.org/combinat/MercurialStepByStep|step by step tutorial]]. | This installs a modified version of Sage. For more on what this command does or how to reverse it, you can read this [[http://wiki.sagemath.org/combinat/MercurialStepByStep|step by step tutorial]]. |
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| === Link to documentations and tutorials === | === Link to documentation and tutorials === |
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| To get introduced to Sage, look at the documentation on [[http://sagemath.org]] | For an introduction to Sage, check the documentation at [[http://sagemath.org/]]. |
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| === Square tiled surfaces === | === Square-tiled surfaces === |
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| And now, we build its Teichmueller curve and compute some of its invariant (rk: it is not yet clear which property should be attached to the teichmueller curve and which one should be attached to the Veech group) | And now, we build its Teichmueller curve and compute some of its invariants (rk: it is not clear yet which properties should be attached to the Teichmueller curve and which should be attached to the Veech group) |
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| sage: G.nu2() #elliptic points of order 2 | sage: G.nu2() # elliptic points of order 2 |
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| sage: G.nu3() #elliptic points of order3 | sage: G.nu3() # elliptic points of order3 |
Flat surfaces examples
Installation
You need to install sage-combinat which is done with the following command
$ sage -combinat install
This installs a modified version of Sage. For more on what this command does or how to reverse it, you can read this step by step tutorial.
Link to documentation and tutorials
For an introduction to Sage, check the documentation at http://sagemath.org/.
Using interval exchange transformations
Permutations of interval exchange transformations are created
sage: p = iet.Permutation('a b c d','d c b a')
sage: p.connected_component()
H_hyp(2)
Square-tiled surfaces
Let us build the genus 2 origami with three squares
sage: o = Origami('(1,2)', '(1,3)')
sage: print o
(1, 2)
(1, 3)And now, we build its Teichmueller curve and compute some of its invariants (rk: it is not clear yet which properties should be attached to the Teichmueller curve and which should be attached to the Veech group)
sage: t = o.teichmueller_curve() sage: G = t.veech_group() sage: G.index() 3 sage: G.nu2() # elliptic points of order 2 1 sage: G.nu3() # elliptic points of order3 1 sage: G.ncusps() # number of cusps 2 sage: t.sum_of_lyapunov_exponents() 4/3