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@@ -13,7 +13,7 @@ A full documentation is conatined in [Appendix E](doc/PyNormaliz.pdf) of the Nor
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## Requirements
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* python 3.4 or higher
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* Normaliz 3.9.0 or higher <https://github.com/Normaliz/Normaliz/releases>
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* Normaliz 3.10.2 or higher <https://github.com/Normaliz/Normaliz/releases>
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The source packages of the Normaliz realeases contain PyNormaliz.
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to be read as follows: [1] is the numerator polynomial, [1,1] is the vector of exponents of t that occur in the denominator, which is (1-t)(1-t) in our case, and 0 is the shift. So the Hilbert series is given by the rational function 1/(1-t)(1-t). (Aoso see ee [this introduction](doc/PyNormaliz_Tutorial.pdf).) But we can use
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print_series(C.HilbertSeries(HSOP = True))
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with the result
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(1)
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One can also compute several data simultaneously and specify options ("PrimalMode" only added as an example, not because ot is particularly useful here):
This is the lattice length of the diagonal in the square. The euclidean length, that has been computed simultaneously, is returned by
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C.EuclideanVolume()
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with the expected value
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'1.4142'
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Floating point numbers are formatted with 4 decimal places and returned as strings (may change). If you want the euclideal volume at the maximum floating point precision, you can use the low level interface which is intermediate between the class Cone and libnormaliz:
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NmzResult(C.cone,"EuclideanVolume")
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1.4142135623730951
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One can find out whether a single goal has been computed by asking
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C.IsComputed("Automorphisms")
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False
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If you use Compute instead of IsComputed, then Normaliz tries to compute the goal, and there are situations in which the computation is undesirable.
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Algebraic polyhedra can be computed by PyNormaliz as well:
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Very hard to read! Somewhat better:
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print_matrix(S)
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-1470/433*a+280/433 -1
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-32204/555417*a-668233/555417 -1
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-4.1545 -1.0000
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-1.2851 -1.0000
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By using Python functions, the functionality of Normaliz can be extended. For example,
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By using Python functions, the functionality of Normaliz can be extended. For example,
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