From: Danielle Bolan Date: Wed, 30 Jul 2014 13:31:27 +0000 (+0200) Subject: Need to merge X-Git-Tag: 1.0~91 X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/commitdiff_plain/e50b2facb441d96febf17a6210370489bbcb9dbf?hp=7a0183259951bd80aef293e8f12b128d7c32956e Need to merge --- diff --git a/doc/domain.rst b/doc/domain.rst index 91b96f8..7098c32 100644 --- a/doc/domain.rst +++ b/doc/domain.rst @@ -3,12 +3,8 @@ Domains Module .. py:class :: Domain - .. py:method:: polyhedra(self) - - Return . - -Domain Properties ------------------ + The properties of a domain can be are found using the following + .. py:method:: symbols Returns a tuple of the symbols that exsist in a domain. @@ -29,8 +25,8 @@ Domain Properties Returns ``True`` if a domain depends on the given dimensions. -Unary Properties ----------------- + The unary properties of a domain can be inspected using the following methods. + .. py:method:: isempty(self) Return ``True`` is a domain is empty. @@ -41,14 +37,13 @@ Unary Properties .. py:method:: isbounded(self) - Return ``True`` if a domain is bounded + Return ``True`` if a domain is bounded. .. py:method:: disjoint(self) - Returns a domain as disjoint. + It is not guarenteed that a domain is disjoint. If it is necessary, this method will return a domain as disjoint. -Binary Properties ------------------ + The following methods compare two domains to find the binary properties. .. py:method:: isdisjoint(self, other) @@ -144,7 +139,7 @@ Binary Properties .. py:method:: points(self) - Return a list of the points contained in a domain. + Return a list of the points contained in a domain as :class:`Points` objects. .. py:method:: vertices(self) diff --git a/doc/examples.rst b/doc/examples.rst index 793ecbe..f3fbfb3 100644 --- a/doc/examples.rst +++ b/doc/examples.rst @@ -1,22 +1,67 @@ Pypol Examples ============== -Creating a Square +Creating a Polyhedron ----------------- - To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints for the polyhedron. This example creates a square:: + To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints for the polyhedron. This example creates a square. + >>> from pypol import * >>> x, y = symbols('x y') >>> # define the constraints of the polyhedron - >>> square = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2) - >>> print(square) - >>> And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)) + >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2) + >>> print(square1) + And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)) - Several unary operations can be performed on a polyhedron. For example: :: +Urnary Operations +----------------- - >>> Â¬square - + >>> square1.isempty() + False + >>> square1.isbounded() + True + +Binary Operations +----------------- + + >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4) + >>> square1 + square2 + Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 2, 0), Ge(-x + 4, 0), Ge(y - 2, 0), Ge(-y + 4, 0))) + >>> # check if square1 and square2 are disjoint + >>> square1.disjoint(square2) + False Plot Examples ------------- - - + + Linpy uses matplotlib plotting library to plot 2D and 3D polygons. The user has the option to pass subplots to the :meth:`plot` method. This can be a useful tool to compare polygons. Also, key word arguments can be passed such as color and the degree of transparency of a polygon. + + >>> import matplotlib.pyplot as plt + >>> from matplotlib import pylab + >>> from mpl_toolkits.mplot3d import Axes3D + >>> from pypol import * + >>> # define the symbols + >>> x, y, z = symbols('x y z') + >>> fig = plt.figure() + >>> cham_plot = fig.add_subplot(2, 2, 3, projection='3d') + >>> cham_plot.set_title('Chamfered cube') + >>> cham = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3) & Le(0, z) & Le(z, 3) & Le(z - 2, x) & Le(x, z + 2) & Le(1 - z, x) & Le(x, 5 - z) & Le(z - 2, y) & Le(y, z + 2) & Le(1 - z, y) & Le(y, 5 - z) & Le(y - 2, x) & Le(x, y + 2) & Le(1 - y, x) & Le(x, 5 - y) + >>> cham.plot(cham_plot, facecolors=(1, 0, 0, 0.75)) + >>> pylab.show() + + .. figure:: images/cube.jpg + :align: center + + The user can also inspect a polygon's vertices and the integer points included in the polygon. + + >>> diamond = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1) + >>> diamond.vertices() + [Point({x: Fraction(0, 1), y: Fraction(1, 1)}), Point({x: Fraction(-1, 1), y: Fraction(0, 1)}), Point({x: Fraction(1, 1), y: Fraction(0, 1)}), Point({x: Fraction(0, 1), y: Fraction(-1, 1)})] + >>> diamond.points() + [Point({x: -1, y: 0}), Point({x: 0, y: -1}), Point({x: 0, y: 0}), Point({x: 0, y: 1}), Point({x: 1, y: 0})] + + + + + + + diff --git a/doc/images/cube.jpg b/doc/images/cube.jpg new file mode 100644 index 0000000..d10cdaa Binary files /dev/null and b/doc/images/cube.jpg differ diff --git a/doc/polyhedra.rst b/doc/polyhedra.rst index 779be46..de0dfd5 100644 --- a/doc/polyhedra.rst +++ b/doc/polyhedra.rst @@ -31,7 +31,7 @@ Polyhedra Module Subsitutes an expression into a polyhedron and returns the result. -To create a polyhedron, the user must use the folloing functions to define the equalities and inequalities which are the contraints of a polyhedron. +To create a polyhedron, the user must use the folloing functions to define equalities and inequalities as the contraints. .. py:function:: Eq(left, right)