{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "def zonotope(L):\n", " \"\"\"\n", " Input: list L\n", " Output: zonotope associated to L\n", " \"\"\"\n", " return sum([Polyhedron(vertices = [-vector(v),vector(v)]) for v in L])" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def fiber_zonotope(L,n):\n", " '''\n", " Input: list L, associated to a zonotope Z\n", " integer n\n", " Output: list F_π, whose associated zonotope is the fiber zonotope of Z\n", " with respect to the projection onto the first n coordinates\n", " '''\n", " N = len(L[1])\n", " s = len(L)\n", " X = [ℓ[0:n] for ℓ in L]\n", " Y = [ℓ[n:N] for ℓ in L]\n", " F_π = []\n", " for I in Subsets(range(s),n+1,submultiset=True):\n", " f = []\n", " for j in range(n+1): # we compute now the summands of F_π\n", " II = copy(I)\n", " II.remove(II[j])\n", " XX = [X[ii] for ii in II]\n", " M = matrix(XX)\n", " dd = M.determinant()\n", " g = 1/(factorial(n+1))*(-1)^(n+1-j)*dd*matrix(Y[I[j]])\n", " f.append(g)\n", " F = factorial(n+1)*sum(f) # this is F_π for the set of indices I\n", " F_π.append(F)\n", " return F_π" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "L = [[1, 0, 1], [1, 1, 0], [1, -1, 0]]" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "Z = zonotope(L)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Z.plot()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zonotope(fiber_zonotope(L,1)).plot()" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.2", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }