{ "cells": [ { "cell_type": "markdown", "id": "78a17ef8", "metadata": {}, "source": [ "# On visualizing number fields #\n", "\n", "In a group with Kate Stange, Ian Whitehead, Hanson Smith, Caleb Springer, and a few others, I explored a few different ways to visualize number fields. We are hoping to come up with something that would be appropriate as images for the LMFDB --- which currently doesn't have number field portraits.\n", "\n", "In this note, I summarize some of the ideas that we discussed and give examples. This also includes implementations in sage. This note is also available as a jupyter notebook independently on [my website](https://davidlowryduda.com)." ] }, { "cell_type": "markdown", "id": "6eef3010", "metadata": {}, "source": [ "## Broad ideas and challenges ##\n", "\n", "Two natural sets of objects to try to visualize are collections of points in the number field, or collections of points in the ring of integers associated to the number field.\n", "\n", "- For the ring of integers, we might visualize\n", " * just the basis elements,\n", " * elements that are *small* combinations of basis elements, or\n", " * elements that are a *power integral basis*, i.e. elements $\\alpha_i$ such that the ring of integers is given by the **ring** $\\mathbb{Z}[\\alpha_1, ..., \\alpha_n]$. If the ring of integers is monogenic, then there is a single $\\alpha_i$.\n", "- For collections of points in the number field, we might visualize\n", " * all points of height up to some bound, or\n", " * random points.\n", " \n", "There is a difference between a number field and embeddings of that number field into the complex numbers. Although number fields have various embeddings into two-dimensional complex space, it is often more natural to consider a degree $n$ number field as living in a natural degree $n$ space spanned by the lattice of the ring of integers.\n", "\n", "The possible elements to visualize above are for subsets of elements of the number field. What do we do with the various embeddings?\n", "\n", "In many of the visualizations below, we use color to distinguish between the varied embeddings, and plot the same sets of points in different embeddings.\n", "\n", "Note that there are already sources of indeterminism:\n", "\n", "1. Which basis does one choose for the ring of integers?\n", "2. How does one order the embeddings?\n", "\n", "\n", "## Characteristics of visualizations ##\n", "\n", "Fundamentally, each visualization below are plots of sets of disks of certain sizes and colors. Thus for each visualization below, we specify \n", "\n", "- what disks are plotted,\n", "- how we determine the sizes of each disk, and\n", "- how we determine the color of each disk." ] }, { "cell_type": "markdown", "id": "abf27947", "metadata": {}, "source": [ "## Visualizing points of bounded height ##\n", "\n", "Given a number field $F$, compute all points of height below some fixed bound $B$ (for some choice of height function). This is cannonical and independent of the chosen basis.\n", "\n", "In this plot, we compute all embeddings $\\{ \\sigma_1, \\ldots, \\sigma_n \\}$ and fix an ordering of them. (Here we use whatever ordering sage uses). For each point $z$ in the number field of height up to $B$ and for each embedding $\\sigma_i$, we plot the point $\\sigma_i(z)$ with size inversely proportional to the height of $z$, and with color ranging from red (for the first embedding) to blue (for the last embedding)." ] }, { "cell_type": "code", "execution_count": 1, "id": "a3794920", "metadata": {}, "outputs": [], "source": [ "from sage.plot.colors import red, blue, white\n", "\n", "\n", "def draw_fieldelts_bdd_height(F,bd):\n", " embs = F.embeddings(CC)\n", " pts = list(F.elements_of_bounded_height(bound=bd))\n", " vis = Graphics()\n", " for emb in embs:\n", " pts_emb = [emb(pt) for pt in pts]\n", " disk_sizer = lambda x : 0.02/(x.global_height())\n", " for index in range(len(pts_emb)):\n", " size = disk_sizer(pts[index])\n", " if size > 0.0001:\n", " vis += disk( (pts_emb[index].real(),pts_emb[index].imag()),\n", " size, (0, 2*pi), alpha=1.0,\n", " color=red.blend(blue, embs.index(emb)/len(embs))\n", " )\n", " return vis" ] }, { "cell_type": "markdown", "id": "9bde264f", "metadata": {}, "source": [ "This sort of plot is particularly pleasant for quadratic imaginary number fields, where the lattice structure is completely visible." ] }, { "cell_type": "code", "execution_count": 2, "id": "2841a001", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 1520 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Fgauss. = NumberField(x^2 + 1)\n", "gauss = draw_fieldelts_bdd_height(Fgauss, 20)\n", "gauss.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 3, "id": "76524ed8", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 1440 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Feis. = NumberField(x^2 + x + 1)\n", "eis = draw_fieldelts_bdd_height(Feis, 20)\n", "eis.show(axes=False)" ] }, { "cell_type": "markdown", "id": "d2c2747d", "metadata": {}, "source": [ "These plots reveal that points of low height *repel* each other. These plots are a bit less satisfying for real quadratic fields." ] }, { "cell_type": "code", "execution_count": 4, "id": "cff62792", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/davidlowryduda/sagebuild/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/matplotlib/patches.py:1189: RuntimeWarning: invalid value encountered in multiply\n", " v *= self.r\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 982 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Frq. = NumberField(x^2 - 2)\n", "fig = draw_fieldelts_bdd_height(Frq, 20)\n", "fig.set_axes_range(xmin=-5, xmax=5, ymin=-1, ymax=1) # it complains that ymin, ymax are both 0 otherwise.\n", "fig.show(axes=False, fig_tight=False) # similarly, with fig_tight it has no height." ] }, { "cell_type": "code", "execution_count": 5, "id": "25855197", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 1980 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Fd3. = NumberField(x^3 - x^2 + 2*x - 1)\n", "fig = draw_fieldelts_bdd_height(Fd3, 20)\n", "fig.set_axes_range(xmin=-3, xmax=3, ymin=-3, ymax=3)\n", "fig.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 6, "id": "73aefc03", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 1536 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Fd4. = NumberField(x^4 + 7*x^2 + 13)\n", "fig = draw_fieldelts_bdd_height(Fd4, 20)\n", "fig.set_axes_range(xmin=-3, xmax=3, ymin=-3, ymax=3)\n", "fig.show(axes=False)" ] }, { "cell_type": "markdown", "id": "630f9d8b", "metadata": {}, "source": [ "For higher degrees, it would probably be necessary to reduce the height bound. But in fact sage uses a sophisticated algorithm to generate points of bounded height, which requires computing the class number of the field. We haven't looked into an alternative, but this prevents us from currently producing high degree visualizations.\n", "\n", "We noticed that overlaying different embeddings is confusing. Each individual embedding is natural, but overlaying them obscures the underlying lattice structure. One way around this is to fix an embedding and plotting it. To add some color, we color the point $z$ from red to blue based on the real part of *a different fixed embedding* of $z$." ] }, { "cell_type": "code", "execution_count": 7, "id": "38b8f991", "metadata": {}, "outputs": [], "source": [ "def draw_fieldelts_one_embed(F, bd):\n", " embs = F.embeddings(CC)\n", " emb = embs[-1]\n", " emb2 = embs[0]\n", " pts = list(F.elements_of_bounded_height(bound=bd))\n", " pts_emb = [emb(pt) for pt in pts]\n", " disk_sizer = lambda x : 0.02/(x.global_height())\n", " vis = Graphics()\n", " for index in range(len(pts_emb)):\n", " size = disk_sizer(pts[index])\n", " if size > 0.0001:\n", " vis += disk( (pts_emb[index].real(),pts_emb[index].imag()),\n", " size, (0, 2*pi), alpha=1.0,\n", " color=red.blend(white, emb2(pts[index]).real())\n", " )\n", " return vis" ] }, { "cell_type": "code", "execution_count": 8, "id": "73782839", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 760 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gauss = draw_fieldelts_one_embed(Fgauss, 20)\n", "gauss.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 9, "id": "78d73549", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 720 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eis = draw_fieldelts_one_embed(Feis, 20)\n", "eis.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 10, "id": "9cfc84dc", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 491 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = draw_fieldelts_one_embed(Frq, 20)\n", "fig.set_axes_range(xmin=-5, xmax=5, ymin=-1, ymax=1) # it complains that ymin, ymax are both 0 otherwise.\n", "fig.show(axes=False, fig_tight=False) # similarly, with fig_tight it has no height." ] }, { "cell_type": "code", "execution_count": 11, "id": "54c82740", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 660 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = draw_fieldelts_one_embed(Fd3, 20)\n", "fig.set_axes_range(xmin=-3, xmax=3, ymin=-3, ymax=3)\n", "fig.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 12, "id": "a2ed9142", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 384 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = draw_fieldelts_one_embed(Fd4, 20)\n", "fig.set_axes_range(xmin=-3, xmax=3, ymin=-3, ymax=3)\n", "fig.show(axes=False)" ] }, { "cell_type": "markdown", "id": "58b65ca4", "metadata": {}, "source": [ "These aren't particularly successful, but it might be reasonable to tweak these." ] }, { "cell_type": "markdown", "id": "e21ab08c", "metadata": {}, "source": [ "## Choose linear combination of embeddings ##\n", "\n", "Choose a linear combination of embeddings. (Below, we choose a random linear combination with coefficients in $(0, 1)$). For each point $z \\in O_K$, we plot $\\sum_i c_i \\sigma_i(z)$. This doesn't use color. Disks are sized to be inversely proportional to the square of the global height of $z$. We plot all points in the ring of integers" ] }, { "cell_type": "code", "execution_count": 13, "id": "6dee565a", "metadata": {}, "outputs": [], "source": [ "import itertools\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "\n", "cm = mpl.colormaps.get('inferno')" ] }, { "cell_type": "code", "execution_count": 14, "id": "d090b449", "metadata": {}, "outputs": [], "source": [ "def random_list(num):\n", " ret = []\n", " for idx in range(num):\n", " ret.append(random())\n", " return ret\n", "\n", "def linear_comb_embed_viz(K, size=10, decexp=2):\n", " pts = list(K.elements_of_bounded_height(bound=size))\n", " all_embeds = K.embeddings(CC)\n", " \n", " xs = []\n", " ys = []\n", " ss = []\n", " \n", " coeffs = random_list(len(all_embeds))\n", " for pt in pts:\n", " z = 0\n", " for idx, embed in enumerate(all_embeds):\n", " z += coeffs[idx] * embed(pt)\n", " x = real(z)\n", " y = imag(z)\n", " xs.append(x)\n", " ys.append(y)\n", " ss.append(float(20. / (pt.global_height()^decexp + 1)))\n", " \n", " fig = plt.figure(figsize=[8, 8])\n", " ax = fig.subplots(1, 1)\n", " ax.set_frame_on(False)\n", " ax.set_xticks([])\n", " ax.set_yticks([])\n", " ax.scatter(xs, ys, c='k', s=ss)\n", " \n", " return fig" ] }, { "cell_type": "code", "execution_count": 15, "id": "e26de522", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "