hgn

{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## The constructible image of $$f: \\mathbb{A}_\\mathbb{Q}^2 \\to \\mathbb{A}_\\mathbb{Q}^2, (x,y) \\mapsto (a,b) := (x,xy).$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CapAndHomalg v\u001b[32m1.6.0\u001b[39m\n", "Imported OSCAR's components GAP and Singular_jll\n", "Type: ?CapAndHomalg for more information\n" ] } ], "source": [ "using CapAndHomalg" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "LoadPackage( \"ZariskiFrames\" )" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "GAP: Q" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ℚ = HomalgFieldOfRationalsInSingular()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "GAP: Q[a,b]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B = ℚ[\"a,b\"]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "GAP: Q[x,y]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T = ℚ[\"x,y\"]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "ϕ = RingMap( HomalgMatrix( \"x,x*y\", 2, 1, T ), B, T );" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Q[x,y]\n", " ^\n", " |\n", "[ x, x*y ]\n", " |\n", " |\n", "Q[a,b]\n" ] } ], "source": [ "Display( ϕ )" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "GAP: ( V_{Q[a,b]}( I1 ) \\ V_{Q[a,b]}( J1_1 ) ) ∪ ( V_{Q[a,b]}( I2 ) \\ V_{Q[a,b]}( J2_1 ) )" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "im = ConstructibleImage( ϕ )" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "( V( <> )\n", "\n", "\\ V( ) )\n", "\n", "∪\n", "\n", "( V( )\n", "\n", "\\ ∅ )\n" ] } ], "source": [ "Display( im )" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Visualize( im )" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Julia 1.10.3", "language": "julia", "name": "julia-1.10" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.10.3" } }, "nbformat": 4, "nbformat_minor": 2 }