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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,196 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "id": "26c91d51-9f62-4c3e-9d02-2ca3a0977913", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from galgebra.ga import Ga\n", | ||
| "import sympy as S\n", | ||
| "\n", | ||
| "x,y,z = coords = S.symbols('x y z', real=True)\n", | ||
| "ga = Ga('e', g=[1,1,1], coords=coords, wedge=False)\n", | ||
| "ex,ey,ez = ga.mv()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 2, | ||
| "id": "5d541f6c-f9f8-4adb-a4b5-5ab27a9293dc", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle \\mathbf{e}_{x} \\frac{\\partial}{\\partial x} + \\mathbf{e}_{y} \\frac{\\partial}{\\partial y} + \\mathbf{e}_{z} \\frac{\\partial}{\\partial z}$" | ||
| ], | ||
| "text/plain": [ | ||
| "e_x*D{x} + e_y*D{y} + e_z*D{z}" | ||
| ] | ||
| }, | ||
| "execution_count": 2, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "ga.grad" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "id": "d07a0e79-b467-4cef-9ea6-3b49e925bf0e", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle 1$" | ||
| ], | ||
| "text/plain": [ | ||
| "1" | ||
| ] | ||
| }, | ||
| "execution_count": 3, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "ga.grad * (x*ex)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 4, | ||
| "id": "417d322c-30f5-4353-9f32-cc39cb7b2d8e", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle \\mathbf{e}_{x}$" | ||
| ], | ||
| "text/plain": [ | ||
| "e_x" | ||
| ] | ||
| }, | ||
| "execution_count": 4, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "(x*ex).diff(x)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 5, | ||
| "id": "7d66fe00-5011-4946-ad4f-9ae6f38c315d", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "x,y,z = coords = S.symbols('x y z', real=True)\n", | ||
| "ga = Ga('e', g=[1,1,1], coords=coords, wedge=False)\n", | ||
| "ex,ey,ez = ga.mv()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 6, | ||
| "id": "7bac45e6-985f-497d-b13e-b40f9150dfd5", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle \\mathbf{e}_{x} \\frac{\\partial}{\\partial x} + \\mathbf{e}_{y} \\frac{\\partial}{\\partial y} + \\mathbf{e}_{z} \\frac{\\partial}{\\partial z}$" | ||
| ], | ||
| "text/plain": [ | ||
| "e_x*D{x} + e_y*D{y} + e_z*D{z}" | ||
| ] | ||
| }, | ||
| "execution_count": 6, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "ga.grad" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 7, | ||
| "id": "2f8161af-c147-4fcf-adfa-53613b24210f", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle 1$" | ||
| ], | ||
| "text/plain": [ | ||
| "1" | ||
| ] | ||
| }, | ||
| "execution_count": 7, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "ga.grad * (x*ex)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 8, | ||
| "id": "231177c9-3422-4e33-9ace-d914502ba060", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle \\mathbf{e}_{x}$" | ||
| ], | ||
| "text/plain": [ | ||
| "e_x" | ||
| ] | ||
| }, | ||
| "execution_count": 8, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "(x*ex).pdiff(x) # notice this is pdiff() not diff() this tim" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3 (ipykernel)", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "codemirror_mode": { | ||
| "name": "ipython", | ||
| "version": 3 | ||
| }, | ||
| "file_extension": ".py", | ||
| "mimetype": "text/x-python", | ||
| "name": "python", | ||
| "nbconvert_exporter": "python", | ||
| "pygments_lexer": "ipython3", | ||
| "version": "3.9.18" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |
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