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Polynomials in Python
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‎Displaying polynomials-Adding and multiplying polynomials.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Python Everything:\n",
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"8) **Showing polynomials in Jupyter Notebook**\n",
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"<br>Also, writing functions to add and multiply two polynomials $p(x)$ and $q(x).$\n",
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"<br>**Hint:** Here, polynomials are represented by *lists*.\n",
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"<br>\n",
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"<br> $p(x)=a_0+a_1x+a_2x^2+a_3x^3+...+a_nx^n$\n",
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"# نمایش بُلنامی‌ها، در جوپیتر نوتبوک\n",
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"By Hamed Shah-Hosseini<br>\n",
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"Explanation in English:<br>\n",
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"https://www.pinterest.com/HamedShahHosseini/programming-languages/python\n",
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"<br> Explanation in Persian: https://www.instagram.com/words.persian\n",
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"<br>The code is at: https://github.com/ostad-ai/Python-Everything"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [],
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"source": [
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"from IPython.display import Math, display"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"metadata": {},
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"outputs": [],
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"source": [
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"# the function to show polynomials represented by lists\n",
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"def show(poly,variable='x'):\n",
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" s=''\n",
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" for power,coef in enumerate(poly):\n",
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" if coef==0: continue\n",
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" if power==0:\n",
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" s+=f'{coef}+'\n",
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" elif power==1:\n",
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" s+=f'{coef}{variable}+'\n",
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" else:\n",
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" s+=f'{coef}{variable}^{{{power}}}+'\n",
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" display(Math(s[:-1]))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"ِExample of displaying polynomials:<br>\n",
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"نمونه‌ای از نمایش بُلنامی‌ها"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 1+3x+7x^{2}+11x^{3}+3x^{11}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"poly1=[1,3,7,11,0,0,0,0,0,0,0,3]\n",
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"show(poly1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 4+8x^{2}+10x^{4}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 4+8y^{2}+10y^{4}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"poly2=[4,0,8,0,10]\n",
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"show(poly2,'x')\n",
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"show(poly2,'y')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"# adding two polynomials P and Q\n",
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"# P and Q are represented by lists\n",
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"def add_polys(P,Q):\n",
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" m=len(P)\n",
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" n=len(Q)\n",
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" if m < n:\n",
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" result=Q.copy()\n",
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" for i in range(m):\n",
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" result[i]+=P[i]\n",
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" else:\n",
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" result=P.copy()\n",
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" for i in range(n):\n",
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" result[i]+=Q[i]\n",
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" return result"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Example of adding two polynomials: <br>\n",
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"نمونه‌ای از افزا کردن دو بُلنامی"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 1+3x+7x^{2}+11x^{3}+3x^{11}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 4+8x^{2}+10x^{4}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The summation:\n"
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]
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 5+3x+15x^{2}+11x^{3}+10x^{4}+3x^{11}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"poly1_add_poly2=add_polys(poly1,poly2)\n",
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"show(poly1)\n",
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"show(poly2)\n",
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"print('The summation:')\n",
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"show(poly1_add_poly2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {},
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"outputs": [],
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"source": [
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"# multiplying two polynomials P and Q\n",
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"# P and Q are represented by lists\n",
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"def mult_polys(P,Q):\n",
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" m=len(P)\n",
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" n=len(Q)\n",
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" R=[0]*(m+n-1)\n",
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" for i in range(m):\n",
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" for j in range(n):\n",
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" R[i+j]+=P[i]*Q[j]\n",
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" return R"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Example of multiplying two polynomials: <br>\n",
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"نمونه‌ای از چندینکرد دو بُلنامی"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 1+3x+7x^{2}+11x^{3}+3x^{11}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 4+8x^{2}+10x^{4}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The multiplication:\n"
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]
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 4+12x+36x^{2}+68x^{3}+66x^{4}+118x^{5}+70x^{6}+110x^{7}+12x^{11}+24x^{13}+30x^{15}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"show(poly1); show(poly2)\n",
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"poly1_mult_poly2=mult_polys(poly1,poly2)\n",
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"print('The multiplication:')\n",
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"show(poly1_mult_poly2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The multiplication:\n"
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]
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 4.0+12.0x+36.0x^{2}+68.0x^{3}+66.0x^{4}+118.0x^{5}+70.0x^{6}+110.0x^{7}+12.0x^{11}+24.0x^{13}+30.0x^{15}$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"# you can check the multiplication with numpy polynomial\n",
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"from numpy.polynomial.polynomial import polymul\n",
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"print('The multiplication:')\n",
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"show(polymul(poly1,poly2))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

‎README.md

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5) Stacks are implemented by lists. An example to reverse a list with stack is also included.
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6) strings in Python: Introduction.
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7) Emojis in Python with some examples.
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8) Working with polynomials represented by lists in Python. Here, we implement, from scratch, addition and multiplication of two polynomials.

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