{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f22c6655",
   "metadata": {},
   "source": [
    "\n",
    "# Uvod v Python za Višjo dinamiko\n",
    "\n",
    "Pregled osnovnih orodij za simbolno in numerično računanje v Pythonu:\n",
    "`sympy` (simbolika), `numpy`/`scipy` (numerika) in `matplotlib` (izris).\n",
    "Notebook sledi istemu zaporedju tem kot uvodni Mathematica notebook tega\n",
    "predmeta, a je prilagojen orodjem, ki jih ponuja Python."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4f13a46",
   "metadata": {},
   "source": [
    "\n",
    "## Delovno okolje\n",
    "\n",
    "V Jupyter notebooku se celica izvede s `Shift+Enter`, nova celica se doda z\n",
    "gumbom `+` oz. tipko `b`/`a` v ukaznem načinu. Mathematica pozna tudi\n",
    "*free-form input* (naravni jezik, npr. `integrate sin(x)`, ki se prevede v\n",
    "`Integrate[Sin[x], x]`) — Python te funkcionalnosti nima, zato se v tem\n",
    "notebooku vsa koda piše neposredno v Pythonu."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e51eca00",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:04.618897Z",
     "iopub.status.busy": "2026-09-25T06:44:04.618784Z",
     "iopub.status.idle": "2026-09-25T06:44:05.287205Z",
     "shell.execute_reply": "2026-09-25T06:44:05.286760Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "from scipy.optimize import brentq, fsolve\n",
    "\n",
    "sp.init_printing(use_unicode=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c40beba",
   "metadata": {},
   "source": [
    "\n",
    "## Poljubna natančnost in velika števila\n",
    "\n",
    "`sympy` ohranja simbole natančno (`sp.pi` ni decimalno število), numerično\n",
    "vrednost pa dobimo z `sp.N`, ki sprejme tudi zahtevano število mest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5557e2e7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:05.288729Z",
     "iopub.status.busy": "2026-09-25T06:44:05.288549Z",
     "iopub.status.idle": "2026-09-25T06:44:05.544008Z",
     "shell.execute_reply": "2026-09-25T06:44:05.543499Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAAJCAYAAAAGuM1UAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtUlEQVQYGXWQsQ3CMBREE2AAZmCECHpLkI45YARat1BSpqUCsQEpPAElZVpaOkrzTvKPTKR86XT/7t+345QxxkLlvT9COzCXHqmm1EIKK/MAWliBK1gm3cLKPadwBb6Is3OuCyFs0Rf0i35N3yrI7E1fzCRgwarGOyWhmxobiCe5IKjbPplX4eX6f4HgHugdVgtrjPsbOEmP1V+62VCMv8l1v4CpcDf8BLx6bEGDQz6kvw908QNYwThArcyywAAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle \\pi$"
      ],
      "text/plain": [
       "π"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5c6cbbac",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:05.545498Z",
     "iopub.status.busy": "2026-09-25T06:44:05.545370Z",
     "iopub.status.idle": "2026-09-25T06:44:05.756290Z",
     "shell.execute_reply": "2026-09-25T06:44:05.755876Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 3.14159265358979$"
      ],
      "text/plain": [
       "3.14159265358979"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.N(sp.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "963c03bc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:05.757663Z",
     "iopub.status.busy": "2026-09-25T06:44:05.757547Z",
     "iopub.status.idle": "2026-09-25T06:44:05.972586Z",
     "shell.execute_reply": "2026-09-25T06:44:05.972201Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 3.14159265358979323846264338328$"
      ],
      "text/plain": [
       "3.14159265358979323846264338328"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.N(sp.pi, 30)  # 30-mestna natančnost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e5aca74",
   "metadata": {},
   "source": [
    "\n",
    "Pythonova cela števila (`int`) so že privzeto poljubno velika — za razliko\n",
    "od `numpy` tipov (npr. `np.int64`), ki prekoračitev tiho preskočijo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f5c6c2ad",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:05.974154Z",
     "iopub.status.busy": "2026-09-25T06:44:05.974036Z",
     "iopub.status.idle": "2026-09-25T06:44:06.210386Z",
     "shell.execute_reply": "2026-09-25T06:44:06.209993Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle 1606938044258990275541962092341162602522202993782792835301376$"
      ],
      "text/plain": [
       "1606938044258990275541962092341162602522202993782792835301376"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "2**200"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1617ddb",
   "metadata": {},
   "source": [
    "\n",
    "Jupyter/IPython hrani zgodovino rezultatov podobno kot Mathematica `%`,\n",
    "`%%`, `%1`: `_` je zadnji rezultat, `__` predzadnji, `_n` pa rezultat iz\n",
    "celice `Out[n]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "18cd2766",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.211784Z",
     "iopub.status.busy": "2026-09-25T06:44:06.211676Z",
     "iopub.status.idle": "2026-09-25T06:44:06.429855Z",
     "shell.execute_reply": "2026-09-25T06:44:06.429431Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 1606938044258990275541962092341162602522202993782792835301376$"
      ],
      "text/plain": [
       "1606938044258990275541962092341162602522202993782792835301376"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "_  # zadnji rezultat (enako kot % v Mathematici)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2ab1023",
   "metadata": {},
   "source": [
    "\n",
    "## Prirejanje vrednosti: takoj ali odloženo (`=` in `:=`)\n",
    "\n",
    "Python `=` vedno izračuna vrednost takoj. Mathematica `:=` (odloženo\n",
    "prirejanje, ponovno izračuna ob vsakem klicu) najbolje ustreza Pythonovi\n",
    "funkciji ali sympyjevemu simbolnemu izrazu, ki ga po potrebi znova\n",
    "ovrednotimo (`subs`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1088d375",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.430878Z",
     "iopub.status.busy": "2026-09-25T06:44:06.430767Z",
     "iopub.status.idle": "2026-09-25T06:44:06.433268Z",
     "shell.execute_reply": "2026-09-25T06:44:06.432860Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c = 3\n",
      "b_odlozeno() = 4\n"
     ]
    }
   ],
   "source": [
    "\n",
    "a = 1\n",
    "b_takoj = 2 * a  # izračunano takoj, tako kot Mathematica `=`\n",
    "\n",
    "\n",
    "def b_odlozeno():  # ponovno izračuna ob vsakem klicu, tako kot Mathematica `:=`\n",
    "    return 2 * a\n",
    "\n",
    "\n",
    "c = a + b_takoj\n",
    "a = 2  # sprememba a\n",
    "print(f\"c = {c}\")  # c ostane 3, ker je bil izračunan, preden se je a spremenil\n",
    "print(f\"b_odlozeno() = {b_odlozeno()}\")  # uporabi trenutno vrednost a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbfbeb53",
   "metadata": {},
   "source": [
    "\n",
    "Isto na simbolni ravni: sympyjev izraz se ne izračuna, dokler eksplicitno\n",
    "ne vstavimo vrednosti (`subs`) — to je simbolni analog `:=`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dad8b996",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.434196Z",
     "iopub.status.busy": "2026-09-25T06:44:06.434083Z",
     "iopub.status.idle": "2026-09-25T06:44:06.660053Z",
     "shell.execute_reply": "2026-09-25T06:44:06.659575Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( 2, \\  4\\right)$"
      ],
      "text/plain": [
       "(2, 4)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "a_s = sp.Symbol(\"a\")\n",
    "izraz = 2 * a_s  # ostane simbolen, dokler ga ne ovrednotimo\n",
    "izraz.subs(a_s, 1), izraz.subs(a_s, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d8d0e76",
   "metadata": {},
   "source": [
    "\n",
    "### Brisanje prirejanja\n",
    "\n",
    "Mathematica `c=.` spremenljivko počisti nazaj v simbol; Python spremenljivko\n",
    "lahko le izbriše (`del`) — dostop do izbrisanega imena po tem vrne\n",
    "`NameError`, ne simbola."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "92ebf5bc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.661083Z",
     "iopub.status.busy": "2026-09-25T06:44:06.660973Z",
     "iopub.status.idle": "2026-09-25T06:44:06.663154Z",
     "shell.execute_reply": "2026-09-25T06:44:06.662757Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "NameError: name 'c' is not defined\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(c)\n",
    "del c\n",
    "try:\n",
    "    print(c)\n",
    "except NameError as napaka:\n",
    "    print(f\"NameError: {napaka}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02ee9868",
   "metadata": {},
   "source": [
    "\n",
    "## Enakost: `==` in `===`\n",
    "\n",
    "Mathematica `==` (`Equal`) tvori *simbolno enačbo*, ki ostane v tej obliki,\n",
    "dokler je ne rešimo ali poenostavimo — temu ustreza sympyjev `sp.Eq`.\n",
    "Mathematica `===` (`SameQ`) preveri *strukturno* enakost dveh izrazov in\n",
    "vrne `True`/`False` takoj — temu ustreza navaden Pythonov/sympyjev `==`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "744b04ce",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.664314Z",
     "iopub.status.busy": "2026-09-25T06:44:06.664207Z",
     "iopub.status.idle": "2026-09-25T06:44:06.890431Z",
     "shell.execute_reply": "2026-09-25T06:44:06.889979Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\sqrt{x^{2}} = x$"
      ],
      "text/plain": [
       "   ____    \n",
       "  ╱  2     \n",
       "╲╱  x   = x"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "x, y = sp.symbols(\"x y\")\n",
    "enacba = sp.Eq(sp.sqrt(x**2), x)  # simbolna enačba (analogija Mathematica ==)\n",
    "enacba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d637baf6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.891742Z",
     "iopub.status.busy": "2026-09-25T06:44:06.891612Z",
     "iopub.status.idle": "2026-09-25T06:44:06.893931Z",
     "shell.execute_reply": "2026-09-25T06:44:06.893562Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.sqrt(x**2) == x  # strukturna primerjava (analogija Mathematica ===)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f55f8f86",
   "metadata": {},
   "source": [
    "\n",
    "Matematično enakost dveh izrazov (ob dodatnih predpostavkah) preverimo s\n",
    "`sp.simplify` razlike."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "54c9806f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.894953Z",
     "iopub.status.busy": "2026-09-25T06:44:06.894855Z",
     "iopub.status.idle": "2026-09-25T06:44:06.955608Z",
     "shell.execute_reply": "2026-09-25T06:44:06.955174Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.simplify(sp.sqrt(x**2) - x) == 0  # ni nujno enako 0 (x je lahko negativen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b716dcc8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.956813Z",
     "iopub.status.busy": "2026-09-25T06:44:06.956680Z",
     "iopub.status.idle": "2026-09-25T06:44:06.959273Z",
     "shell.execute_reply": "2026-09-25T06:44:06.958910Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "x_pozitiven = sp.Symbol(\"x\", positive=True)\n",
    "sp.simplify(sp.sqrt(x_pozitiven**2) - x_pozitiven) == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d7c466c",
   "metadata": {},
   "source": [
    "\n",
    "## Odvajanje in integriranje"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "75c11fe2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:06.960490Z",
     "iopub.status.busy": "2026-09-25T06:44:06.960390Z",
     "iopub.status.idle": "2026-09-25T06:44:07.175757Z",
     "shell.execute_reply": "2026-09-25T06:44:07.175260Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{x^{2}}{2}$"
      ],
      "text/plain": [
       " 2\n",
       "x \n",
       "──\n",
       "2 "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.integrate(x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "23ffd8b0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:07.177058Z",
     "iopub.status.busy": "2026-09-25T06:44:07.176939Z",
     "iopub.status.idle": "2026-09-25T06:44:07.382862Z",
     "shell.execute_reply": "2026-09-25T06:44:07.382416Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle x^{x} \\left(\\log{\\left(x \\right)} + 1\\right) \\cos{\\left(x^{x} \\right)}$"
      ],
      "text/plain": [
       " x                 ⎛ x⎞\n",
       "x ⋅(log(x) + 1)⋅cos⎝x ⎠"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.diff(sp.sin(x**x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1185318c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:07.384262Z",
     "iopub.status.busy": "2026-09-25T06:44:07.384147Z",
     "iopub.status.idle": "2026-09-25T06:44:07.612622Z",
     "shell.execute_reply": "2026-09-25T06:44:07.612148Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle x^{x} \\left(- x^{2 x} \\left(\\log{\\left(x \\right)} + 1\\right)^{3} \\cos{\\left(x^{x} \\right)} - 3 x^{x} \\left(\\log{\\left(x \\right)} + 1\\right)^{3} \\sin{\\left(x^{x} \\right)} + \\left(\\log{\\left(x \\right)} + 1\\right)^{3} \\cos{\\left(x^{x} \\right)} - \\frac{3 x^{x} \\left(\\log{\\left(x \\right)} + 1\\right) \\sin{\\left(x^{x} \\right)}}{x} + \\frac{3 \\left(\\log{\\left(x \\right)} + 1\\right) \\cos{\\left(x^{x} \\right)}}{x} - \\frac{\\cos{\\left(x^{x} \\right)}}{x^{2}}\\right)$"
      ],
      "text/plain": [
       "   ⎛                                                                           ↪\n",
       " x ⎜   2⋅x             3    ⎛ x⎞      x             3    ⎛ x⎞               3  ↪\n",
       "x ⋅⎜- x   ⋅(log(x) + 1) ⋅cos⎝x ⎠ - 3⋅x ⋅(log(x) + 1) ⋅sin⎝x ⎠ + (log(x) + 1) ⋅ ↪\n",
       "   ⎜                                                                           ↪\n",
       "   ⎝                                                                           ↪\n",
       "\n",
       "↪              x                 ⎛ x⎞                     ⎛ x⎞      ⎛ x⎞⎞\n",
       "↪    ⎛ x⎞   3⋅x ⋅(log(x) + 1)⋅sin⎝x ⎠   3⋅(log(x) + 1)⋅cos⎝x ⎠   cos⎝x ⎠⎟\n",
       "↪ cos⎝x ⎠ - ───────────────────────── + ────────────────────── - ───────⎟\n",
       "↪                       x                         x                 2   ⎟\n",
       "↪                                                                  x    ⎠"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.diff(sp.sin(x**x), x, 3)  # odvod tretjega reda"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84328c3b",
   "metadata": {},
   "source": [
    "\n",
    "## Uporabne funkcije: odsekoma definirane funkcije\n",
    "\n",
    "`sp.Piecewise` je sympyjev analog Mathematica `Piecewise`; za izris v\n",
    "`matplotlib` izraz z `sp.lambdify` pretvorimo v numerično funkcijo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3530d211",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:07.613961Z",
     "iopub.status.busy": "2026-09-25T06:44:07.613845Z",
     "iopub.status.idle": "2026-09-25T06:44:07.679375Z",
     "shell.execute_reply": "2026-09-25T06:44:07.678927Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "t = sp.Symbol(\"t\")\n",
    "h = sp.Piecewise((t, t < 5), (-t, True))\n",
    "h_num = sp.lambdify(t, h, \"numpy\")\n",
    "\n",
    "t_vals = np.linspace(0, 10, 300)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(t_vals, h_num(t_vals), linewidth=1.5)\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.set_xlabel(\"t\")\n",
    "ax.set_ylabel(\"h(t)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cd24298",
   "metadata": {},
   "source": [
    "\n",
    "## Algebrajske enačbe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a4fdec0f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:07.680774Z",
     "iopub.status.busy": "2026-09-25T06:44:07.680659Z",
     "iopub.status.idle": "2026-09-25T06:44:07.884242Z",
     "shell.execute_reply": "2026-09-25T06:44:07.883701Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHwAAAAXCAYAAADJLSsnAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAD7UlEQVRoBe2Z7VEbMRCGDeMCCCVAByR0YDqAUAHQQTL88z+GdACUAB1AB3x0AB2EcQfO+9xIGp3mZHySzncE74ysvT19vLsrrVbnjfl8PmpL0+l0S33OTb8dU59IPms71rp9eQss8s84cbpLDXpm+4q/Ev+ssmtl67pXC0T9s5kI61ROnnh9L8XvSLbnydZsfxaI+ifV4ezup/70Wc/8gQWi/tlIOcPDybSz2eGHqtchPTTOAJ59/6Se4U4NE8YPJfjuhCtmhIHE8beZ9ofqd54lfzGyL1uF/sna4cbQJGxH4nvJ0C0G1QfWq+KJOL9UDsQ/WPlXq61tpLfzT/ION4OxiypDm+eR6re2hlUfEkCSvuu2fdUe57obA/01DrhOxd6qfEM2BBKmHD1bqaC5qqinuuafpKTNDMbOvhK/RxFPSCWUphD3ekoKYcRXYQj7s7O3DNaUcbvok6Pn0niMzo3+Sd3h3LkBT+1IE9V2mnvRLYNjWXSzyDThQog0+6/EUf84h8tgGIYwCO2rnKgQFo5VoEe1uYNRPaQweQSmBqq+CQirS9zEt9HRtuXm8ay+7rgx49yojs3dACdP5GH/EI/aRv3jh3S+zvyhCNqjyo3KRM+EapTnrPwUJMw4m8VqM3eLu42O58YW9+oc6v5TMm4mq6QieKodLsXY2b5SMz2jELsc2lbx31fCAf+QrN0Zh1Uw2+iotiwYFj1E0hPmJshWlv2XxGND+pMG9bNr7tQvkuH4keoioUvjkEhMGDMgFhTzNOUA4Fh6fjPHW0OfNjrS3x4F7OaLAC86hDLXxGAoqWcWHgdMTOVwTzn7rklJ+y651jxNDh1JTjThWsZxkkzqT6TaVs0OrJFk1oFWHtVRbe1Cx2kcZ/75ze5HFt3h6l9Uz1w8wurIP8MroQa3SlYJGkLJuN6g5GBJ+Fg0u6pdNBDPIuIsr5Fky+rIWC7SmUHoO9MY4QKqzdHRQzaesYDjSM48EhpWLasThfwQT8IQJkBqNgwSNnbdfgNGFsG15Kk6slh8O6DwSs9vJvQoG89Yg7FiKXydwjC1BEUy3tkERuywSPgwAgv2QTw5gk8Tybh54PgUHXF2lV8wqMaxtmoM2bTpmLLxjAWQXc0ZhTIodaZyr4LxuMC/i3fhnTYDI65NON1+Q/Dh2bCbqiNRjfs2N5S/KvbfwOj57U/eAZ+NJ+vPk1IKyaBFkrZSeGLjGMcTNZL+GSytZwqezZhyK5bPNB9lMIQxVdynY/Ecd0SRiwyQyXqWwkNI752kTF8hcpHuRB0/J+DLIwlg8vGWqWcRPIMI6Yus3tc7OQcDk7Cxszm7bzMdpiHSqRSef1R58L1i6Q8GAAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle x^{2} + 2 x y + y^{2}$"
      ],
      "text/plain": [
       " 2            2\n",
       "x  + 2⋅x⋅y + y "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.expand((x + y) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "276cb4ec",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:07.885623Z",
     "iopub.status.busy": "2026-09-25T06:44:07.885480Z",
     "iopub.status.idle": "2026-09-25T06:44:08.113755Z",
     "shell.execute_reply": "2026-09-25T06:44:08.113345Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left(x + y\\right)^{2}$"
      ],
      "text/plain": [
       "       2\n",
       "(x + y) "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.factor(sp.expand((x + y) ** 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8ec5fe01",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:08.115140Z",
     "iopub.status.busy": "2026-09-25T06:44:08.115022Z",
     "iopub.status.idle": "2026-09-25T06:44:08.409179Z",
     "shell.execute_reply": "2026-09-25T06:44:08.408667Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{2 x - 1}{6 \\left(x^{2} - x + 1\\right)} + \\frac{2}{3 \\left(\\left(\\frac{2 \\sqrt{3} x}{3} - \\frac{\\sqrt{3}}{3}\\right)^{2} + 1\\right)} + \\frac{1}{3 \\left(x + 1\\right)}$"
      ],
      "text/plain": [
       "     2⋅x - 1                 2                  1    \n",
       "- ────────────── + ────────────────────── + ─────────\n",
       "    ⎛ 2        ⎞     ⎛             2    ⎞   3⋅(x + 1)\n",
       "  6⋅⎝x  - x + 1⎠     ⎜⎛2⋅√3⋅x   √3⎞     ⎟            \n",
       "                   3⋅⎜⎜────── - ──⎟  + 1⎟            \n",
       "                     ⎝⎝  3      3 ⎠     ⎠            "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "odvod_integrala = sp.diff(sp.integrate(1 / (x**3 + 1), x), x)\n",
    "odvod_integrala"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "421af4d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:08.410428Z",
     "iopub.status.busy": "2026-09-25T06:44:08.410306Z",
     "iopub.status.idle": "2026-09-25T06:44:08.665897Z",
     "shell.execute_reply": "2026-09-25T06:44:08.665382Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{1}{x^{3} + 1}$"
      ],
      "text/plain": [
       "  1   \n",
       "──────\n",
       " 3    \n",
       "x  + 1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "sp.simplify(odvod_integrala)  # vrne izvorno funkcijo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9fb1d0ca",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:08.667177Z",
     "iopub.status.busy": "2026-09-25T06:44:08.667042Z",
     "iopub.status.idle": "2026-09-25T06:44:08.897813Z",
     "shell.execute_reply": "2026-09-25T06:44:08.897365Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ - \\frac{1}{2} + \\frac{\\sqrt{5}}{2}, \\  - \\frac{\\sqrt{5}}{2} - \\frac{1}{2}\\right]$"
      ],
      "text/plain": [
       "⎡  1   √5    √5   1⎤\n",
       "⎢- ─ + ──, - ── - ─⎥\n",
       "⎣  2   2     2    2⎦"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "resitve = sp.solve(sp.Eq(x**2 + x, 1), x)  # sp.solve vrne kar seznam vrednosti\n",
    "resitve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "785aa5f4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:08.899183Z",
     "iopub.status.busy": "2026-09-25T06:44:08.899065Z",
     "iopub.status.idle": "2026-09-25T06:44:09.129699Z",
     "shell.execute_reply": "2026-09-25T06:44:09.129272Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{1}{2} + \\frac{\\sqrt{5}}{2}$"
      ],
      "text/plain": [
       "  1   √5\n",
       "- ─ + ──\n",
       "  2   2 "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "resitve[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8f1bc87",
   "metadata": {},
   "source": [
    "\n",
    "## Iskanje ničel\n",
    "\n",
    "Za nelinearne enačbe, ki jih `sp.solve` ne reši v zaprti obliki, uporabimo\n",
    "numerične metode iz `scipy.optimize`: `fsolve` (iterativno iskanje z\n",
    "začetnim približkom, analog Mathematica `FindRoot`) ali `brentq` (iskanje\n",
    "znotraj intervala z zagotovljeno konvergenco)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "33e922f7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:09.130999Z",
     "iopub.status.busy": "2026-09-25T06:44:09.130886Z",
     "iopub.status.idle": "2026-09-25T06:44:09.187144Z",
     "shell.execute_reply": "2026-09-25T06:44:09.186716Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "k = lambda x: np.sin(x) + np.exp(x)\n",
    "\n",
    "x_vals = np.linspace(-2, 2, 300)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(x_vals, k(x_vals), linewidth=1.5)\n",
    "ax.axhline(0, color=\"black\", linewidth=0.8)\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"k(x)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7099536b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:09.188603Z",
     "iopub.status.busy": "2026-09-25T06:44:09.188470Z",
     "iopub.status.idle": "2026-09-25T06:44:09.190986Z",
     "shell.execute_reply": "2026-09-25T06:44:09.190590Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fsolve: -0.5885327440\n",
      "brentq: -0.5885327440\n"
     ]
    }
   ],
   "source": [
    "\n",
    "nicla_fsolve = fsolve(k, 0)[0]  # začetni približek x=0, tako kot FindRoot\n",
    "nicla_brentq = brentq(k, -2, 0)  # iskanje znotraj intervala [-2, 0]\n",
    "print(f\"fsolve: {nicla_fsolve:.10f}\")\n",
    "print(f\"brentq: {nicla_brentq:.10f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8edb31c7",
   "metadata": {},
   "source": [
    "\n",
    "## Diferencialne enačbe\n",
    "\n",
    "Simbolno reševanje z `sp.dsolve` — najprej brez, nato z začetnimi pogoji."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7f594650",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:09.192152Z",
     "iopub.status.busy": "2026-09-25T06:44:09.192053Z",
     "iopub.status.idle": "2026-09-25T06:44:09.513909Z",
     "shell.execute_reply": "2026-09-25T06:44:09.513441Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gpIuypxSuYd1hRadA5LPDbphI5ZLum2H4wue1PFpYTTr5SozSBbYTYzJBX9rLrZY18a2zDEfiGQv7W9AXbYp8ps/vObYEmlzmVlval8osYznbF1dOPAhzyVXEwgCVk7TYP+6VNZzomKi4hittsiCkz/CMuE45UMWAwUpvbCKDqLHwkSKPF6Q2MSixwugmYoUxITFh2Mrh4q0Khfcdlh+wwWrQOT0z4Bgun8jPB44os+9Iw5sZZu3g7RoTPEvHs8VbWP9+1zwUXsg7PGDr54IHgKSw57qCAqE7vM51c3k05CP10qfcNYqA5GcTWVM5jAOMMckBPUK099jSKKeaJZtxyhaWoRGSFaz/WPBtLinWuCe9kjGF8z0ICGI/zcxhYxPRj4pnFTzmKAczehiYdU+t8mj0kS0MY20bhtFZwYzDLGiC4IIFgImJMJg46hTPauJ9RZKWdPYdCLALCp3uWDEYMMI+VCwIpYVn4wsTHKsVTPO6BQctlHuhGMY4u909D4UP1h7efQYrlGVTFl7Kzz502B4ywDLukzxSPUwOL3SF1aOe6Vuf6YLXhBOPtYVwrCKEW99BOWG7BVl0d42AKWDwdDcn/mTJmvLDc8ZmXvk1OR1tj+L3HltG6bqjwFyZW5Rf/MbyjNKAfNg8wrONEUWhT/6LZySI1dio1qtwiO2/qTCbUOWlQ3By1BSV2Xk94XYI7M1D1c+qas1BtSsQVBYfP6HjVNu/j/SjgDQhx3tgdMWoygFqM4oXcsZYdbEtuJQU5d9MXpfUrXoZL1k4hEkhPj/oPrVIWFJFsbSisXq/LNaYmQWrzVkyl5t/JpmbJQuWCBGNBtMpDHp+R89YElgNpRx5EOo12g4rPPK72xeBvXnIimpyVbUAHlaaKBFcW5W5oPomklbFSHwIk19EBisL9TMZ/l4RLcYy3BYT7pby+oaqG78RQyyV4IZFCseYu5WVLBRY8KeqzNGOiJnhs4fc5cpcbv6C7Lwu+nEMQsP+sRf9g/yYSJKau+IwobOKZKCY7WJ68g0PDM0uwxNug8DePFT9fD9hKzmwSWKRPK5BUjQjvyhgbDUEv57Zvjq6q4qRwGBrjg/g2Ae5UB74SBpbmbWcyQMKQJYT3VvK61xaOBUPXtztYusyuz1zCchMV03moFO4wO+95S5X5nLzZ7JsWfZgiVAWtLb3xAAGQkyzMMH23PWYdOzDYrrhHMBch1a9xnoxt3xPtwyBs/DQBivbT1yGwoLU6hvUZSudBTl3T1oNI7XUrFxdo4Ubq2ksnIwZ4Tv8XWQ5T5CHyLNytRQqWXTXwqlQCzoLUPF+GRtwBLnLlbnc/KV4OVruY0IlqBz6wfLAiX9WDXMUiAelQxsm/axVWExHehvMRonywHoInIiHdqDItPh6ILZTU02MWD3/Ifky06yhxNjCllMtPlF/K6t2w+hM95oyB25HkLtcmcvNX1V+zBKxutKoEKTewLgoV2lnpbvI5A/FETgJD22iaOKQY3GmjldQEyOUBb6qaHUOKWKgLOpUtykq7Mu72wcB43+tfrmr3OXKXG7+PVicrUTsQbTX6QiMIGDWLZs4RpLcfVA1jDQYpl45/QguKL7G4UqThRp13b1wJQCoJnNRrvaWu1yZy82fYEO54MflivaSHYGqCNgHvqwTVq28kcp2xUiKAwoE/Kl1nsRk4ddG+HNGMneVOQCtLHe5Mpebv7oMPa5eo1foCBRAQAMFZlNWPWGlW6CK5os8AEYcqOT8Va1tTfvGzawzXs0z+IANOIDMgUpNucuVudz81aXAlYjqkHuFBREIk4UGLtPmC1bVbNG7YCSe8FYWX1JMmZtLAMo3Ah5Up29nlEB3fpm7yFzkfW25y5W53PzzubJRSlciNgLSizkEArxHj+OEtrtxBKpjpEmc1zp5hXzJq+Dj1C8LxSple/LLcnrqLRGoLnMQv5Pc5cpcbv4t+TarLFciZsHkiRpBwMzWZhJshOyqZFbFSAM5H7L7UPfOAiH/4o/ULUVIddi2VvKDeUvL9PSrEagqc1Ap/leXu1yZy82/mjuZGV2JyATQsx8HAXVCVp2cjXBLRIItNTGKgyJ/DjY8SMkAX/q1S5OB/pd4E6h4cEkEasoc7dhR7nJlLjd/STYmy36SjPEIR6BNBPiM9pcaSPw/NNL8K46R8OdcCgfa+FQ0+9J991xhpQ9XsnXySvX4eYg+8vv5i8scTRO/95S7XJnLzb8Ld90SsQvsXmlBBGzCCn9FX7CelouugRF/rc6ADh+Gl32AqAiGmkjeUcGs6syMXqQeL3QRAjVkDoJ2kbtcmcvNv4gTGyd2S8TGgHpx+yKgzsgbAKw+/6ar9Gp338aurL0GRqqj1hcKx1D4NAZ+MxbpYfURqCFztGpHucuVudz89Zkaa3RLxG7Qe8UFEWDVwyeXWQm7G0fgzBjxB3+mTI633kP3QMBlLo16szLrSkSaqR7TLgI/RdL932LTPDwlRlFx5M0M/s3R3bEQcJkb4UfrMutKxAhTPahtBNQp2XPnIJefi0iw8sQYBcVR7YP/7g6EgMtckhlNy6wrEUm+ekTjCPBaIW9ozPqb+sbbupb8U2EkXnOgEn4PXyldi4/n2x4Bl7kepmeQWVciegx173kQiKseBqwX52nVti05IUZsYXAWwg/Ubisqm5XmMncFZfMy60rEFU894CwIxMnkpe5ujUgw9SwYqR0fqIlsX/k5mASvjxLsMveGE2eRWVcijtKznI5SCDCpfBs7bKk6Wi/3DBixouMfQv3bEG1Io8vcm8O/zcusKxFtdDinciUCcVLBvM3XE92NINA6RqIfCwQfl/pspHkedEAE7l3mziSzj16/fn1AEXOSHIFtEVCn5Ut2v+ju++UJaFvESDSzjcG/RH4iv3/iOsHbowbfo8ydTWbdEnHU3uV0bY0A/yL5hTqw/bvj1uWfobwWMcLC9JUrEM2K3z3K3Klk1pWIZvueE74EAU0yfDuCP7hxl0CgNYxEL690okD4NyESPD168L3J3Bll9v8RymUC77s/GgAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle y{\\left(t \\right)} = - a \\cos{\\left(t \\right)} + \\left(C_{1} \\sin{\\left(\\frac{\\sqrt{3} t}{2} \\right)} + C_{2} \\cos{\\left(\\frac{\\sqrt{3} t}{2} \\right)}\\right) e^{- \\frac{t}{2}}$"
      ],
      "text/plain": [
       "                                                  -t \n",
       "                                                  ───\n",
       "                   ⎛      ⎛√3⋅t⎞         ⎛√3⋅t⎞⎞   2 \n",
       "y(t) = -a⋅cos(t) + ⎜C₁⋅sin⎜────⎟ + C₂⋅cos⎜────⎟⎟⋅ℯ   \n",
       "                   ⎝      ⎝ 2  ⎠         ⎝ 2  ⎠⎠     "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "y = sp.Function(\"y\")\n",
    "a = sp.Symbol(\"a\")\n",
    "enacba_ode = sp.Eq(y(t).diff(t, 2) + y(t).diff(t) + y(t), a * sp.sin(t))\n",
    "sp.dsolve(enacba_ode, y(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c56622eb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:09.515234Z",
     "iopub.status.busy": "2026-09-25T06:44:09.515119Z",
     "iopub.status.idle": "2026-09-25T06:44:09.817430Z",
     "shell.execute_reply": "2026-09-25T06:44:09.816963Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle y{\\left(t \\right)} = - a \\cos{\\left(t \\right)} + \\left(\\left(a + 1\\right) \\cos{\\left(\\frac{\\sqrt{3} t}{2} \\right)} + \\left(\\frac{\\sqrt{3} a}{3} + \\frac{\\sqrt{3}}{3}\\right) \\sin{\\left(\\frac{\\sqrt{3} t}{2} \\right)}\\right) e^{- \\frac{t}{2}}$"
      ],
      "text/plain": [
       "                                                                -t \n",
       "                                                                ───\n",
       "                   ⎛           ⎛√3⋅t⎞   ⎛√3⋅a   √3⎞    ⎛√3⋅t⎞⎞   2 \n",
       "y(t) = -a⋅cos(t) + ⎜(a + 1)⋅cos⎜────⎟ + ⎜──── + ──⎟⋅sin⎜────⎟⎟⋅ℯ   \n",
       "                   ⎝           ⎝ 2  ⎠   ⎝ 3     3 ⎠    ⎝ 2  ⎠⎠     "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "resitev = sp.dsolve(\n",
    "    enacba_ode,\n",
    "    y(t),\n",
    "    ics={y(0): 1, y(t).diff(t).subs(t, 0): 0},\n",
    ")\n",
    "resitev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9e5464ee",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:09.818741Z",
     "iopub.status.busy": "2026-09-25T06:44:09.818622Z",
     "iopub.status.idle": "2026-09-25T06:44:09.880945Z",
     "shell.execute_reply": "2026-09-25T06:44:09.880509Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "y_sol = sp.lambdify(t, resitev.rhs.subs(a, 1), \"numpy\")\n",
    "t_vals = np.linspace(0, 100, 1000)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(t_vals, y_sol(t_vals), linewidth=1.5)\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.set_xlabel(\"t\")\n",
    "ax.set_ylabel(\"y(t)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4a5fe8f",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "\n",
    "Za enačbe, ki jih `dsolve` ne reši v zaprti obliki, uporabimo numerično\n",
    "integracijo (`solve_ivp`), sistem prvega reda: $y_1 = y,\\ y_2 = \\dot y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "d8319855",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:09.882561Z",
     "iopub.status.busy": "2026-09-25T06:44:09.882453Z",
     "iopub.status.idle": "2026-09-25T06:44:10.082458Z",
     "shell.execute_reply": "2026-09-25T06:44:10.081814Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def odvod(t, stanje):\n",
    "    y1, y2 = stanje\n",
    "    return [y2, np.sin(t) - y2 - y1]\n",
    "\n",
    "\n",
    "resitev_num = solve_ivp(odvod, [0, 100], [1, 0], dense_output=True, rtol=1e-10, atol=1e-12)\n",
    "\n",
    "t_vals = np.linspace(0, 20, 400)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(t_vals, y_sol(t_vals), label=\"simbolna rešitev\", linewidth=1.5)\n",
    "ax.plot(\n",
    "    t_vals,\n",
    "    resitev_num.sol(t_vals)[0],\n",
    "    \"--\",\n",
    "    label=\"solve_ivp\",\n",
    "    linewidth=1.5,\n",
    ")\n",
    "ax.legend()\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.set_xlabel(\"t\")\n",
    "ax.set_ylabel(\"y(t)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ed48fc5a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:10.083842Z",
     "iopub.status.busy": "2026-09-25T06:44:10.083655Z",
     "iopub.status.idle": "2026-09-25T06:44:10.086617Z",
     "shell.execute_reply": "2026-09-25T06:44:10.086097Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y(1) simbolno:  0.7790980009\n",
      "y(1) solve_ivp: 0.7790980009\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(f\"y(1) simbolno:  {y_sol(1.0):.10f}\")\n",
    "print(f\"y(1) solve_ivp: {resitev_num.sol(1.0)[0]:.10f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f15e50a0",
   "metadata": {},
   "source": [
    "\n",
    "## Risanje: `matplotlib` namesto `Plot`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8fe4a6cb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:10.087872Z",
     "iopub.status.busy": "2026-09-25T06:44:10.087710Z",
     "iopub.status.idle": "2026-09-25T06:44:10.228373Z",
     "shell.execute_reply": "2026-09-25T06:44:10.227865Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x_vals = np.linspace(-3, 3, 300)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(x_vals, x_vals, color=\"red\", linewidth=2.5, label=\"$x$\")\n",
    "ax.plot(x_vals, x_vals**3 - 5, color=\"blue\", linewidth=1.0, linestyle=\"--\", label=\"$x^3-5$\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\")\n",
    "ax.legend()\n",
    "ax.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23212ec5",
   "metadata": {},
   "source": [
    "\n",
    "## Animacije in interaktivnost\n",
    "\n",
    "Mathematica `Animate`/`Manipulate` v Pythonu ustrezata dvema orodjema:\n",
    "`matplotlib.animation.FuncAnimation` za vnaprej pripravljeno animacijo, ki\n",
    "jo prikažemo z `HTML(anim.to_jshtml())`, ter `ipywidgets.interact` za\n",
    "interaktivno upravljanje s parametrom prek drsnika."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "76f32959",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:10.229694Z",
     "iopub.status.busy": "2026-09-25T06:44:10.229592Z",
     "iopub.status.idle": "2026-09-25T06:44:11.068137Z",
     "shell.execute_reply": "2026-09-25T06:44:11.067601Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_imgd459139515dd440b95d95db7d6a59aba\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_sliderd459139515dd440b95d95db7d6a59aba\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"animd459139515dd440b95d95db7d6a59aba.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animd459139515dd440b95d95db7d6a59aba.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animd459139515dd440b95d95db7d6a59aba.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animd459139515dd440b95d95db7d6a59aba.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animd459139515dd440b95d95db7d6a59aba.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animd459139515dd440b95d95db7d6a59aba.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animd459139515dd440b95d95db7d6a59aba.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animd459139515dd440b95d95db7d6a59aba.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animd459139515dd440b95d95db7d6a59aba.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animd459139515dd440b95d95db7d6a59aba.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectd459139515dd440b95d95db7d6a59aba\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_d459139515dd440b95d95db7d6a59aba\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_d459139515dd440b95d95db7d6a59aba\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_d459139515dd440b95d95db7d6a59aba\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_d459139515dd440b95d95db7d6a59aba\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_d459139515dd440b95d95db7d6a59aba\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_d459139515dd440b95d95db7d6a59aba\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgd459139515dd440b95d95db7d6a59aba\";\n",
       "    var slider_id = \"_anim_sliderd459139515dd440b95d95db7d6a59aba\";\n",
       "    var loop_select_id = \"_anim_loop_selectd459139515dd440b95d95db7d6a59aba\";\n",
       "    var frames = new Array(30);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAGQCAYAAACAvzbMAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animd459139515dd440b95d95db7d6a59aba = new Animation(frames, img_id, slider_id, 59.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import HTML\n",
    "\n",
    "barve = [\"tab:red\", \"tab:blue\", \"tab:green\"]\n",
    "st_okvirjev = 30\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "ax.set_xlim(-3, 6)\n",
    "ax.set_ylim(-3, 6)\n",
    "ax.set_aspect(\"equal\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "\n",
    "krogi = [plt.Circle((0, 0), 1, fill=False, linewidth=2, color=barva) for barva in barve]\n",
    "for krog in krogi:\n",
    "    ax.add_patch(krog)\n",
    "\n",
    "\n",
    "def animiraj(i):\n",
    "    t = i / (st_okvirjev - 1)\n",
    "    parametri = [(t, 1 + t, t), (1 - t, 2 - t, 1 - t), (0.5, 1.5, 0.5)]\n",
    "    for krog, (sredisce, polmer, prosojnost) in zip(krogi, parametri):\n",
    "        krog.center = (sredisce, sredisce)\n",
    "        krog.radius = polmer\n",
    "        krog.set_alpha(max(prosojnost, 0.05))\n",
    "    return krogi\n",
    "\n",
    "\n",
    "anim = FuncAnimation(fig, animiraj, frames=st_okvirjev, interval=60, blit=True)\n",
    "plt.close(fig)\n",
    "HTML(anim.to_jshtml())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "56e3be19",
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    "execution": {
     "iopub.execute_input": "2026-09-25T06:44:11.073098Z",
     "iopub.status.busy": "2026-09-25T06:44:11.072978Z",
     "iopub.status.idle": "2026-09-25T06:44:11.161359Z",
     "shell.execute_reply": "2026-09-25T06:44:11.161013Z"
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   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "455ac7be4a6a4fbca63f1ec4e800058d",
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       "interactive(children=(FloatSlider(value=0.25, description='t', max=1.0, step=0.05), Output()), _dom_classes=('…"
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     "data": {
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       "<function __main__.slika(t=0.25)>"
      ]
     },
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     "metadata": {},
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   ],
   "source": [
    "\n",
    "from ipywidgets import interact\n",
    "\n",
    "\n",
    "def slika(t=0.25):\n",
    "    fig, ax = plt.subplots(figsize=(4, 4))\n",
    "    ax.set_xlim(-3, 6)\n",
    "    ax.set_ylim(-3, 6)\n",
    "    ax.set_aspect(\"equal\")\n",
    "    ax.grid(True, alpha=0.3)\n",
    "    ax.add_patch(\n",
    "        plt.Circle((t, t), 1 + t, color=\"tab:red\", alpha=max(t, 0.05), fill=False, linewidth=2)\n",
    "    )\n",
    "    ax.add_patch(\n",
    "        plt.Circle(\n",
    "            (1 - t, 1 - t), 2 - t, color=\"tab:blue\", alpha=max(1 - t, 0.05), fill=False, linewidth=2\n",
    "        )\n",
    "    )\n",
    "    ax.add_patch(\n",
    "        plt.Circle((0.5, 0.5), 1.5, color=\"tab:green\", alpha=0.5, fill=False, linewidth=2)\n",
    "    )\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "interact(slika, t=(0.0, 1.0, 0.05))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85a706e4",
   "metadata": {},
   "source": [
    "\n",
    "## Viri\n",
    "\n",
    "- https://numpy.org/doc/\n",
    "- https://docs.scipy.org/doc/scipy/\n",
    "- https://docs.sympy.org/latest/index.html\n",
    "- https://matplotlib.org/stable/"
   ]
  }
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