{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 6 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T, t, pi, pt = var('T', 't', 'pi', 'pt')\n",
    "\n",
    "#pi = 0\n",
    "#pt = 100\n",
    "\n",
    "A = -6*pi + 6*pt\n",
    "B = 15*pi - 15*pt\n",
    "C = -10*pi + 10*pt\n",
    "D = 0\n",
    "E = 0\n",
    "F = pi\n",
    "\n",
    "p_t = 120*A*t   +  24*B\n",
    "s_t =  60*A*t^2 +  24*B*t   +   6*C\n",
    "j_t =  20*A*t^3 +  12*B*t^2 +   6*C*t   +   2*D\n",
    "a_t =   5*A*t^4 +   4*B*t^3 +   3*C*t^2 +   2*D*t   +     E\n",
    "v_t =     A*t^5 +     B*t^4 +     C*t^3 +     D*t^2 +     E*t +   F\n",
    "x_t = 1/6*A*t^6 + 1/5*B*t^5 + 1/4*C*t^4 + 1/3*D*t^3 + 1/2*E*t^2 + F*t\n",
    "f = 5.333333333333333\n",
    "\n",
    "plot_p = plot(p_t(t=T, pi=0, pt=5) / 10, (T, 0, 1), color=\"cyan\")\n",
    "plot_s = plot(s_t(t=T, pi=0, pt=5), (T, 0, 1), color=\"blue\")\n",
    "plot_j = plot(j_t(t=T, pi=0, pt=5) * f, (T, 0, 1), color=\"pink\")\n",
    "plot_a = plot(a_t(t=T, pi=0, pt=5) * f, (T, 0, 1), color=\"green\")\n",
    "plot_v = plot(v_t(t=T, pi=0, pt=5) * 100, (T, 0, 1), color=\"red\")\n",
    "plot_x = plot(x_t(t=T, pi=0, pt=5) / f * 100, (T, 0, 1), color=\"black\")\n",
    "\n",
    "#plot_al = plot( (pt - pi)/10, (t, 0, 1), color=\"green\")\n",
    "#plot_vl = plot( pi*(1-t) + pt*t, (t, 0, 1), color=hue(0.2))\n",
    "#plot_xl = plot( -1/2*pi*(1-t)^2 + 1/2*pt*t^2 + 1/2*pi, (t, 0, 1), color=\"gray\")\n",
    "\n",
    "show(plot_p + plot_s + plot_j + plot_a + plot_v + plot_x)\n",
    "#show(plot_x + plot_v + plot_a + plot_j)\n",
    "#show(plot_x + plot_v + plot_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-15/8*pi, pt*t^6 - 3*pt*t^5 + 5/2*pt*t^4, 6*pt*t^5 - 15*pt*t^4 + 10*pt*t^3)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_t(t=1/2, pt=0), x_t(pi=0), v_t(pi=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0 == a*t^6 + b*t^5 + c*t^4 + f*t - x]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, b, c, f, x = var('a', 'b', 'c', 'f', 'x')\n",
    "solve([a*t^6 + b*t^5 + c*t^4 + f*t - x == 0], t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u == -25/9*T^2*v + 10/3*T*v - v, u == v]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T, u, v = var('T', 'u', 'v')\n",
    "\n",
    "solve([9/25*u^2 + v*T*(T-6/5)*u - v^2*(T-3/5)^2 == 0], u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "u=-25/9*T^2*v + 10/3*T*v - v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0277777777777777*v"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u(T=0.50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-15/8*pi + 15/8*pt, 5)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_t(t=1/2), v_t(t=1, pi=0, pt=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "codemirror_mode": {
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