tutorial5.ipynb

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   "source": [
    "# Assumptions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "outputs": [],
   "source": [
    "import sympy as sym"
   ],
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   "cell_type": "code",
   "execution_count": 105,
   "outputs": [
    {
     "data": {
      "text/plain": "{'integer': True,\n 'hermitian': True,\n 'complex': True,\n 'real': True,\n 'noninteger': False,\n 'rational': True,\n 'infinite': False,\n 'irrational': False,\n 'finite': True,\n 'algebraic': True,\n 'imaginary': False,\n 'extended_real': True,\n 'commutative': True,\n 'transcendental': False,\n 'positive': True,\n 'negative': False,\n 'extended_nonpositive': False,\n 'extended_negative': False,\n 'nonzero': True,\n 'nonpositive': False,\n 'extended_nonnegative': True,\n 'nonnegative': True,\n 'zero': False,\n 'extended_positive': True,\n 'extended_nonzero': True}"
     },
     "execution_count": 105,
     "metadata": {},
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   "source": [
    "x = sym.symbols(\"x\")\n",
    "# n = sym.Symbol('n')\n",
    "n = sym.Symbol('n', integer=True, positive=True)\n",
    "n.assumptions0"
   ],
   "metadata": {
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   "cell_type": "code",
   "execution_count": 106,
   "outputs": [
    {
     "data": {
      "text/plain": "sin(n*x)",
      "text/latex": "$\\displaystyle \\sin{\\left(n x \\right)}$"
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = sym.sin(n * x)\n",
    "eq"
   ],
   "metadata": {
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  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "outputs": [
    {
     "data": {
      "text/plain": "0",
      "text/latex": "$\\displaystyle 0$"
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "eq1 = eq.integrate((x, 0, 2 * sym.pi))\n",
    "eq1"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Functions"
   ],
   "metadata": {
    "collapsed": false
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  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "outputs": [
    {
     "data": {
      "text/plain": "f"
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = sym.Function('f')\n",
    "f\n",
    "# g = sym.Symbol('g', cls='Function')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "outputs": [
    {
     "data": {
      "text/plain": "Derivative(f(x), x)",
      "text/latex": "$\\displaystyle \\frac{d}{d x} f{\\left(x \\right)}$"
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_ = sym.diff(f(x), x)\n",
    "f_"
   ],
   "metadata": {
    "collapsed": false
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  },
  {
   "cell_type": "markdown",
   "source": [
    "# f(x) = sin(x) => f`(x) - sin(x) = 0"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "outputs": [
    {
     "data": {
      "text/plain": "-sin(x) + Derivative(f(x), x)",
      "text/latex": "$\\displaystyle - \\sin{\\left(x \\right)} + \\frac{d}{d x} f{\\left(x \\right)}$"
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f2 = f_ - sym.sin(x)\n",
    "f2"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "outputs": [
    {
     "data": {
      "text/plain": "Eq(f(x), C1 - cos(x))",
      "text/latex": "$\\displaystyle f{\\left(x \\right)} = C_{1} - \\cos{\\left(x \\right)}$"
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f3 = sym.dsolve(f2, f(x))\n",
    "f3"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "outputs": [
    {
     "data": {
      "text/plain": "f(x) - 2*Derivative(f(x), x) + Derivative(f(x), (x, 2))",
      "text/latex": "$\\displaystyle f{\\left(x \\right)} - 2 \\frac{d}{d x} f{\\left(x \\right)} + \\frac{d^{2}}{d x^{2}} f{\\left(x \\right)}$"
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f4 = sym.Derivative(f(x), x, 2) - 2 * sym.Derivative(f(x), x) + f(x)\n",
    "f4"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Solve ordinary differential equation eq for function f(x)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "outputs": [
    {
     "data": {
      "text/plain": "Eq(f(x), (C1 + C2*x)*exp(x))",
      "text/latex": "$\\displaystyle f{\\left(x \\right)} = \\left(C_{1} + C_{2} x\\right) e^{x}$"
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.dsolve(f4, f(x))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
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