Lec011_sympy-example.ipynb

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   "source": [
    "import sympy"
   ]
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   "id": "48d302bb-4720-421b-94ea-d35ac911529f",
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   "source": [
    "sympy.pi.evalf(100)"
   ]
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   "source": [
    "s3=sympy.sqrt(3)\n",
    "s3"
   ]
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    "s3.evalf(100)"
   ]
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   "id": "0712c82f-0387-4b58-8734-b53dd236fcfc",
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   "outputs": [],
   "source": [
    "s3*s3"
   ]
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   "id": "96be78ba-f156-4ec2-b806-fab298db270e",
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   "source": [
    "3**0.5 * 3**0.5"
   ]
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   "id": "c80d14dd-b27f-4a6e-90b4-83b96f416b28",
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   "outputs": [],
   "source": [
    "sympy.pi"
   ]
  },
  {
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   "id": "e47dbf94-cea0-4f4e-b676-1d5f1f189565",
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   "source": [
    "x, y = sympy.symbols('x y')\n",
    "expr = x + 2*y\n",
    "expr"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "f2da8a0e-53d8-4839-813e-00373122bd31",
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   "source": [
    "expr-x  # sympy simplifies expressions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2492a0bb-2fc5-43ab-9846-53a60ab9b5a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "x*expr"
   ]
  },
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   "execution_count": null,
   "id": "aa1f4e0f-93d7-4972-a9d5-7b99e2b1cfb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "sympy.expand(x*expr)"
   ]
  },
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   "id": "4c55ebef-62d2-44cc-813b-2405d13c574a",
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   "source": [
    "# Differentiation\n",
    "sympy.diff(sympy.sin(x)*sympy.exp(x), x)"
   ]
  },
  {
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   "execution_count": null,
   "id": "c47d0b2c-5d77-47af-a66f-09190b1798f1",
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   "source": [
    "t=sympy.symbols('t')\n",
    "y = sympy.Function('y')\n",
    "sympy.dsolve(sympy.Eq(y(t).diff(t) , -y(t)), y(t) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5b2fb2d0-9ed4-412a-a011-fe7d9e142e91",
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b,c,d = sympy.symbols('a b c d')\n",
    "sympy.Matrix([[a, b], [c, d]]).eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9440438c-1531-4b6c-8fcc-f6d54f577a14",
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   "outputs": [],
   "source": [
    "sympy.Matrix([[a, b], [c, d]]).inv()"
   ]
  },
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   "execution_count": null,
   "id": "4cb78567-7c39-4cc1-bb60-ff4b5f64ea6d",
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   "outputs": [],
   "source": [
    "sympy.Matrix([[a, b], [c, d]]).det()"
   ]
  },
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   "source": [
    "a,b,c,d,e,f,g,h,i = sympy.symbols('a b c d e f g h i')"
   ]
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   "id": "1e40e39a-fa7b-425f-9a5d-32e4f790d182",
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   "outputs": [],
   "source": [
    "sympy.Matrix([[a, b, c], [d, e, f], [g, h,i ]]).det()"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "id": "b63d315a-14d9-42d6-b378-06a1df8009f6",
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   "source": [
    "sympy.Matrix([[a, b, c], [d, e, f], [g, h,i ]]).inv()"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "c60a106f-eabd-4847-adfb-107a68c95977",
   "metadata": {},
   "outputs": [],
   "source": [
    "sympy.Matrix([[a, b, c], [d, e, f], [g, h,i ]]).eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f215965-af4e-44f8-850a-510d72cc791b",
   "metadata": {},
   "outputs": [],
   "source": [
    "sympy.Matrix([[a, b, c], [d, e, f], [g, h,i ]]).eigenvects()"
   ]
  },
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