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fixed a few typos (#912)
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tutorials/optimization/1_quadratic_program.ipynb

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"metadata": {},
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"source": [
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"The `QuadraticProgram` supports three types of variables:\n",
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"- Binary varible\n",
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"- Binary variable\n",
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"- Integer variable\n",
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"- Continuous variable\n",
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"\n",
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"You can substitue some of variables with constants or other variables.\n",
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"You can substitute some of variables with constants or other variables.\n",
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"More precicely, `QuadraticProgram` has a method `substitute_variables(constants=..., variables=...)` to deal with the following two cases.\n",
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"- $x \\leftarrow c$: when `constants` have a dictionary `{x: c}`. \n",
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"- $x \\leftarrow c y$: when `variables` have a dictuinary `{x: (y, c)}`."
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"- $x \\leftarrow c y$: when `variables` have a dictionary `{x: (y, c)}`."
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]
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},
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{
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"metadata": {},
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"source": [
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"You cannot substitute variables multiple times. \n",
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"The metdod raises an error in such a case."
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"The method raises an error in such a case."
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]
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},
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{
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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": "3.7.4"
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"version": "3.7.7"
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}
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},
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"nbformat": 4,

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