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genkuroki/17_julia.ipynb

Created January 14, 2018 13:15
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17_julia.ipynb
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "Julia tranlation of https://gist.github.com/7shi/f951d88e31ad01bb2457e61bada8bdda"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "using SymPy",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@vars x",
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
"text/plain": "(x,)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t1=solve(x^2+x-4,x)",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/2 + sqrt(17)/2\n -sqrt(17)/2 - 1/2",
"text/latex": "\\begin{bmatrix}- \\frac{1}{2} + \\frac{\\sqrt{17}}{2}\\\\- \\frac{\\sqrt{17}}{2} - \\frac{1}{2}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t1",
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 4,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/2 + sqrt(17)/2\n -sqrt(17)/2 - 1/2",
"text/latex": "\\begin{bmatrix}- \\frac{1}{2} + \\frac{\\sqrt{17}}{2}\\\\- \\frac{\\sqrt{17}}{2} - \\frac{1}{2}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "a8_1,a8_3=t1",
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 5,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/2 + sqrt(17)/2\n -sqrt(17)/2 - 1/2",
"text/latex": "\\begin{bmatrix}- \\frac{1}{2} + \\frac{\\sqrt{17}}{2}\\\\- \\frac{\\sqrt{17}}{2} - \\frac{1}{2}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t2=solve(x^2-a8_1*x-1,x)",
"execution_count": 6,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 6,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/4 + sqrt(17)/4 + sqrt(-2*sqrt(17) + 34)/4\n -sqrt(-2*sqrt(17) + 34)/4 - 1/4 + sqrt(17)/4",
"text/latex": "\\begin{bmatrix}- \\frac{1}{4} + \\frac{\\sqrt{17}}{4} + \\frac{1}{4} \\sqrt{- 2 \\sqrt{17} + 34}\\\\- \\frac{1}{4} \\sqrt{- 2 \\sqrt{17} + 34} - \\frac{1}{4} + \\frac{\\sqrt{17}}{4}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t2",
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 7,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/4 + sqrt(17)/4 + sqrt(-2*sqrt(17) + 34)/4\n -sqrt(-2*sqrt(17) + 34)/4 - 1/4 + sqrt(17)/4",
"text/latex": "\\begin{bmatrix}- \\frac{1}{4} + \\frac{\\sqrt{17}}{4} + \\frac{1}{4} \\sqrt{- 2 \\sqrt{17} + 34}\\\\- \\frac{1}{4} \\sqrt{- 2 \\sqrt{17} + 34} - \\frac{1}{4} + \\frac{\\sqrt{17}}{4}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "a4_1,a4_9=t2",
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 8,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/4 + sqrt(17)/4 + sqrt(-2*sqrt(17) + 34)/4\n -sqrt(-2*sqrt(17) + 34)/4 - 1/4 + sqrt(17)/4",
"text/latex": "\\begin{bmatrix}- \\frac{1}{4} + \\frac{\\sqrt{17}}{4} + \\frac{1}{4} \\sqrt{- 2 \\sqrt{17} + 34}\\\\- \\frac{1}{4} \\sqrt{- 2 \\sqrt{17} + 34} - \\frac{1}{4} + \\frac{\\sqrt{17}}{4}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t3=solve(x^2-a8_3*x-1,x)",
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 9,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -sqrt(17)/4 - 1/4 + sqrt(2*sqrt(17) + 34)/4\n -sqrt(2*sqrt(17) + 34)/4 - sqrt(17)/4 - 1/4",
"text/latex": "\\begin{bmatrix}- \\frac{\\sqrt{17}}{4} - \\frac{1}{4} + \\frac{1}{4} \\sqrt{2 \\sqrt{17} + 34}\\\\- \\frac{1}{4} \\sqrt{2 \\sqrt{17} + 34} - \\frac{\\sqrt{17}}{4} - \\frac{1}{4}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t3",
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 10,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -sqrt(17)/4 - 1/4 + sqrt(2*sqrt(17) + 34)/4\n -sqrt(2*sqrt(17) + 34)/4 - sqrt(17)/4 - 1/4",
"text/latex": "\\begin{bmatrix}- \\frac{\\sqrt{17}}{4} - \\frac{1}{4} + \\frac{1}{4} \\sqrt{2 \\sqrt{17} + 34}\\\\- \\frac{1}{4} \\sqrt{2 \\sqrt{17} + 34} - \\frac{\\sqrt{17}}{4} - \\frac{1}{4}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "a4_3,a4_10=t3",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -sqrt(17)/4 - 1/4 + sqrt(2*sqrt(17) + 34)/4\n -sqrt(2*sqrt(17) + 34)/4 - sqrt(17)/4 - 1/4",
"text/latex": "\\begin{bmatrix}- \\frac{\\sqrt{17}}{4} - \\frac{1}{4} + \\frac{1}{4} \\sqrt{2 \\sqrt{17} + 34}\\\\- \\frac{1}{4} \\sqrt{2 \\sqrt{17} + 34} - \\frac{\\sqrt{17}}{4} - \\frac{1}{4}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t4=solve(x^2-a4_1*x+a4_3,x)",
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 12,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/8 + sqrt(17)/8 + sqrt(-2*sqrt(17) + 34)/8 + sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/8\n -sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/8 - 1/8 + sqrt(17)/8 + sqrt(-2*sqrt(17) + 34)/8",
"text/latex": "\\begin{bmatrix}- \\frac{1}{8} + \\frac{\\sqrt{17}}{8} + \\frac{1}{8} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{8} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68}\\\\- \\frac{1}{8} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} - \\frac{1}{8} + \\frac{\\sqrt{17}}{8} + \\frac{1}{8} \\sqrt{- 2 \\sqrt{17} + 34}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t4",
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 13,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/8 + sqrt(17)/8 + sqrt(-2*sqrt(17) + 34)/8 + sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/8\n -sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/8 - 1/8 + sqrt(17)/8 + sqrt(-2*sqrt(17) + 34)/8",
"text/latex": "\\begin{bmatrix}- \\frac{1}{8} + \\frac{\\sqrt{17}}{8} + \\frac{1}{8} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{8} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68}\\\\- \\frac{1}{8} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} - \\frac{1}{8} + \\frac{\\sqrt{17}}{8} + \\frac{1}{8} \\sqrt{- 2 \\sqrt{17} + 34}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "a2_1,a2_13=t4",
"execution_count": 14,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 14,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/8 + sqrt(17)/8 + sqrt(-2*sqrt(17) + 34)/8 + sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/8\n -sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/8 - 1/8 + sqrt(17)/8 + sqrt(-2*sqrt(17) + 34)/8",
"text/latex": "\\begin{bmatrix}- \\frac{1}{8} + \\frac{\\sqrt{17}}{8} + \\frac{1}{8} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{8} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68}\\\\- \\frac{1}{8} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} - \\frac{1}{8} + \\frac{\\sqrt{17}}{8} + \\frac{1}{8} \\sqrt{- 2 \\sqrt{17} + 34}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t5=solve(x^2-a2_1*x+1,x)",
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 15,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/16 + sqrt(17)/16 + sqrt(-2*sqrt(17) + 34)/16 + sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/16 - sqrt(-136 - 16*sqrt(2)*sqrt(sqrt(17) + 17) - 4*sqrt(2)*sqrt(-sqrt(17) + 17) - 2*sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 8*sqrt(17) + 2*sqrt(34)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(-sqrt(17) + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(34)*sqrt(-sqrt(17) + 17))/16\n -1/16 + sqrt(17)/16 + sqrt(-2*sqrt(17) + 34)/16 + sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/16 + sqrt(-136 - 16*sqrt(2)*sqrt(sqrt(17) + 17) - 4*sqrt(2)*sqrt(-sqrt(17) + 17) - 2*sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 8*sqrt(17) + 2*sqrt(34)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(-sqrt(17) + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(34)*sqrt(-sqrt(17) + 17))/16",
"text/latex": "\\begin{bmatrix}- \\frac{1}{16} + \\frac{\\sqrt{17}}{16} + \\frac{1}{16} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{16} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} - \\frac{1}{16} \\sqrt{-136 - 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 4 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 8 \\sqrt{17} + 2 \\sqrt{34} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{- \\sqrt{17} + 17} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17}}\\\\- \\frac{1}{16} + \\frac{\\sqrt{17}}{16} + \\frac{1}{16} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{16} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} + \\frac{1}{16} \\sqrt{-136 - 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 4 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 8 \\sqrt{17} + 2 \\sqrt{34} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{- \\sqrt{17} + 17} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17}}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t5[1][:evalf](),t5[2][:evalf]()",
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 16,
"data": {
"text/plain": "(0.932472229404356 - 0.361241666187153*I, 0.932472229404356 + 0.361241666187153*I)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "r16,r1=t5",
"execution_count": 17,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 17,
"data": {
"text/plain": "2-element Array{SymPy.Sym,1}:\n -1/16 + sqrt(17)/16 + sqrt(-2*sqrt(17) + 34)/16 + sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/16 - sqrt(-136 - 16*sqrt(2)*sqrt(sqrt(17) + 17) - 4*sqrt(2)*sqrt(-sqrt(17) + 17) - 2*sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 8*sqrt(17) + 2*sqrt(34)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(-sqrt(17) + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(34)*sqrt(-sqrt(17) + 17))/16\n -1/16 + sqrt(17)/16 + sqrt(-2*sqrt(17) + 34)/16 + sqrt(-16*sqrt(2)*sqrt(sqrt(17) + 17) - 2*sqrt(2)*sqrt(-sqrt(17) + 17) + 2*sqrt(34)*sqrt(-sqrt(17) + 17) + 12*sqrt(17) + 68)/16 + sqrt(-136 - 16*sqrt(2)*sqrt(sqrt(17) + 17) - 4*sqrt(2)*sqrt(-sqrt(17) + 17) - 2*sqrt(2)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 8*sqrt(17) + 2*sqrt(34)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(-sqrt(17) + 17)*sqrt(-8*sqrt(2)*sqrt(sqrt(17) + 17) - sqrt(2)*sqrt(-sqrt(17) + 17) + sqrt(34)*sqrt(-sqrt(17) + 17) + 6*sqrt(17) + 34) + 4*sqrt(34)*sqrt(-sqrt(17) + 17))/16",
"text/latex": "\\begin{bmatrix}- \\frac{1}{16} + \\frac{\\sqrt{17}}{16} + \\frac{1}{16} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{16} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} - \\frac{1}{16} \\sqrt{-136 - 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 4 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 8 \\sqrt{17} + 2 \\sqrt{34} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{- \\sqrt{17} + 17} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17}}\\\\- \\frac{1}{16} + \\frac{\\sqrt{17}}{16} + \\frac{1}{16} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{16} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} + \\frac{1}{16} \\sqrt{-136 - 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 4 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 8 \\sqrt{17} + 2 \\sqrt{34} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{- \\sqrt{17} + 17} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17}}\\end{bmatrix}"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "f(n) = exp(2π*im*n/17)",
"execution_count": 18,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 18,
"data": {
"text/plain": "f (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "f(16),f(1)",
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 19,
"data": {
"text/plain": "(0.9324722294043558 - 0.36124166618715303im, 0.9324722294043558 + 0.3612416661871529im)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "r1",
"execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 20,
"data": {
"text/plain": " \n ___________________________________\n _________________ / _____________ \n ____ / ____ / ___ / ____ \n 1 \\/ 17 \\/ - 2*\\/ 17 + 34 \\/ - 16*\\/ 2 *\\/ \\/ 17 + 17 - 2*\\/\n- -- + ------ + -------------------- + ---------------------------------------\n 16 16 16 \n\n \n______________________________________________________________________ /\n _______________ _______________ / \n___ / ____ ____ / ____ ____ / \n 2 *\\/ - \\/ 17 + 17 + 2*\\/ 34 *\\/ - \\/ 17 + 17 + 12*\\/ 17 + 68 \\/ \n---------------------------------------------------------------------- + -----\n 16 \n\n______________________________________________________________________________\n _\n _____________ _______________ / \n ___ / ____ ___ / ____ ___ / \n -136 - 16*\\/ 2 *\\/ \\/ 17 + 17 - 4*\\/ 2 *\\/ - \\/ 17 + 17 - 2*\\/ 2 *\\/ \n------------------------------------------------------------------------------\n \n\n______________________________________________________________________________\n______________________________________________________________________________\n _____________ _______________ ____________\n ___ / ____ ___ / ____ ____ / ____ \n- 8*\\/ 2 *\\/ \\/ 17 + 17 - \\/ 2 *\\/ - \\/ 17 + 17 + \\/ 34 *\\/ - \\/ 17 + \n------------------------------------------------------------------------------\n \n\n______________________________________________________________________________\n____________________ _______________________________\n___ / _____________ \n ____ ____ ____ / ___ / ____ \n17 + 6*\\/ 17 + 34 + 8*\\/ 17 + 2*\\/ 34 *\\/ - 8*\\/ 2 *\\/ \\/ 17 + 17 - \\\n------------------------------------------------------------------------------\n 16 \n\n______________________________________________________________________________\n____________________________________________________________________ \n _______________ _______________ __\n ___ / ____ ____ / ____ ____ / \n/ 2 *\\/ - \\/ 17 + 17 + \\/ 34 *\\/ - \\/ 17 + 17 + 6*\\/ 17 + 34 + 4*\\/ -\n------------------------------------------------------------------------------\n \n\n______________________________________________________________________________\n ____________________________________________________________\n_____________ / _____________ _______________ \n ____ / ___ / ____ ___ / ____ _\n \\/ 17 + 17 *\\/ - 8*\\/ 2 *\\/ \\/ 17 + 17 - \\/ 2 *\\/ - \\/ 17 + 17 + \\/ \n------------------------------------------------------------------------------\n \n\n______________________________________________________________________\n_______________________________________ \n _______________ _______________ \n___ / ____ ____ ____ / ____ \n34 *\\/ - \\/ 17 + 17 + 6*\\/ 17 + 34 + 4*\\/ 34 *\\/ - \\/ 17 + 17 \n----------------------------------------------------------------------\n ",
"text/latex": "$$- \\frac{1}{16} + \\frac{\\sqrt{17}}{16} + \\frac{1}{16} \\sqrt{- 2 \\sqrt{17} + 34} + \\frac{1}{16} \\sqrt{- 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + 2 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 12 \\sqrt{17} + 68} + \\frac{1}{16} \\sqrt{-136 - 16 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - 4 \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} - 2 \\sqrt{2} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 8 \\sqrt{17} + 2 \\sqrt{34} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{- \\sqrt{17} + 17} \\sqrt{- 8 \\sqrt{2} \\sqrt{\\sqrt{17} + 17} - \\sqrt{2} \\sqrt{- \\sqrt{17} + 17} + \\sqrt{34} \\sqrt{- \\sqrt{17} + 17} + 6 \\sqrt{17} + 34} + 4 \\sqrt{34} \\sqrt{- \\sqrt{17} + 17}}$$"
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