## plot – flow on the circle

I'm trying to draw a vector field on a circle, especially the vector field in this plot:

VectorPlot[{(Sin[x]) ^ 3, 0}, {x, 0, 2 [Pi]}, {y, -0.001, 0.001},
FrameTicks -> {{[Pi]/ 2, [Pi], 3 [Pi]/ 2, 2 [Pi]}, {-1, 1}},
Epilog ->

Ground[(Sin[x]) ^ 3, {x, 0, 2 [Pi]}, PlotStyle -> Red,
Ticks -> None][[1]], PlotRange -> {{0, 2 [Pi]}, {-1, 1}},
GridLines -> Automatic
]


It was my way of drawing a vector field on the line. But I want to draw this one-dimensional on a circle.

## calculation and analysis – How to find and plot the intersection of these three surfaces?

I know how to find the intersection region of these cylinders using integration, but how could I plot this in mathematica? That's what I've

ContourPlot3D[{x^2 + y^2 == 1, x^2 + z^2 == 1,
y^2 + z^2 == 1}, {x, -3, 3}, {y, -3, 3}, {z, -3, 3},
AxesLabel -> Automatic, PlotLegends -> "Expressions"]


## Plot with a different color for a single curve

How to draw a function $$f (x) = frac {3 (4 + x)} {3 (2-x) -16}$$ (say $$x in [-15,15]$$ ) on the condition that I want to give a different color for each of the following cases

(i) when $$frac {x + 4} {3x + 10}> 0$$ and $$frac {x ^ 2 + 8x + 12} {3x + 10}> 0$$

(ii) when $$frac {x + 4} {3x + 10}> 0$$ and $$frac {x ^ 2 + 8x + 12} {3x + 10} <0$$

(iii) when $$frac {x + 4} {3x + 10} <0$$ and $$frac {x ^ 2 + 8x + 12} {3x + 10}> 0$$

## Plot of the numerical integration of several variables

I'm trying to plot a multivariate integral. But in a way, it does not work. This is my code.

a = 5;
b = 0.1;
f = (1 + Exp[(k - a)])
B = f * (1 / (z - (q ^ 2 + k * q * x) + I * b) +
1 / (z - (q ^ 2 - k * q * x) + I * b));
ListContourPlot[
NIntegrate[Re[B], {x, -1, 1}, {k, -a, a}], {z, 0, 5,
1}, {q, 0, 5, 1}]


I will be more interested in keeping the size of the z and q steps fixed. Any help will be greatly appreciated

## Automatic manipulation of experimental data and plot

I have experimental data that looks like this

In the regions of the x positive and negative high, my data is always linear. I want to extract the slope of the data in these regions, take an average and subtract this linear slope from these experimental data.

BMoment = {-0.0000331, -0.0000354, -0.0000334, -0.0000315, -0.0000291,
-0.0000269, -0.0000251, -0.0000234, -0.0000211, -0.0000189,
-0.0000173, -0.0000152, -0.0000131, -0.0000114, -9.51 * 10 ^ -6,
-9.51 * 10 ^ -6, -5.75 * 10 ^ -6, -3.96 * 10 ^ -6, -2.5 * 10 ^ -6, -6.15 * 10 ^ -7,
1.29 * 10 -6, 3.28 * 10 -6, 4.95 * 10 -6, 6.9 * 10 -6,
8.81 * 10 ^ -6, 0.0000107, 0.000012, 0.0000139, 0.0000156, 0.0000172,
0.0000186, 0.0000199, 0.0000214, 0.0000229, 0.000024, 0.0000259,
0.0000271, 0.0000284, 0.0000294, 0.0000302, 0.0000314, 0.0000322,
0.0000331, 0.0000334, 0.0000332, 0.0000331, 0.0000321, 0.0000303,
0.0000276, "",
7.27 * 10 ^ -6, -8.61 * 10 ^ -6, -0.000013, -0.0000166, -0.0000189,
-0.0000208, -0.0000221, -0.0000229, -0.0000236, -0.0000241,
-0.0000242, -0.0000242, "", -0.0000238, -0.0000224, -0.0000214,
-0.0000205, -0.0000192, -0.000018, -0.0000168, -0.0000154,
-0.0000137, -0.0000125, -0.0000109, -9.51 * 10 ^ -6, -7.62 * 10 ^ -6,
-6.17 * 10 ^ -6, -4.43 * 10 ^ -6, -2.91 * 10 ^ -6, -1.1 * 10 ^ -6, 4.78 * 10 ^ -7,
2.29 * 10 -6, 3.93 * 10 -6, 5.83 * 10 -6, 7.16 * 10 -6,
9.76 * 10 ^ -6, 0.0000116, 0.0000132, 0.0000152, "0.0000198,
0.0000236, 0.0000257, 0.0000273, 0.0000287, 0.0000303, 0.0000294,
0.0000278, 0.0000257, 0.0000239, 0.0000223, 0.00002, 0.0000184,
0.0000163, 0.0000147, 0.0000129, 0.0000111, 9.1 * 10 ^ -6, 7.39 * 10 ^ -6,
5.42 * 10 ^ -6, 3.53 * 10 ^ -6, 2.1 * 10 ^ -6,
6,21 * 10 ^ -7, -1,29 * 10 ^ -6, -2,77 * 10 ^ -6, -3,92 * 10 ^ -6, -6,09 * 10 ^ -6,
-7.55 * 10 ^ -6, -7.55 * 10 ^ -6, -0.0000111, -0.0000127, -0.0000146,
-0.000016, -0.0000176, -0.0000193, -0.0000208, -0.0000223,
-0.0000237, -0.0000252, -0.0000262, -0.0000262, -0.0000295,
-0.0000305, -0.0000314, -0.0000327, -0.0000334, -0.0000344,
-0.0000347, -0.0000353, -0.0000351, -0.0000349, -0.0000342,
-0.0000326, "", -0.0000197, 5.36 * 10 ^ -7,
7.15 * 10 ^ -6, 0.0000117, 0.0000154, 0.0000177, 0.0000192, 0.0000209,
0.0000214, 0.0000221, 0.0000225, 0.0000225, "", 0.0000229, 0.0000216,
0.0000202, 0.0000194, 0.0000181, 0.0000171, 0.0000164, 0.000015,
0.0000133, 0.0000122, 0.0000103, "", 5.69 * 10 ^ -6,
2.4 * 10 ^ -6, -7.92 * 10 ^ -7, -2.57 * 10 ^ -6, -3.8 * 10 ^ -6, -5.73 * 10 ^ -6,
-7.57 * 10 ^ -6, -9.38 * 10 ^ -6, -0.0000111, -0.0000132, -0.0000148,
-0.0000169, -0.0000183, -0.0000202, -0.0000218, -0.0000237,
-0.0000253, -0.000027, -0.0000284, -0.0000306, -0.0000317};

BField = {"ï" 10000.39258 ", 9926.71, 9753.31, 9553.6, 9353.67, 9153.66,
8953.65, 8753.5, 8553.29, 8353.13, 8153.14, 7953.13, 7752.97,
7552.86, 7353.25, 7153.36, 6953.29, 6753.62, 6553.47, 6353.31,
6153.6, 5953.9, 5753.44, 5552.94, 5353.2, 5153.07, 4953.16, 4753.47,
4553.01, 4353.3, 4153.54, 3953.03, 3752.89, 3552.98, 3353.06,
3152.92, 2952.87, 2752.98, 2553.19, 2353.5, 2153.44, 1952.88,
1752.74, 1552.62, 1352.12, 1152.4, 952.428, 752.302, 552.574, 352.34,
-151,947, -556,781, -652,343, -847,615, -1047,75, -1247,28, -1447,3,
-1647.63, -1847.38, -2047.14, -2247.47, -2447.92, -2647.83, -3154.02,
-3559.45, -3653.04, -3846.57, -4047.03, -4247.54, -4446.88, -4646.19,
-4846.62, -5047.05, -5247.21, -5447.34, -5647.21, -5847.3, -6047.42,
-6247.12, -6446.82, -6646.87, -6846.88, -7046.54, -7246.27, -7446.34,
-7646.43, -7846.78, -8046.89, -8246.18, -8446.21, -8951.32, -9356.78,
-9451.92, -9647.21, -9846.9, -9973.31, -9926.79, -9753.78, -9554.16,
-9354.13, -9154.55, -8954.45, -8753.93, -8554.08, -8354.06, -8153.96,
-7954.24, -7754.61, -7554.58, -7354.49, -7154.46, -6954.43, -6754.8,
-6555.13, -6354.76, -6154.64, -5955.32, -5755.24, -5554.82, -5354.72,
-5154.56, -4954.41, -4754.38, -4554.55, -4354.45, -4154.76, -3954.64,
-3754.54, -3555.01, -3355.44, -3155.4, -2954.92, -2755.14, -2555.44,
-2355.56, -2155.53, -1955.45, -1755.26, -1555.16, -1355.13, -1155.11,
-954.979, -755.29, -555.501, -51.2047, 353.059, 449.119, 645.156,
844,884, 1044.6, 1245.1, 1445.18, 1644.92, 1845.08, 2045.35, 2245.77,
2443.42, 2949.21, 3354.2, 3449.83, 3645.43, 3845.47, 4045.53, 4245.5,
4445.27, 4644.96, 4845.01, 5045.58, 5245.87, 5750.52, 6154.81,
6350.27, 6645.9, 6846.01, 7045.71, 7245.51, 7445.61, 7645.62,
7845.34, 8045.41, 8245.76, 8445.88, 8645.97, 8845.68, 9045.82,
9246.4, 9446.06, 9645.72, 9845.93, 9973.12};

datalist300K = Transpose @ {BField, BMoment};
p1 = ListLinePlot[datalist300K, PlotStyle -> {Blue}];
BMomentDia = (-7.61 * 10 ^ -9) * BField; (* I found the slope in Excel and I put it here, but I want to automatically find the slope *)
data2 = Transpose @ {BField, BMomentDia};
p2 = ListLinePlot[data2, PlotStyle -> {Dashed, Black}];
BMomentProcessed = BMoment - BMomentDia;
data3 = Transpose @ {BField, BMomentProcessed};
p3 = ListLinePlot[data3,  PlotStyle -> Red, Frame -> True,
FrameTicks -> True, Joined -> True,
FrameLabel -> {"Magnetic Field(Oe)", "Magnetization(emu)"},
PlotRange -> {{-10000, 10000}, Automatic}, PlotStyle -> Thick,
BaseStyle -> {FontSize -> 15}, AspectRatio -> 3/5, Mesh -> {{0}},
MeshFunctions -> {#2 &},
MeshStyle -> Directive[Black, PointSize[.02]]]



Finally, the curve drawn should look like the one in red, but I also want to extrapolate the missing points between the two. How to proceed?

## plot – Möbius band in mathematica

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## plot – problem with old commands in maths

I'm trying to follow an example in an old book about this software, but it's impossible, because it uses old commands. it's very frustrating.

That's the example

it's the code:

monopolo[q_: 1, r0_: {0, 0, 0}, r_: {x, y, x}] : = q / Sqrt[Sum[(r0[[i]]- r[[i]]) ^ 2, {i, 1, length[r0]}]]


square quadrapole:

square = (Monopolo[+q, {d/2, 0, d/2}] + Monopolo[-q, {d/2, 0, -d/2}] + Monopolo[+q, {-d/2, 0, -d/2}] + Monopolo[-q, {-d/2, 0, d/2}])


I need to represent this:

I had this:

and also graphic this: VEPlot I do not know was he is …

It seems very simple to follow,
but it does not work for me.
Thanks in advance 🙂

## plot – Can not trace function

I have a function P that depends on x, I've tried to plot the function but I do not get anything in the plot. I am also interested in finding the roots of the equation.
P = 2.686350117820842 * 10 ^ 2406 – 3.509147003769840 * 10 ^ 2403 x ^ 2 +
2.232334766012457 * 10 ^ 2400 x ^ 4 – 9.23321306009387 * 10 ^ 2396 x ^ 6 +
2.797063590071589 * 10 ^ 2393 x ^ 8 – 6.628019419459146 * 10 ^ 2389 x ^ 10 +
1.281285155718557 * 10 ^ 2386 x ^ 12 – 2.080706919967667 * 10 ^ 2382 x ^ 14 +
2.900600749513771 * 10 ^ 2378 x ^ 16 – 3.529683274215479 * 10 ^ 2374 x ^ 18 +
3.799572525545543 * 10 ^ 2370 x ^ 20 – 3.657654959609442 * 10 ^ 2366 x ^ 22 +
3.177358914380688 * 10 ^ 2362 x ^ 24 – 2.509839111095646 * 10 ^ 2358 x ^ 26 +
1.814625240727776 * 10 ^ 2354 x ^ 28 – 1.207688796217551 * 10 ^ 2350 x ^ 30 +
7.435446299837606 * 10 ^ 2345 x ^ 32 – 4.253490093370832 * 10 ^ 2341 x ^ 34 +
2.269657765882891 * 10 ^ 2337 x ^ 36 – 1.133608420161897 * 10 ^ 2333 x ^ 38 +
5.316334073138192 * 10 ^ 2328 x ^ 40 – 2.347664003997277 * 10 ^ 2324 x ^ 42 +
9.78698498875831 * 10 ^ 2319 x ^ 44 – 3.860713086508757 * 10 ^ 2315 x ^ 46 +
1.444181525125296 * 10 ^ 2311 x ^ 48 – 5.132934302120220 * 10 ^ 2306 x ^ 50 +
1.736544827340320 * 10 ^ 2302 x ^ 52 – 5.601566614600686 * 10 ^ 2297 x ^ 54 +
1.725478614191356 * 10 ^ 2293 x ^ 56 – 5.082900519602480 * 10 ^ 2288 x ^ 58 +
1.433830406931773 * 10 ^ 2284 x ^ 60 – 3.878031085948603 * 10 ^ 2279 x ^ 62 +
1,006838752933342 * 10 ^ 2275 x ^ 64 – 2.511998423431655 * 10 ^ 2270 x ^ 66 +
6.028870570737217 * 10 ^ 2265 x ^ 68 – 1.393250733667592 * 10 ^ 2261 x ^ 70 +
3.103089714603463 * 10 ^ 2256 x ^ 72 – 6.666587245054238 * 10 ^ 2251 x ^ 74 +
1.382638575445950 * 10 ^ 2247 x ^ 76 – 2.770397956252858 * 10 ^ 2242 x ^ 78 +
5.366842280628789 * 10 ^ 2237 x ^ 80 – 1,005858930607984 * 10 ^ 2233 x ^ 82 +
1.825072143393833 * 10 ^ 2228 x ^ 84 – 3.207869510983551 * 10 ^ 2223 x ^ 86 +
5.465159420757082 * 10 ^ 2218 x ^ 88 – 9,02987914428045 * 10 ^ 2213 x ^ 90 +
1.447724685668347 * 10 ^ 2209 x ^ 92 – 2,253389040532460 * 10 ^ 2204 x ^ 94 +
3.406776673880169 * 10 ^ 2199 x ^ 96 – 5.005069504865876 * 10 ^ 2194 x ^ 98 +
7.148720260786071 * 10 ^ 2189 x ^ 100 – 9.93076381228350 * 10 ^ 2184 x ^ 102 +
1.342300350538044 * 10 ^ 2180 x ^ 104 –
1.766031989976773 * 10 ^ 2175 x ^ 106 +
2.262514329562340 * 10 ^ 2170 x ^ 108 –
2.823472028631675 * 10 ^ 2165 x ^ 110 +
3.433398530687380 * 10 ^ 2160 x ^ 112 –
4.069647349352201 * 10 ^ 2155 x ^ 114 +
4.703474536791501 * 10 ^ 2150 x ^ 116 –
5.302034601457534 * 10 ^ 2145 x ^ 118 +
5.831164114332556 * 10 ^ 2140 x ^ 120 –
6.258630293213825 * 10 ^ 2135 x ^ 122 +
6.557411618941536 * 10 ^ 2130 x ^ 124 –
6.708541700709386 * 10 ^ 2125 x ^ 126 +
6.703098152426357 * 10 ^ 2120 x ^ 128 –
6.543047641701977 * 10 ^ 2115 x ^ 130 +
6.240840903503749 * 10 ^ 2110 x ^ 132 –
5.817849945123738 * 10 ^ 2105 x ^ 134 +
5.301914007185092 * 10 ^ 2100 x ^ 136 –
4.724378349510931 * 10 ^ 2095 x ^ 138 +
4.117052274652728 * 10 ^ 2090 x ^ 140 –
3.509479115559841 * 10 ^ 2085 x ^ 142 +
2.926816185721846 * 10 ^ 2080 x ^ 144 –
2.388492465214735 * 10 ^ 2075 x ^ 146 +
1.907675036517837 * 10 ^ 2070 x ^ 148 –
1.491457505406822 * 10 ^ 2065 x ^ 150 +
1.141602028087492 * 10 ^ 2060 x ^ 152 –
8.556279254594532 * 10 ^ 2054 x ^ 154 +
6.280413776807839 * 10 ^ 2049 x ^ 156 –
4.515326540439904 * 10 ^ 2044 x ^ 158 +
3.180167907726034 * 10 ^ 2039 x ^ 160 –
2.194478115710771 * 10 ^ 2034 x ^ 162 +
1.483853865742252 * 10 ^ 2029 x ^ 164 – 9.83300223305664 * 10 ^ 2023 x ^ 166 +
6,386617152824788 * 10 ^ 2018 x ^ 168 –
4.066288654597450 * 10 ^ 2013 x ^ 170 +
2.538161330896050 * 10 ^ 2008 x ^ 172 –
1.553400356631517 * 10 ^ 2003 x ^ 174 + 9.32263314135091 * 10 ^ 1997 x ^ 176 –
5.486951378176007 * 10 ^ 1992 x ^ 178 +
3.167420751645592 * 10 ^ 1987 x ^ 180 –
1.793518595659501 * 10 ^ 1982 x ^ 182 + 9.96261698489905 * 10 ^ 1976 x ^ 184 –
5.429364360014730 * 10 ^ 1971 x ^ 186 +
2.903165552666326 * 10 ^ 1966 x ^ 188 –
1,523280393092388 * 10 ^ 1961 x ^ 190 +
7.843499419670845 * 10 ^ 1955 x ^ 192 –
3.963668964374835 * 10 ^ 1950 x ^ 194 +
1.965969276987846 * 10 ^ 1945 x ^ 196 – 9.57152492960029 * 10 ^ 1939 x ^ 198 +
4.574490289152389 * 10 ^ 1934 x ^ 200 –
2.146310190307600 * 10 ^ 1929 x ^ 202 + 9.88690722332728 * 10 ^ 1923 x ^ 204 –
4.471730279011893 * 10 ^ 1918 x ^ 206 +
1.985938984779357 * 10 ^ 1913 x ^ 208 –
8.660807588686577 * 10 ^ 1907 x ^ 210 +
3.709190693138281 * 10 ^ 1902 x ^ 212 –
1.560103455468367 * 10 ^ 1897 x ^ 214 +
6.444739988049591 * 10 ^ 1891 x ^ 216 –
2.614921174621156 * 10 ^ 1886 x ^ 218 +
1,042162872740786 * 10 ^ 1881 x ^ 220 –
4.079981202301375 * 10 ^ 1875 x ^ 222 +
1.569087899814386 * 10 ^ 1870 x ^ 224 –
5.928203849050795 * 10 ^ 1864 x ^ 226 +
2.200417896059673 * 10 ^ 1859 x ^ 228 –
8,024391148585218 * 10 ^ 1853 x ^ 230 +
2.875159025345020 * 10 ^ 1848 x ^ 232 –
1.012212697232504 * 10 ^ 1843 x ^ 234 +
3.501534455222515 * 10 ^ 1837 x ^ 236 –
1.190248525711444 * 10 ^ 1832 x ^ 238 +
3.975802300137773 * 10 ^ 1826 x ^ 240 –
1.305071797366944 * 10 ^ 1821 x ^ 242 +
4.209984664855359 * 10 ^ 1815 x ^ 244 –
1.334677953421113 * 10 ^ 1810 x ^ 246 +
4.158484665287774 * 10 ^ 1804 x ^ 248 –
1.273410903504800 * 10 ^ 1799 x ^ 250 +
3.832555857332483 * 10 ^ 1793 x ^ 252 –
1.133720397800658 * 10 ^ 1788 x ^ 254 +
3.296336124395826 * 10 ^ 1782 x ^ 256 – 9.42052424742060 * 10 ^ 1776 x ^ 258 +
2.646343249978066 * 10 ^ 1771 x ^ 260 –
7.307246483464030 * 10 ^ 1765 x ^ 262 +
1.983381588790684 * 10 ^ 1760 x ^ 264 –
5.291900946277332 * 10 ^ 1754 x ^ 266 +
1.387961871579574 * 10 ^ 1749 x ^ 268 –
3.578580485948212 * 10 ^ 1743 x ^ 270 + 9.07022441316217 * 10 ^ 1737 x ^ 272 –
2,259984088022122 * 10 ^ 1732 x ^ 274 +
5.535776061884918 * 10 ^ 1726 x ^ 276 –
1.333038444619680 * 10 ^ 1721 x ^ 278 +
3.155750717810446 * 10 ^ 1715 x ^ 280 –
7.344512424651015 * 10 ^ 1709 x ^ 282 +
1.680457453641542 * 10 ^ 1704 x ^ 284 –
3.780070966485888 * 10 ^ 1698 x ^ 286 +
8.359561279291154 * 10 ^ 1692 x ^ 288 –
1.817527358656161 * 10 ^ 1687 x ^ 290 +
3.885034062551937 * 10 ^ 1681 x ^ 292 –
8.164455093279046 * 10 ^ 1675 x ^ 294 +
1.686863009334956 * 10 ^ 1670 x ^ 296 –
3.426526103596986 * 10 ^ 1664 x ^ 298 +
6.843069177401753 * 10 ^ 1658 x ^ 300 –
1.343603626786899 * 10 ^ 1653 x ^ 302 +
2.593672378394226 * 10 ^ 1647 x ^ 304 –
4.922466977085678 * 10 ^ 1641 x ^ 306 + 9.18489000822497 * 10 ^ 1635 x ^ 308 –
1.684953634573095 * 10 ^ 1630 x ^ 310 +
3.038952248333740 * 10 ^ 1624 x ^ 312 –
5.388656454536683 * 10 ^ 1618 x ^ 314 + 9.39412399337185 * 10 ^ 1612 x ^ 316 –
1.610087299983996 * 10 ^ 1607 x ^ 318 +
2.713049933388496 * 10 ^ 1601 x ^ 320 –
4.494475002293981 * 10 ^ 1595 x ^ 322 +
7.319986511537511 * 10 ^ 1589 x ^ 324 –
1.172057048939555 * 10 ^ 1584 x ^ 326 +
1.844977753834419 * 10 ^ 1578 x ^ 328 –
2.855182746212618 * 10 ^ 1572 x ^ 330 +
4.343834731262068 * 10 ^ 1566 x ^ 332 –
6.496885750019254 * 10 ^ 1560 x ^ 334 + 9.55268382834428 * 10 ^ 1554 x ^ 336 –
1.380795113437095 * 10 ^ 1549 x ^ 338 +
1.962058315283751 * 10 ^ 1543 x ^ 340 –
2.740743088982950 * 10 ^ 1537 x ^ 342 +
3,763510693306638 * 10 ^ 1531 x ^ 344 –
5.080199940292004 * 10 ^ 1525 x ^ 346 +
6.741017374907996 * 10 ^ 1519 x ^ 348 –
8.792674582153970 * 10 ^ 1513 x ^ 350 +
1.127356164004770 * 10 ^ 1508 x ^ 352 –
1.420820821885134 * 10 ^ 1502 x ^ 354 +
1.760146039983033 * 10 ^ 1496 x ^ 356 –
2.143296569804627 * 10 ^ 1490 x ^ 358 +
2.565267907439039 * 10 ^ 1484 x ^ 360 –
3.017814628293543 * 10 ^ 1478 x ^ 362 +
3.489426100729698 * 10 ^ 1472 x ^ 364 –
3.965601509627411 * 10 ^ 1466 x ^ 366 +
4.429447174196560 * 10 ^ 1460 x ^ 368 –
4.862581625296601 * 10 ^ 1454 x ^ 370 +
5.246292521230257 * 10 ^ 1448 x ^ 372 –
5.562850387720804 * 10 ^ 1442 x ^ 374 +
5.796853983427411 * 10 ^ 1436 x ^ 376 –
5.936466649461109 * 10 ^ 1430 x ^ 378 +
5.974406125055940 * 10 ^ 1424 x ^ 380 –
5.908572891940683 * 10 ^ 1418 x ^ 382 +
5.742241709894746 * 10 ^ 1412 x ^ 384 –
5.483792133412483 * 10 ^ 1406 x ^ 386 +
5.146008822434077 * 10 ^ 1400 x ^ 388 –
4.745032987972388 * 10 ^ 1394 x ^ 390 +
4.299084750681276 * 10 ^ 1388 x ^ 392 –
3.827097125901663 * 10 ^ 1382 x ^ 394 +
3.347403481153394 * 10 ^ 1376 x ^ 396 –
2.876602725419878 * 10 ^ 1370 x ^ 398 +
2.428694249104125 * 10 ^ 1364 x ^ 400 –
2.014533828230008 * 10 ^ 1358 x ^ 402 +
1.641619181562812 * 10 ^ 1352 x ^ 404 –
1.314175940961979 * 10 ^ 1346 x ^ 406 +
1.033486214800720 * 10 ^ 1340 x ^ 408 –
7.983852739018635 * 10 ^ 1333 x ^ 410 +
6.058474727899986 * 10 ^ 1327 x ^ 412 –
4.515886933994255 * 10 ^ 1321 x ^ 414 +
3.306264081366439 * 10 ^ 1315 x ^ 416 –
2.377563904131392 * 10 ^ 1309 x ^ 418 +
1.679237839489421 * 10 ^ 1303 x ^ 420 –
1.164829767485104 * 10 ^ 1297 x ^ 422 +
7.935376392911023 * 10 ^ 1290 x ^ 424 –
5.308987593571449 * 10 ^ 1284 x ^ 426 +
3.488020119181430 * 10 ^ 1278 x ^ 428 –
2.250365276668083 * 10 ^ 1272 x ^ 430 +
1.425663994840285 * 10 ^ 1266 x ^ 432 –
8.868588727457016 * 10 ^ 1259 x ^ 434 +
5.416861600574322 * 10 ^ 1253 x ^ 436 –
3,248472892534088 * 10 ^ 1247 x ^ 438 +
1.912630590577480 * 10 ^ 1241 x ^ 440 –
1.105566862790935 * 10 ^ 1235 x ^ 442 +
6.273680133767686 * 10 ^ 1228 x ^ 444 –
3.494815112791049 * 10 ^ 1222 x ^ 446 +
1.911046205638163 * 10 ^ 1216 x ^ 448 –
1,025754985147126 * 10 ^ 1210 x ^ 450 +
5.404076674469516 * 10 ^ 1203 x ^ 452 –
2.794372932035669 * 10 ^ 1197 x ^ 454 +
1.418114933715901 * 10 ^ 1191 x ^ 456 –
7.062874953045376 * 10 ^ 1184 x ^ 458 +
3.452018055249632 * 10 ^ 1178 x ^ 460 –
1.655633070050951 * 10 ^ 1172 x ^ 462 +
7,791700607210830 * 10 ^ 1165 x ^ 464 –
3.597947165977340 * 10 ^ 1159 x ^ 466 +
1.630078374010770 * 10 ^ 1153 x ^ 468 –
7.245523475293265 * 10 ^ 1146 x ^ 470 +
3.159472661882223 * 10 ^ 1140 x ^ 472 –
1,351507717181499 * 10 ^ 1134 x ^ 474 +
5.670960942548448 * 10 ^ 1127 x ^ 476 –
2.334014989068994 * 10 ^ 1121 x ^ 478 + 9.42179591677835 * 10 ^ 1114 x ^ 480 –
3.730100770024781 * 10 ^ 1108 x ^ 482 +
1.448230016133533 * 10 ^ 1102 x ^ 484 –
5.513881785888662 * 10 ^ 1095 x ^ 486 +
2.058508315152457 * 10 ^ 1089 x ^ 488 –
7.535202490236606 * 10 ^ 1082 x ^ 490 +
2.704305337139761 * 10 ^ 1076 x ^ 492 – 9.51493645106292 * 10 ^ 1069 x ^ 494 +
3.281827862724674 * 10 ^ 1063 x ^ 496 –
1.109571526718667 * 10 ^ 1057 x ^ 498 +
3.677001052421732 * 10 ^ 1050 x ^ 500 –
1.194262986031659 * 10 ^ 1044 x ^ 502 +
3,801388459062310 * 10 ^ 1037 x ^ 504 –
1.185736943005922 * 10 ^ 1031 x ^ 506 +
3.624144340194998 * 10 ^ 1024 x ^ 508 –
1,085326295119428 * 10 ^ 1018 x ^ 510 +
3.184336690499094 * 10 ^ 1011 x ^ 512 – 9.15265315360722 * 10 ^ 1004 x ^ 514 +
2.576970104042530 * 10 ^ 998 x ^ 516 – 7.106741460354884 * 10 ^ 991 x ^ 518 +
1.919527070100305 * 10 ^ 985 x ^ 520 – 5.077428255070817 * 10 ^ 978 x ^ 522 +
1.315169795939462 * 10 ^ 972 x ^ 524 – 3,335572468709188 * 10 ^ 965 x ^ 526 +
8.282680296727712 * 10 ^ 958 x ^ 528 – 2.013465565926689 * 10 ^ 952 x ^ 530 +
4.791268546923877 * 10 ^ 945 x ^ 532 – 1.115961983238396 * 10 ^ 939 x ^ 534 +
2.543898714625890 * 10 ^ 932 x ^ 536 – 5.674924283553106 * 10 ^ 925 x ^ 538 +
1.238761877862649 * 10 ^ 919 x ^ 540 – 2.645697031412988 * 10 ^ 912 x ^ 542 +
5.528066528310169 * 10 ^ 905 x ^ 544 – 1.129907715451902 * 10 ^ 899 x ^ 546 +
2.258937772190814 * 10 ^ 892 x ^ 548 – 4.416838093793809 * 10 ^ 885 x ^ 550 +
8.445361906230247 * 10 ^ 878 x ^ 552 – 1.578983472142473 * 10 ^ 872 x ^ 554 +
2.886301523822343 * 10 ^ 865 x ^ 556 – 5.157772274030366 * 10 ^ 858 x ^ 558 +
9.00927447280871 * 10 ^ 851 x ^ 560 – 1.538065326188156 * 10 ^ 845 x ^ 562 +
2.566057844702199 * 10 ^ 838 x ^ 564 – 4.183246440184080 * 10 ^ 831 x ^ 566 +
6.662906363258365 * 10 ^ 824 x ^ 568 – 1.036726908534393 * 10 ^ 818 x ^ 570 +
1.575657490425618 * 10 ^ 811 x ^ 572 – 2.338846202524272 * 10 ^ 804 x ^ 574 +
3.390226688499028 * 10 ^ 797 x ^ 576 – 4.798296448841429 * 10 ^ 790 x ^ 578 +
6.630097417686452 * 10 ^ 783 x ^ 580 – 8.942720476487491 * 10 ^ 776 x ^ 582 +
1.177274957509828 * 10 ^ 770 x ^ 584 – 1.512465267645572 * 10 ^ 763 x ^ 586 +
1.895972649294613 * 10 ^ 756 x ^ 588 – 2.318765940004212 * 10 ^ 749 x ^ 590 +
2.766292480448929 * 10 ^ 742 x ^ 592 – 3.218791725652668 * 10 ^ 735 x ^ 594 +
3.652393804987598 * 10 ^ 728 x ^ 596 – 4.040989068586522 * 10 ^ 721 x ^ 598 +
4.358706025852007 * 10 ^ 714 x ^ 600 – 4.582693468544262 * 10 ^ 707 x ^ 602 +
4.695803111075273 * 10 ^ 700 x ^ 604 – 4.688741559807496 * 10 ^ 693 x ^ 606 +
4.561319881825257 * 10 ^ 686 x ^ 608 – 4.322569644411743 * 10 ^ 679 x ^ 610 +
3.989688936013741 * 10 ^ 672 x ^ 612 – 3.585988266929982 * 10 ^ 665 x ^ 614 +
3.138177945893562 * 10 ^ 658 x ^ 616 – 2.673437612187067 * 10 ^ 651 x ^ 618 +
2.216715896777711 * 10 ^ 644 x ^ 620 – 1,788627818060961 * 10 ^ 637 x ^ 622 +
1.404174500186407 * 10 ^ 630 x ^ 624 – 1.072341751792931 * 10 ^ 623 x ^ 626 +
7.964800475641478 * 10 ^ 615 x ^ 628 – 5.752587779349611 * 10 ^ 608 x ^ 630 +
4.039372861699552 * 10 ^ 601 x ^ 632 – 2.757027740769818 * 10 ^ 594 x ^ 634 +
1.828763089939277 * 10 ^ 587 x ^ 636 – 1,178620216644649 * 10 ^ 580 x ^ 638 +
7.379038749201475 * 10 ^ 572 x ^ 640 – 4.486862605957440 * 10 ^ 565 x ^ 642 +
2.649162740835810 * 10 ^ 558 x ^ 644 – 1.518452940120143 * 10 ^ 551 x ^ 646 +
8.447396286832695 * 10 ^ 543 x ^ 648 – 4.560087893863542 * 10 ^ 536 x ^ 650 +
2.388087569454717 * 10 ^ 529 x ^ 652 – 1.212968867012339 * 10 ^ 522 x ^ 654 +
5.973994622973118 * 10 ^ 514 x ^ 656 – 2.852244673191626 * 10 ^ 507 x ^ 658 +
1.319787541596352 * 10 ^ 500 x ^ 660 – 5.917012482879806 * 10 ^ 492 x ^ 662 +
2.569599033701511 * 10 ^ 485 x ^ 664 – 1.080620010752694 * 10 ^ 478 x ^ 666 +
4.399494748327280 * 10 ^ 470 x ^ 668 – 1.733520668334456 * 10 ^ 463 x ^ 670 +
6.608801006599677 * 10 ^ 455 x ^ 672 – 2.436976545587831 * 10 ^ 448 x ^ 674 +
8.689185240682283 * 10 ^ 440 x ^ 676 – 2.994787739224995 * 10 ^ 433 x ^ 678 +
9.97398312034905 * 10 ^ 425 x ^ 680 – 3.208772811716005 * 10 ^ 418 x ^ 682 +
9.96838679970145 * 10 ^ 410 x ^ 684 – 2.989300706409979 * 10 ^ 403 x ^ 686 +
8.649909540838832 * 10 ^ 395 x ^ 688 – 2.414260480021974 * 10 ^ 388 x ^ 690 +
6.497036542475437 * 10 ^ 380 x ^ 692 – 1.685107150526525 * 10 ^ 373 x ^ 694 +
4.210534545492902 * 10 ^ 365 x ^ 696 – 1.013105481444205 * 10 ^ 358 x ^ 698 +
2.346299337286123 * 10 ^ 350 x ^ 700 – 5.227813821621668 * 10 ^ 342 x ^ 702 +
1.120092727822506 * 10 ^ 335 x ^ 704 – 2,306568812170204 * 10 ^ 327 x ^ 706 +
4.562790569051598 * 10 ^ 319 x ^ 708 – 8.665839615324031 * 10 ^ 311 x ^ 710 +
1.57929 * 10 ^ 304 x ^ 712 – 2.76013 * 10 ^ 296 x ^ 714 +
4.62324 * 10 ^ 288 x ^ 716 – 7,41716 * 10 ^ 280 x ^ 718 +
1,133897 * 10 ^ 273 x ^ 720 – 1.67291 * 10 ^ 265 x ^ 722 +
2.34855 * 10 ^ 257 x ^ 724 – 3.14893 * 10 ^ 249 x ^ 726 +
4.0292 * 10 ^ 241 x ^ 728 – 4.9159 * 10 ^ 233 x ^ 730 + 5.71392 * 10 ^ 225 x ^ 732 –
6.32137 * 10 ^ 217 x ^ 734 + 6.64985 * 10 ^ 209 x ^ 736 –
6.64492 * 10 ^ 201 x ^ 738 + 6.30048 * 10 ^ 193 x ^ 740 –
5.66194 * 10 ^ 185 x ^ 742 + 4.81655 * 10 ^ 177 x ^ 744 –
3.87369 * 10 ^ 169 x ^ 746 + 2.94125 * 10 ^ 161 x ^ 748 –
2.10534 * 10 ^ 153 x ^ 750 + 1.41845 * 10 ^ 145 x ^ 752 – 8.98 * 10 ^ 136 x ^ 754 +
5.33242 * 10 ^ 128 x ^ 756 – 2.96423 * 10 ^ 120 x ^ 758 +
1.53931 * 10 ^ 112 x ^ 760 – 7.45037 * 10 ^ 103 x ^ 762 +
3.35264 * 10 ^ 95 x ^ 764 – 1.39887 * 10 ^ 87 x ^ 766 + 5,39579 * 10 ^ 78 x ^ 768 –
1.91778 * 10 ^ 70 x ^ 770 + 6.25793 * 10 ^ 61 x ^ 772 – 1.86721 * 10 ^ 53 x ^ 774 +
5.07121 * 10 ^ 44 x ^ 776 – 1.24727 * 10 ^ 36 x ^ 778 + 2.76185 * 10 ^ 27 x ^ 780 –
5 46899 * 10 ^ 18 x ^ 782 + 9.60895 * 10 ^ 9 x ^ 784 – 14.8419 x ^ 786 +
1.9931 * 10 ^ -8 x ^ 788 – 2.29559 * 10 ^ -17 x ^ 790 + 2.22936 * 10 ^ -26 x ^ 792 –
1.78565 * 10 ^ -35 x ^ 794 + 1.14492 * 10 ^ -44 x ^ 796 –
5.63037 * 10 ^ -54 x ^ 798 + 1.98626 * 10 ^ -63 x ^ 800 –
4.45525 * 10? -73 x? 802 + 4.74795 * 10? -83 x? 804;
Ground[P, {x, 0, 100},PlotRange->All]

## plot – handling issues

I trace geodetic data on an ellipsoid. My problem is that I can not do the manipulation, of a, b, c. From the starting point and the initial vector, the manipulation works well, but parameters of the ellipsoid (a, b, c) does not work.
My code:

Clear[a, b, c];
r[u_, v_] : = {a * Cos[u]* Cos[v], b * Cos[u]*Peach[v], c * Sin[u]};
Index[r, 1][u_, v_]    : = !  (
* SubscriptBox[([PartialD]),  (u )] (r[u, v]) );
Index[r, 2][u_, v_]    : = !  (
* SubscriptBox[([PartialD]),  (v )] (r[u, v]) );
g = table[
Subscript[r, i][Subscript[u, 1], Index[u, 2]].Index[r, j][
Subscript[u, 1], Index[u, 2]], {i, 2}, {j, 2}

;
invg = Inverse[g] // Simplify;
g[i_, j_, k_] : = 1/2 !  (
* UnderoverscriptBox[([Sum]),  (l = 1 ),  (2 )

(
* SubscriptBox[(invg), (([[)(l, k)(]]) )] ((
* SubscriptBox[([PartialD]),
SubscriptBox[(u), (j)]] * SubscriptBox[(g), (([[)(i, l)(]]) )] +
* SubscriptBox[([PartialD]),
SubscriptBox[(u), (i)]] * SubscriptBox[(g), (([[)(j, l)(]]) )] -
* SubscriptBox[([PartialD]),
SubscriptBox[(u), (l)]] * SubscriptBox[(g), (([[)(i, j)(]]) )]) ) ) ) /.
Index[u, m_] :> Index[u, m]

eqns = Table[ Subscript[u, k]& # 39; & # 39;
* UnderoverscriptBox[([Sum]),  (i = 1 ),  (2 )] (
* UnderoverscriptBox[([Sum]),  (j = 1 ),  (2 )]g[i, j, k]*  (
* SubscriptBox[(u), (j)]& # 39; )
* SubscriptBox[(u), (i)]& # 39; )

;
Manipulate[
geod = NDSolve[
Join[eqns, {Subscript[u, 1][0]    == Index[l, 1],
Index[u, 2][0]    == Index[l, 2],
Index[u, 1]& # 39;[0] == Index[v, 1],
Index[u, 2]& # 39;[0] == Index[v, 2]}],
{Index[u, 1]
a = 1;
b = 2;
c = 1;
Show[Graphics3D[{Purple, Ellipsoid[{0, 0, 0}, {a, b, c}], Green,
PointSize[Large], Point[Dr[Index[Dr[subscript[r[Indice[r[Subscript[l, 1], Index[l, 2]]]}],
ParametricPlot3D[
r[Assess[Evaluate[Évaluer[Evaluate[Subscript[u, 1]
Assess[Index[subscript[Indice[Subscript[u, 2]
Plot Style -> Pink],
Image size -> 500,
Boxed -> False], {{Index[l, 1], 1}, - ([Pi]/ 2), [Pi]/
2}, {{Index[l, 2], 1}, - [Pi][Pi]}, {{T, 1}, 3,
100}, {{Index[v, 1], 1}, -3, 3}, {{Hint[v, 2], 1}, -3, 3}]


Someone can help me?

## plot – ContourPlot: Defining global options for the bar legend

In my Mathematica notebook, I try to specify the overall appearance of contour curves. This is easily done with SetOptions:

SetOptions[ContourPlot,
BaseStyle -> {FontFamily -> "Latin Modern Math",
FontSize -> 14}];


However, this does not apply to BarLegend:

    ContourPlot[Abs[Gamma[u + I v]]{u, -1.5, 1.5},
{v, -1.5, 1.5}, PlotLegends -> Automatic]


I've tried to set global options for BarLegend:

SetOptions[BarLegend, LabelStyle -> {FontFamily
-> "Latin Modern Math", FontSize -> 14}];


but that seems to have no effect! How can I achieve this goal?

PS: Use v.10.3.0