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创建于：2025年5月21日

使用 O4 Mini High 回答 Chat01

问题

(------------------------------------------------)(一、参数与函数)
ClearAll["Global`"];
M = 1; (质量参数)
L = 4; (角动量)
gs = {0, 0.5, 0.7}; (不同磁荷 g)
cols = {Blue, Orange, Green}; (每条曲线的颜色)
f[r_, g_] := 1 - (2 M r^2)/(r^2 + g^2)^(3/2);
Veff[r_, L_, g_] := f[r, g] (1 + L^2/r^2);
legend =
LineLegend[cols, Thread["g = " <> ToString /@ gs],
LegendMarkers -> "Line", LabelStyle -> 12];
(------------------------------------------------)
(二、极值计算：FindMaximum 找局部峰值)
extrema =
Table[Module[{res =
FindMaximum[{Veff[r, L, g], r > 0}, {r, 3}]}, {g, res[[2, 1, 2]],
res[[1]]} ({g,r_max,V_max})], {g, gs}];
(表格形式展示结果)
extremaTable =
Grid[Prepend[extrema, Style[{"g", "r_max", "V_max"}, Bold]],
Frame -> All, Alignment -> Center, ItemSize -> {{3, 5, 5}}];
(------------------------------------------------)
(三、绘图函数（全局/局部共用）)
makePlot[{ymin_, ymax_}] :=
Plot[Evaluate@Table[Veff[r, L, g], {g, gs}], {r, 1, 10},
PlotRange -> {All, {ymin, ymax}}, PlotStyle -> cols,
Epilog ->
MapThread[{#1, PointSize[0.015],
Point[{#2[[2]], #2[[3]]}]} &, {cols, extrema}],
PlotLegends ->
Placed[LineLegend[cols, {"g = 0", "g = 0.5", "g = 0.7"},
LabelStyle -> 12], Scaled[{0.80, 0.20}] (右下角，绝对看得见)],
AxesLabel -> {Style["r", Italic, 12],
Style[Subscript[V, eff][r], Italic, 12]}, ImageSize -> 500,
ImagePadding -> 25, PlotTheme -> "Scientific"];
globalPlot = makePlot[{-17, 1.1}]; (全范围)
localPlot = makePlot[{0.8, 1.1}]; (局部放大)
(------------------------------------------------*)
(四、一次性输出：全局图、局部图、极值表)
Column[{globalPlot, localPlot, extremaTable}, Spacings -> 2,
Alignment -> Center]

the output of this MMA code has no axes tag, which is awful.

思考

Clarifying axes tags in Mathematica

It looks like the user is working with a Mathematica code snippet that generates plots and a table, but they’re missing axes tags. They clearly want to add labels or tags to the axes. Since the AxesLabel is already set with labels for their axes, they might actually be referring to metadata tags for interactive use, which are different from just labels. It seems "Axes->True" is part of the default for showing axes, but the tag might need additional adjustments for what they're seeking.

Clarifying axes tag in plot

The user seems to be unsure about how to add axes tags to their exported plot. It looks like they might be referring to the "TaggingRules" or "AxesLabel" as potential solutions for tagging or marking the axes. They've already used "AxesLabel," but possibly we need to explicitly include "Axes -> True" and check their use of options like "AxesStyle" or "LabelStyle." It's also possible they're referencing axes in the exported graphics or in the "Options" of the plot.

Understanding axes tags in Mathematica

It looks like the user wants to add an axes tag to a Mathematica plot, but the current output uses "PlotTheme" with "Scientific," which defaults to using a frame instead of axes. The solution could involve adding "Axes -> True" and possibly "Frame -> False" to explicitly display axes. They might also be hoping to add metadata tags for accessibility, like "TaggingRules" or "CellTags" for the axes. Essentially, adding tags for axes in an export or through interactive features like "ExpressionCell" could be key.

Tracking the axes tag issue

It seems the user is having trouble with axes not appearing correctly in Mathematica due to their use of PlotTheme -> "Scientific", which may turn axes into frames. I think their issue is about wanting to include "axes tags" — which likely means axis labels, or tick labels. The solution could be to explicitly set Axes -> True and possibly override the theme to prevent axes from being converted into frames. They could also remove PlotTheme -> "Scientific" or use a custom axes style for clarity.

Thought for 52 seconds

回答

You’re right—PlotTheme→"Scientific" in recent versions of Mathematica will, by default, replace the usual axes with a framed box, and since you only supplied AxesLabel the labels never actually get drawn. You have two simple fixes:

  1. Bring back the classic axes and use your AxesLabel
    Just override the theme’s framing by forcing

    mathematica
    Axes      → True,
Frame     → False

    so that your existing AxesLabel appears. For example:

    mathematica
    makePlot[{ymin_, ymax_}] := 
  Plot[
    Evaluate@Table[Veff[r, L, g], {g, gs}], {r, 1, 10},
    PlotRange     → {All, {ymin, ymax}},
    PlotStyle     → cols,
    Epilog        → MapThread[
                       {#1, PointSize[0.015], 
                        Point[{#2[[2]], #2[[3]]}]}
                     &, {cols, extrema}],
    PlotLegends   → Placed[
                       LineLegend[cols, {"g = 0", "g = 0.5", "g = 0.7"}, 
                         LabelStyle → 12],
                       Scaled[{0.80, 0.20}]
                     ],
    Axes          → True,     (* ← force axes back *)
    Frame         → False,    (* ← turn off the theme’s frame *)
    AxesLabel     → {
                      Style["r",           Italic, 12],
                      Style[Subscript[V, eff][r], Italic, 12]
                    },
    AxesStyle     → Thick,
    ImageSize     → 500,
    ImagePadding  → 25,
    PlotTheme     → "Scientific"
  ];

  2. Stick with the framed style but switch to FrameLabel
    If you actually like the “Scientific” boxed look, then leave Frame→True (the theme default) and replace your AxesLabel with FrameLabel:

    mathematica
    makePlot[{ymin_, ymax_}] := 
  Plot[
    Evaluate@Table[Veff[r, L, g], {g, gs}], {r, 1, 10},
    PlotRange     → {All, {ymin, ymax}},
    PlotStyle     → cols,
    Epilog        → MapThread[
                       {#1, PointSize[0.015], 
                        Point[{#2[[2]], #2[[3]]}]}
                     &, {cols, extrema}],
    PlotLegends   → Placed[
                       LineLegend[cols, {"g = 0", "g = 0.5", "g = 0.7"}, 
                         LabelStyle → 12],
                       Scaled[{0.80, 0.20}]
                     ],
    Frame         → True,     (* ← keep the box *)
    Axes          → False,    (* ← no classic axes *)
    FrameLabel    → {
                      Style["r",           Italic, 12],
                      Style[Subscript[V, eff][r], Italic, 12]
                    },
    FrameStyle    → Thick,
    ImageSize     → 500,
    ImagePadding  → 25,
    PlotTheme     → "Scientific"
  ];

Either approach will give you visible, styled axis labels (“标签”) again.

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