在Mathematica中绘制数字线 [英] Plotting a number line in Mathematica
问题描述
我想在Mathematica中的数字线上绘制一个简单的间隔.我该怎么做?
I would like to plot a simple interval on the number line in Mathematica. How do I do this?
推荐答案
这是另一种尝试用更传统的白色和黑色圆圈绘制数字线的方法,尽管您想要的任何图形元素都可以轻松换出.
Here's another attempt that draws number lines with the more conventional white and black circles, although any graphics element that you want can be easily swapped out.
依靠LogicalExpand[Simplify@Reduce[expr, x]]
和Sort
将表达式转换为类似于替换规则可以使用的规范形式的表达式.这未经广泛测试,可能有点脆弱.例如,如果给定的expr
减少为True
或False
,我的代码将无法正常死掉.
It relies on LogicalExpand[Simplify@Reduce[expr, x]]
and Sort
to get the expression into something resembling a canonical form that the replacement rules can work on. This is not extensively tested and probably a little fragile. For example if the given expr
reduces to True
or False
, my code does not die gracefully.
numLine[expr_, x_Symbol:x, range:{_, _}:{Null, Null},
Optional[hs:_?NumericQ, 1/30], opts:OptionsPattern[]] :=
Module[{le = {LogicalExpand[Simplify@Reduce[expr, x]]} /. Or -> List,
max, min, len, ints = {}, h, disk, hArrow, lt = Less|LessEqual, gt = Greater|GreaterEqual},
If[TrueQ@MatchQ[range, {a_, b_} /; a < b],
{min, max} = range,
{min, max} = Through[{Min, Max}@Cases[le, _?NumericQ, \[Infinity]]]];
len =Max[{max - min, 1}]; h = len hs;
hArrow[{x1_, x2_}, head1_, head2_] := {{Thick, Line[{{x1, h}, {x2, h}}]},
Tooltip[head1, x1], Tooltip[head2, x2]};
disk[a_, ltgt_] := {EdgeForm[{Thick, Black}],
Switch[ltgt, Less | Greater, White, LessEqual | GreaterEqual, Black],
Disk[{a, h}, h]};
With[{p = Position[le, And[_, _]]},
ints = Extract[le, p] /. And -> (SortBy[And[##], First] &);
le = Delete[le, p]];
ints = ints /. (l1 : lt)[a_, x] && (l2 : lt)[x, b_] :>
hArrow[{a, b}, disk[a, l1], disk[b, l2]];
le = le /. {(*_Unequal|True|False:>Null,*)
(l : lt)[x, a_] :> (min = min - .3 len;
hArrow[{a, min}, disk[a, l],
Polygon[{{min, 0}, {min, 2 h}, {min - Sqrt[3] h, h}}]]),
(g : gt)[x, a_] :> (max = max + .3 len;
hArrow[{a, max}, disk[a, g],
Polygon[{{max, 0}, {max, 2 h}, {max + Sqrt[3] h, h}}]])};
Graphics[{ints, le}, opts, Axes -> {True, False},
PlotRange -> {{min - .1 len, max + .1 len}, {-h, 3 h}},
GridLines -> Dynamic[{{#, Gray}} & /@ MousePosition[
{"Graphics", Graphics}, None]],
Method -> {"GridLinesInFront" -> True}]
]
(注意:我本来尝试使用Arrow
和Arrowheads
画线-但由于Arrowheads
会根据周围图形的宽度自动缩放箭头,这让我头疼不已)
(Note: I had originally tried to use Arrow
and Arrowheads
to draw the lines - but since Arrowheads
automatically rescales the arrow heads with respect to the width of the encompassing graphics, it gave me too many headaches.)
好,下面是一些例子:
numLine[0 < x],
numLine[0 > x]
numLine[0 < x <= 1, ImageSize -> Medium]
numLine[0 < x <= 1 || x > 2, Ticks -> {{0, 1, 2}}]
numLine[x <= 1 && x != 0, Ticks -> {{0, 1}}]
GraphicsColumn[{
numLine[0 < x <= 1 || x >= 2 || x < 0],
numLine[0 < x <= 1 || x >= 2 || x <= 0, x, {0, 2}]
}]
编辑:让我们将以上内容与 Wolfram | Alpha
Let's compare the above to the output of Wolfram|Alpha
WolframAlpha["0 < x <= 1 or x >= 2 or x < 0", {{"NumberLine", 1}, "Content"}]
WolframAlpha["0 < x <= 1 or x >= 2 or x <= 0", {{"NumberLine", 1}, "Content"}]
请注意(在Mathematica会话中或在W | A网站上查看以上内容时)有关要点和灰色动态网格线的奇特工具提示.我偷走了这些想法,并将它们并入了上面编辑过的numLine[]
代码中.
Note (when viewing the above in a Mathematica session or the W|A website) the fancy tooltips on the important points and the gray, dynamic grid lines. I've stolen these ideas and incorporated them into the edited numLine[]
code above.
WolframAlpha
的输出不是普通的Graphics
对象,因此很难修改其Options
或使用Show
进行组合.要查看Wolfram | Alpha可以返回的各种数字线对象,请运行WolframAlpha["x>0", {{"NumberLine"}}]
-内容",单元格"和输入"全部返回基本上相同的对象.无论如何,要从
The output from WolframAlpha
is not quite a normal Graphics
object, so it's hard to modify its Options
or combine using Show
. To see the various numberline objects that Wolfram|Alpha can return, run WolframAlpha["x>0", {{"NumberLine"}}]
- "Content", "Cell" and "Input" all return basically the same object. Anyway, to get a graphics object from
wa = WolframAlpha["x>0", {{"NumberLine", 1}, "Content"}]
例如,您可以运行
Graphics@@First@Cases[wa, GraphicsBox[__], Infinity, 1]
然后我们可以修改图形对象并将它们组合在网格中以获得
Then we can modify the graphics objects and combine them in a grid to get
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