问题描述
我正在尝试绘制函数 Fh_1 的图形，但看起来 ezunits 引起了问题。当我输入 x 值时，我可以从中得到结果。但是绘图不起作用，即使是 Dimensionly() 也不行。我怎样才能让它工作？
(%i2) kill(all); load(ezunits); g2r(x):= x*%pi/180;
(%o0) done
(%o1) "C:/maxima-5.44.0/share/maxima/5.44.0/share/ezunits/ezunits.mac"
(%o2) g2r(x):=(x*%pi)/180
1 variables
(%i3) rho: atan(rat(0.35));
rat: replaced 0.35 by 7/20 = 0.35
(rho) atan(7/20)
(%i4) L_FPzuLH: 110`mm;
(L_FPzuLH) 110 ` mm
(%i5) L_Backe: 33`mm;
(L_Backe) 33 ` mm
(%i6) L_HebelLinks: 81`mm;
(L_HebelLinks) 81 ` mm
2 function
(%i7) Fh_1(D_Platte):= L_HebelLinks*sin(g2r(90)-(g2r(90)-(acos((L_FPzuLH-D_Platte-L_Backe)/L_HebelLinks)))-rho);
(%o7) Fh_1(D_Platte):=L_HebelLinks*
sin(g2r(90)-(g2r(90)-acos((L_FPzuLH-D_Platte-L_Backe)/L_HebelLinks))-rho)
3 this works
(%i9) Fh_1(31`mm); float(%);
(%o8) 81*sin(acos(46/81)-atan(7/20)) ` mm
(%o9) 47.73170350716926 ` mm
4 but not this
(%i10) dimensionally(plot2d(Fh_1(x),[x,5`mm,55`mm]));
plotting: range must be of the form [variable,min,max]; found:
[x,5*g1498,55*g1498]
-- an error. To debug this try: debugmode(true);
为千里马粘贴：
/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 21.02.0 ] */
/* [wxMaxima: input start ] */
kill(all); load(ezunits); g2r(x):= x*%pi/180;
/* [wxMaxima: input end ] */
/* [wxMaxima: section start ]
variables
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
rho: atan(rat(0.35));
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
L_FPzuLH: 110`mm;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
L_Backe: 33`mm;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
L_HebelLinks: 81`mm;
/* [wxMaxima: input end ] */
/* [wxMaxima: section start ]
function
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
Fh_1(D_Platte):= L_HebelLinks*sin(g2r(90)-(g2r(90)-(acos((L_FPzuLH-D_Platte-L_Backe)/L_HebelLinks)))-rho);
/* [wxMaxima: input end ] */
/* [wxMaxima: section start ]
this works
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
Fh_1(31`mm); float(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: section start ]
but not this
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
dimensionally(plot2d(Fh_1(x),55`mm]));
/* [wxMaxima: input end ] */
/* Old versions of Maxima abort on loading files that end in a comment. */
"Created with wxMaxima 21.02.0"$
解决方法
正如我在上面的评论中所说，调用 qty 来获取维度表达式的数量。请注意，我将 Fh_1 的参数写为 x ` mm，其中 x 是我们正在绘制的无量纲变量。
plot2d (qty (Fh_1 (x ` mm)),[x,5,55]);
当我尝试使用 Maxima 5.44 时，这很有效。你可能有兴趣看看
(%i11) qty(Fh_1(x ` mm));
77 - x 7
(%o11) 81 sin(acos(------) - atan(--))
81 20
当我尝试使用当前（大约 5.45）版本的 plot2d 时，我遇到了堆栈溢出（与尝试确定某些表达式是否为无量纲有关），我现在正在调查。
这是该错误的解决方法，当我尝试使用当前接近 5.45 的版本时，它成功了。我生成一个点列表，然后绘制这些点。
(%i11) qty(Fh_1(x ` mm));
77 - x 7
(%o11) 81 sin(acos(------) - atan(--))
81 20
(%i12) ev(makelist([y,ev(%,x = y)],y,55),numer);
(%o12) [[5,11.23941870984706],[6,13.34349300482042],[7,15.34276468157134],[8,17.25033934972067],[9,19.07666307706286],[10,20.83022404590423],[11,22.51803233322337],[12,24.14595804280109],[13,25.71897581938176],[14,27.24134562928132],[15,28.71674902665171],[16,30.14839362529976],[17,31.53909440876992],[18,32.89133786911122],[19,34.20733321424233],[20,35.48905369852528],[21,36.73827031267255],[22,37.95657949382723],[23,39.14542610575446],[24,40.30612264125835],[25,41.43986538015634],[26,42.54774807342751],[27,43.63077360174984],[28,44.68986396358886],[29,45.72586887656475],[30,46.73957322048246],[31,47.73170350716926],[32,48.70293352820919],[33,49.65388930464281],[34,50.58515344111066],[35,51.49726896955291],[36,52.39074275352331],[37,53.26604851273431],[38,54.12362951808341],[39,54.96390099970309],[40,55.7872523042014],[41,56.5940488319625],[42,57.38463378095388],[43,58.15932971977946],[44,58.91844000959603],[45,59.6622500918724],[46,60.39102865673311],[47,61.1050287047217],[48,61.80448851319165],[49,62.48963251713631],[50,63.16067211306913],[51,63.81780639352923],[52,64.46122281889194],[53,65.09109783238475],[54,65.70759742353295],[55,66.31087764466791]]
(%i13) plot2d([discrete,%]);