New package for drawing direction fields with gnuplot

Evaluating f(x, y) with symbolic arguments triggers the error.
Try postponing evaluation of f, e.g. drawdf(f, ...) (not sure if that works)
or drawdf('(f(x, y)), ...).

HTH

Robert Dodier

On 11/19/10, Adam Majewski <adammaj1 at o2.pl> wrote:
> Dnia Fri, 19 Nov 2010 15:11:14 -0500, Mark H Weaver napisa?(a):
>
>> Adam Majewski <adammaj1 at o2.pl> writes:
>>> soln_at draw field lines, so how can I draw equipotential lines ?
>>
>> With the attached patch to drawdf.mac, does the following command do
>> what you want?
>>
>> drawdf(x*x+y*y, [x,-2,2], [y,-2,2],
>>   field_color=gray, proportional_axes='xy, aspect_ratio=1, color=red,
>>   solns_at(makelist([k/2,-k/2],k,-3,3)), color=green,
>>   equipots_at(makelist([k/2,k/2],k,-3,3)))$
>>
>> Note that equipots_at uses the same numerical integrator as solns_at, so
>> you may sometimes have to mess around with options such as duration and
>> tstep to get good results.
>>
>>     Mark
>>
>>
>> --- drawdf-orig.mac	2010-11-17 20:09:09.000000000 -0500 +++ drawdf.mac
>> 2010-11-19 14:57:11.000000000 -0500 @@ -204,6 +204,13 @@
>>    if curve=[] then curve:[pt],
>>    [ 'point_type='none, funmake('soln_curve, [curve, 'soln_arrows =
>>    soln_arrows]) ] )$
>>
>> +/*
>> + * Ideally, this should probably detect and remove overlaps in the
>> curve. + */
>> +equipotential_plot(pt) := block(
>> +  [ dxdt:dydt, dydt:-dxdt, soln_arrows:false, soln_direction:'both ], +
>>  solution_plot(pt) )$
>> +
>>  linearize_at(pt, derivs, vars) := block(
>>    [ subs: map("=", vars, pt) ],
>>    subst(subs, apply('matrix, outermap('diff, derivs, vars))))$
>> @@ -348,6 +355,10 @@
>>      then pre_graphics: append(reverse(solution_plot(args(param))),
>>      pre_graphics) else if operatorp(param, 'solns_at)
>>      then for pt in list_of_points_from(param) do pre_graphics:
>>      append(reverse(solution_plot(pt)), pre_graphics)
>> +    else if operatorp(param, 'equipot_at) +    then pre_graphics:
>> append(reverse(equipotential_plot(args(param))), pre_graphics) +    else
>> if operatorp(param, 'equipots_at) +    then for pt in
>> list_of_points_from(param) do pre_graphics:
>> append(reverse(equipotential_plot(pt)), pre_graphics)
>>      else if operatorp(param, 'saddle_at)
>>      then pre_graphics: append(reverse(saddle_plot(args(param))),
>>      pre_graphics) else if operatorp(param, 'saddles_at)
>> _______________________________________________ Maxima mailing list
>> Maxima at math.utexas.edu
>> http://www.math.utexas.edu/mailman/listinfo/maxima
>
> I have done :
>
>  patch < drawdf-equipot.diff
> (Stripping trailing CRs from patch.)
> patching file drawdf.mac
> Hunk #1 succeeded at 206 (offset 2 lines).
> Hunk #2 succeeded at 357 (offset 2 lines).
>
>
> Yes, it works fine.
>
>
> I have also tried :
>
> f(zx,zy):=block([i:0,zx2,zy2,cx:0,cy:0,ER2:4,iMax:20],
> zx2:zx*zx,zy2:zy*zy,
> while zx2+zy2<ER2 and i<iMax do
> (zy:2*zx*zy+cy,zx:zx2-zy2+cx,zx2:zx*zx,zy2:zy*zy,i:i+1),
> return(i));
>
>
> drawdf(f(x,y), [x,-2,2], [y,-2,2]);
>
> Unable to evaluate predicate y^2+x^2<4
> #0: f(zx=x,zy=y)
>  -- an error. To debug this try: debugmode(true);
>
> Adam
>
> _______________________________________________
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> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>