Hello Eric

long time I,m working in other worksheet  to plot 3d but no reselts did you have plenty of time to helo me

View 12448_sys1 union sys2,sp.mw on MapleNet or Download 12448_sys1 union sys2,sp.mw
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  would you please run the above attachment.

the next attachment the same goal to plot 3d( analytical solutions)View 12448_S(D,T)primes.mws.mw on MapleNet or Download 12448_S(D,T)primes.mws.mw
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thanks for all your help

I tried for loop twice (T and D) it give me the same results as one loop.

and i try this :

dTvalues := Vector([seq(seq([d, T], d=-50..50, 10), T=1/2..5, 1/2)]);
hvalues := map(dTv -> evalf[6](eval(h, [d = dTv[1], T = dTv[2]])), dTvalues);
 

I eterupted it longish time.

In fact I got three columns of points ( T,D,sp4) but this isnot the same thing

dTvalues := Vector([seq(seq([d, T], d=-50..50, 10), T=1/2..5, 1/2)]);
hvalues := map(dTv -> evalf[6](eval(h, [d = dTv[1], T = dTv[2]])), dTvalues);
# plotting is now slightly more tricky:
plots:-pointplot3d([seq([op(dTvalues[i]), hvalues[i]]), i=1..nops(dTvalues)]);

cause sp4 depends on D,T( if D,T are 5 points then the total points must be 25)

In the 2D plot I do this:

NII:=1: DD[0]:=-50:LASTD:=50:
HNN:=evalf((LASTD-DD[0])/NII):
DD[0]:=evalf(DD[0]-HNN):
unassign('II'):
ti:=time():
for II from 1 to NII do
DD[II]:=evalf(DD[0]+II*HNN):
d:=DD[II]:
sp:=evalf(sp1(d,tau,t)):
sp2:=unapply(sp,tau,t):
isp:=int(sp2(tau,t),tau=0..T-t):
sp3:=unapply(isp,t):
isp:=Re(int(sp3(t),t=0..T)):
 sp4[II]:=evalf(2*isp/T):
od:time()-ti;
 

points:=[seq([DD[i],sp4[i]],i=1..NII)]:

plot(points,axes=boxed,color=black,font=[2,3,18],thickness=2,tickmarks=[5,3]);

Which is worked.

but for the 3D I dont know?? I need help

I would like to do the double integral of:

sp:=Re((exp(-I*d*tau)*(cp*((1/2)+z1)+(co-(1/2)*cz)*y1))):

but it is not easy to compute it , so I decide to do it in loop( if you have any easy way to integral sp )

I'm not sure this is right way to generate a seq, of sp where sp depends on d,T which are in the loop. 

points:=[seq([dom[i],DD[i],sp4[i]],i=1..NII)]:

For this command i get this error.

plots:-pointplot3d([seq([op(dTvalues[i]), hvalues[i]]), i=rtable_dims(dTvalues)]);
Error, bad index into Vector
 

For the analyticall solutions

sp:=Re((exp(-I*d*tau)*(cp*((1/2)+z1)+(co-(1/2)*cz)*y1))):

where cp,z1,co,cz and y1 have been computed by hand . For the same purpose I want to plot double integral(sp) and because of the huge functions in sp I put it in loop. Where  T:=dom[II]: and d:=DD[II]:
 

Happy holiday,wish you a good helth

I put the double integral in loop because it not easy to generate as function my question how to plot that in 3d

sp:=Re((exp(-I*d*tau)*(cp*((1/2)+z1)+(co-(1/2)*cz)*y1))):# h in recent
sp1:=unapply(sp,d,tau,t):
 

NII:=100:TN:=10:TH:=0.1: DD[0]:=-30:LASTD:=30:
HNN:=evalf((LASTD-DD[0])/NII):
DD[0]:=evalf(DD[0]-HNN):
unassign('II'):
ti:=time():
for II from 1 to NII do:
dom[II]:=evalf(II*TH):
 T:=dom[II]:
DD[II]:=evalf(DD[0]+II*HNN):
d:=DD[II]:
sp:=evalf(sp1(d,tau,t)):
sp2:=unapply(sp,tau,t):
isp:=int(sp2(tau,t),tau=0..T-t):
sp3:=unapply(isp,t):
isp:=int(sp3(t),t=0..T):
sp4[II]:=evalf(2*isp/T)
od:time()-ti;
points:=[seq([dom[i],DD[i],sp4[i]],i=1..NII)]: i know it is not right

how can we creat seq?? and then plot it

Here for the prog. the same goal I want

dTvalues := Vector([seq(seq([d, T], d=-50..50, 10), T=1/2..5, 1/2)]);
hvalues := map(dTv -> evalf[6](eval(h, [d = dTv[1], T = dTv[2]])), dTvalues);
# plotting is now slightly more tricky:
plots:-pointplot3d([seq([op(dTvalues[i]), hvalues[i]]), i=1..nops(dTvalues)]);

                       Vector[column](%id = 169050540)
                       Vector[column](%id = 169050604)
Error, bad index into Vector
 

View 12448_S(D,omega).mw on MapleNet or Download 12448_S(D,omega).mw
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The attach file above is equivalent to the problem but analytical

I solve the systems analytic i put the funtion that i would like to plot in loop Sp0[II]. can you take a look. thanks

This take long time, is there any simple way to define function or sequence.

Thanks.

Thanks,

dvalues := Vector([seq(d/10, d=0..20)]); this mean the x-axis from 0 to 2
 

if I want the domain -50 to 50 and there a singular point what you recomend?

how about 3d

g := 2/T*Re(exp(-I*d*tau)*((1/2+z_R_5(t))*f1(tau)+f4(tau)-f3(tau)/2*y_5(t))); where T positive
 

h := Int(g, [tau = 0..T-t, t=0..1]);
 

computation interrupted after 12 hour

h := Int(g, [tau = 0..1-t, t=0..1]);
evalf[6](eval(h, d=1/2));
 

dvalues := Vector([seq(d/10, d=0..20)]);
hvalues := map(dv -> evalf(eval(h, d = dv)), dvalues);
plots:-pointplot(dvalues, hvalues);

Still I didn't get the value of h .

h := Int(piecewise(tau > 1-t, 0, g), [tau=0..1, t=0..1], digits=5, method=_MonteCarlo));