Re: [sage-support] desolve_system in sage
Many thanks now I solved Lorentz equations and I plot in 2D. But when I try to plot in 3D phase space I get result different about the true "spirals " This is what I did from sage.calculus.desolvers import desolve_system_rk4 x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t') sigma=10 b=8/3 r=10 P=desolve_system_rk4([sigma*(y-x),r*x-y-x*z,x*y-b*z],[x,y,z],ics=[0,0,1,0] ,ivar=t,end_points=20) py=list_plot3d([[x,y,z] for t,x,y,z in P],plotjoined=True,axes_label=True) show(py) Please find the attached file to see the plot Thanks Doaa On 11 October 2012 12:55, David Joyner wrote: > On Thu, Oct 11, 2012 at 7:28 AM, Doaa El-Sakout wrote: > > Dear David, > > I would like to plot x(t) against t similar for y and z > > and after that plot [x,y,z] in phase space > > So I want know the solution first for the system > > before plot the result. > > Thanks > > Doaa > > > Your system is similar to one used to model a Zombie attack (which is > in turn borrowed from an infection model). The sage code is here: > http://wdjoyner.org/zombies/love-war-zombies.sage > The commands I think you want are towards the bottom. > Slides going into more detail is here: > http://wdjoyner.org/zombies/love-war-zombies_slides.pdf > There is even a video:-) > > http://www.mosaic-web.org/go/MCAST/videos/MCAST-2011-04-22/lib/playback.html > > > > > > > > On 11 October 2012 10:55, David Joyner wrote: > >> > >> On Thu, Oct 11, 2012 at 3:20 AM, Doaa El-Sakout > wrote: > >> > Hi everyone, > >> > I try to solve a system of ODE by sage as follows > >> > > >> > x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t') > >> > sigma=10 > >> > b=8/3 > >> > r=10 > >> > x= function('x',t) > >> > y= function('y',t) > >> > z= function('z',t) > >> > d1=(diff(x,t)-sigma*(y-x)==0) > >> > d2=(diff(y,t)-r*x+y+x*z==0) > >> > d3=(diff(z,t)-x*y+b*z==0) > >> > >> This makes it non-linear. Did you intend to type that? > >> > >> > sol=desolve_system([d1,d2,d3],[x,y,z],ics=[0,1,0],ivar=t);show(sol) > >> > > >> > But I got the following error > >> > > >> > TypeError: unable to make sense of Maxima expression > >> > > >> > > 'x(t)=ilt((?g3817-10*laplace(x(t)*z(t),t,?g3817)+1)/(?g3817^2+11*?g3817-90),?g3817,t)' > >> > in Sage > >> > > >> > > >> > > >> > Any suggestion > >> > Doaa > >> > > >> > -- > >> > You received this message because you are subscribed to the Google > >> > Groups > >> > "sage-support" group. > >> > To post to this group, send email to sage-support@googlegroups.com. > >> > To unsubscribe from this group, send email to > >> > sage-support+unsubscr...@googlegroups.com. > >> > Visit this group at http://groups.google.com/group/sage-support?hl=en > . > >> > > >> > > >> > >> -- > >> You received this message because you are subscribed to the Google > Groups > >> "sage-support" group. > >> To post to this group, send email to sage-support@googlegroups.com. > >> To unsubscribe from this group, send email to > >> sage-support+unsubscr...@googlegroups.com. > >> Visit this group at http://groups.google.com/group/sage-support?hl=en. > >> > >> > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sage-support" group. > > To post to this group, send email to sage-support@googlegroups.com. > > To unsubscribe from this group, send email to > > sage-support+unsubscr...@googlegroups.com. > > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > > > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To post to this group, send email to sage-support@googlegroups.com. > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. <>
Re: [sage-support] desolve_system in sage
On Thu, Oct 11, 2012 at 7:28 AM, Doaa El-Sakout wrote: > Dear David, > I would like to plot x(t) against t similar for y and z > and after that plot [x,y,z] in phase space > So I want know the solution first for the system > before plot the result. > Thanks > Doaa Your system is similar to one used to model a Zombie attack (which is in turn borrowed from an infection model). The sage code is here: http://wdjoyner.org/zombies/love-war-zombies.sage The commands I think you want are towards the bottom. Slides going into more detail is here: http://wdjoyner.org/zombies/love-war-zombies_slides.pdf There is even a video:-) http://www.mosaic-web.org/go/MCAST/videos/MCAST-2011-04-22/lib/playback.html > > > On 11 October 2012 10:55, David Joyner wrote: >> >> On Thu, Oct 11, 2012 at 3:20 AM, Doaa El-Sakout wrote: >> > Hi everyone, >> > I try to solve a system of ODE by sage as follows >> > >> > x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t') >> > sigma=10 >> > b=8/3 >> > r=10 >> > x= function('x',t) >> > y= function('y',t) >> > z= function('z',t) >> > d1=(diff(x,t)-sigma*(y-x)==0) >> > d2=(diff(y,t)-r*x+y+x*z==0) >> > d3=(diff(z,t)-x*y+b*z==0) >> >> This makes it non-linear. Did you intend to type that? >> >> > sol=desolve_system([d1,d2,d3],[x,y,z],ics=[0,1,0],ivar=t);show(sol) >> > >> > But I got the following error >> > >> > TypeError: unable to make sense of Maxima expression >> > >> > 'x(t)=ilt((?g3817-10*laplace(x(t)*z(t),t,?g3817)+1)/(?g3817^2+11*?g3817-90),?g3817,t)' >> > in Sage >> > >> > >> > >> > Any suggestion >> > Doaa >> > >> > -- >> > You received this message because you are subscribed to the Google >> > Groups >> > "sage-support" group. >> > To post to this group, send email to sage-support@googlegroups.com. >> > To unsubscribe from this group, send email to >> > sage-support+unsubscr...@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sage-support?hl=en. >> > >> > >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-support" group. >> To post to this group, send email to sage-support@googlegroups.com. >> To unsubscribe from this group, send email to >> sage-support+unsubscr...@googlegroups.com. >> Visit this group at http://groups.google.com/group/sage-support?hl=en. >> >> > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To post to this group, send email to sage-support@googlegroups.com. > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
Re: [sage-support] desolve_system in sage
Dear David, I would like to plot x(t) against t similar for y and z and after that plot [x,y,z] in phase space So I want know the solution first for the system before plot the result. Thanks Doaa On 11 October 2012 10:55, David Joyner wrote: > On Thu, Oct 11, 2012 at 3:20 AM, Doaa El-Sakout wrote: > > Hi everyone, > > I try to solve a system of ODE by sage as follows > > > > x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t') > > sigma=10 > > b=8/3 > > r=10 > > x= function('x',t) > > y= function('y',t) > > z= function('z',t) > > d1=(diff(x,t)-sigma*(y-x)==0) > > d2=(diff(y,t)-r*x+y+x*z==0) > > d3=(diff(z,t)-x*y+b*z==0) > > This makes it non-linear. Did you intend to type that? > > > sol=desolve_system([d1,d2,d3],[x,y,z],ics=[0,1,0],ivar=t);show(sol) > > > > But I got the following error > > > > TypeError: unable to make sense of Maxima expression > > > 'x(t)=ilt((?g3817-10*laplace(x(t)*z(t),t,?g3817)+1)/(?g3817^2+11*?g3817-90),?g3817,t)' > > in Sage > > > > > > > > Any suggestion > > Doaa > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sage-support" group. > > To post to this group, send email to sage-support@googlegroups.com. > > To unsubscribe from this group, send email to > > sage-support+unsubscr...@googlegroups.com. > > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > > > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To post to this group, send email to sage-support@googlegroups.com. > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
Re: [sage-support] desolve_system in sage
On Thu, Oct 11, 2012 at 3:20 AM, Doaa El-Sakout wrote: > Hi everyone, > I try to solve a system of ODE by sage as follows > > x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t') > sigma=10 > b=8/3 > r=10 > x= function('x',t) > y= function('y',t) > z= function('z',t) > d1=(diff(x,t)-sigma*(y-x)==0) > d2=(diff(y,t)-r*x+y+x*z==0) > d3=(diff(z,t)-x*y+b*z==0) This makes it non-linear. Did you intend to type that? > sol=desolve_system([d1,d2,d3],[x,y,z],ics=[0,1,0],ivar=t);show(sol) > > But I got the following error > > TypeError: unable to make sense of Maxima expression > 'x(t)=ilt((?g3817-10*laplace(x(t)*z(t),t,?g3817)+1)/(?g3817^2+11*?g3817-90),?g3817,t)' > in Sage > > > > Any suggestion > Doaa > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To post to this group, send email to sage-support@googlegroups.com. > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] desolve_system in sage
Hi everyone, I try to solve a system of ODE by sage as follows x,y,sigma,r,z,b,t=var('x,y,sigma,r,z,b,t') sigma=10 b=8/3 r=10 x= function('x',t) y= function('y',t) z= function('z',t) d1=(diff(x,t)-sigma*(y-x)==0) d2=(diff(y,t)-r*x+y+x*z==0) d3=(diff(z,t)-x*y+b*z==0) sol=desolve_system([d1,d2,d3],[x,y,z],ics=[0,1,0],ivar=t);show(sol) But I got the following error TypeError: unable to make sense of Maxima expression 'x(t)=ilt((?g3817-10*laplace(x(t)*z(t),t,?g3817)+1)/(?g3817^2+11*?g3817-90),?g3817,t)' in Sage Any suggestion Doaa -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.