On Mon, Mar 9, 2009 at 6:44 AM, Harald Schilly <harald.schi...@gmail.com> wrote: > > Hi, thx, but the correct URL is http://sagenb.org/home/pub/298/
This did not work for me, but the original one did. (FF, amd64 ubuntu 8.04) > > H > > On Mar 8, 10:37 pm, "ma...@mendelu.cz" <ma...@mendelu.cz> wrote: >> Dear readers of this group, I wrote a simple sagelet which describes >> approximation of a function in two variabels using differential. The >> sagelet is published athttp://www.sagenb.org/home/pub/298/ >> >> I hope, somebody finds it useful in her/his courses. >> >> Any suggestions are welcomed. >> >> Robert Marik >> >> --------------- >> code: >> >> x,y=var('x y') >> html('<h2>Explaining approximation of a function in two \ >> variables by differential</h2>') >> html('Points x0 and y0 are values where the exact value of the >> function \ >> is known. Deltax and Deltay are displacements of the new point. Exact >> value \ >> and approximation by differential at shifted point are compared.') >> @interact >> def _(func=input_box('sqrt(x^3+y^3)',label="f(x,y)=",type=str), x0=1, >> y0=2, \ >> deltax=slider(-1,1,0.01,0.2),\ >> deltay=slider(-1,1,0.01,-0.4), xmin=0, xmax=2, ymin=0, ymax=3): >> f=sage_eval('lambda x,y: ' + func) >> derx(x,y)=diff(f(x,y),x) >> dery(x,y)=diff(f(x,y),y) >> tangent(x,y)=f(x0,y0)+derx(x0,y0)*(x-x0)+dery(x0,y0)*(y-y0) >> A=plot3d(f(x,y),(x,xmin,xmax),(y,ymin,ymax),opacity=0.5) >> B=plot3d(tangent(x,y),(x,xmin,xmax), >> (y,ymin,ymax),color='red',opacity=0.5) >> C=point3d((x0,y0,f(x0,y0)),rgbcolor='blue',size=9) >> CC=point3d((x0+deltax,y0+deltay,f >> (x0+deltax,y0+deltay)),rgbcolor='blue',size=9) >> D=point3d((x0+deltax,y0+deltay,tangent >> (x0+deltax,y0+deltay)),rgbcolor='red',size=9) >> exact_value_ori=f(x0,y0).n(digits=10) >> exact_value=f(x0+deltax,y0+deltay) >> approx_value=tangent(x0+deltax,y0+deltay).n(digits=10) >> abs_error=(abs(exact_value-approx_value)) >> html(r'Function $ f(x,y)=%s \approx %s $ '%(latex(f(x,y)),latex >> (tangent(x,y)))) >> html(r' $f %s = %s$'%(latex((x0,y0)),latex(exact_value_ori))) >> html(r'Shifted point $%s$'%latex(((x0+deltax),(y0+deltay)))) >> html(r'Value of the function in shifted point is $%s$'%f >> (x0+deltax,y0+deltay)) >> html(r'Value on the tangent plane in shifted point is $%s$'%latex >> (approx_value)) >> html(r'Error is $%s$'%latex(abs_error)) >> show(A+B+C+CC+D) > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-edu@googlegroups.com To unsubscribe from this group, send email to sage-edu+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en -~----------~----~----~----~------~----~------~--~---
