︠983bb670-c498-4cf2-8f57-f203b7595014ai︠
%hide
%auto
#import os
var('x,y')
def rewrit(expr):
    res='('+str(expr)+')'
    return ((res.replace('x','(A.x)')).replace('y','(A.y)'))
@interact
def _(curve=input_box(default=x^3),F1=input_box(default=sin(y)), F2=input_box(default=x-y),a=input_box(default=-3), b=input_box(default=3)):
    import zipfile
    zf = zipfile.ZipFile(DATA+'Construction.cdy', 'r')
    i2g=zf.read("construction/intergeo.xml")
    certif=zf.read("private/de.cinderella/certificate.bin")
    cdy=zf.read("private/de.cinderella/construction.cdy")
    zf.close()
    import os
    os.remove(DATA+'Construction.cdy')
    temp=cdy.partition('f(x):=')[0]+'f(x):='+str(curve)+';plot(f(x),size->2);drawfield(('+str(F1)+','+str(F2)+'),stream->true,color->(0,0,0));d1(x):=d(f(#),x);if(abs(A.y-f(A.x))'+str('<')+'0.25,draw([A.x,f(A.x)],[A.x+1,f(A.x)+d1(A.x)],linesize->3,color->(128,0,0)));if(abs(A.y-f(A.x))'+str('<')+'0.25,draw([A.x+1,f(A.x)+d1(A.x)],pointcolor->[128,0,0]));draw([A.x,A.y],[A.x+'+rewrit(F1)+',A.y+'+rewrit(F2)+'],linesize->3,color->(0,128,0));draw([A.x+'+rewrit(F1)+',A.y+'+rewrit(F2)+'],pointcolor->[0,128,0]);");Text0'+(cdy.partition('f(x):=')[2]).partition('Text0')[2]
    temp2=temp.partition('"Text0".setText("f(x):=')[0]+'"Text0".setText("f(x):='+str(curve)+';plot(f(x),size->2);drawfield(('+str(F1)+','+str(F2)+'),stream->true,color->(0,0,0));d1(x):=d(f(#),x);if(abs(A.y-f(A.x))'+str('<')+'0.25,draw([A.x,f(A.x)],[A.x+1,f(A.x)+d1(A.x)]),linesize->3,color->(128,0,0));if(abs(A.y-f(A.x))'+str('<')+'0.25,draw([A.x+1,f(A.x)+d1(A.x)],pointcolor->[128,0,0]));draw([A.x,A.y],[A.x+'+rewrit(F1)+',A.y+'+rewrit(F2)+'],linesize->3,color->(0,128,0));draw([A.x+'+rewrit(F1)+',A.y+'+rewrit(F2)+'],pointcolor->[0,128,0]);");Text0'+(temp.partition('"Text0".setText("f(x):=')[2]).partition('Text0')[2]
    cdy=temp2
    zf2 = zipfile.ZipFile(DATA+'Construction.cdy', mode='w')
    zf2.writestr("private/de.cinderella/construction.cdy",cdy)
    zf2.writestr("private/de.cinderella/certificate.bin",certif)
    zf2.writestr("construction/intergeo.xml",i2g)
    zf2.close()
    html('<HTML> <HEAD> <TITLE> Construction.cdy </TITLE><META author = "CAinEE"><META keywords = "cinderella export interactive geometry construction"></HEAD><BODY><applet code="de.cinderella.CindyApplet" archive="cindyrun2.jar" width="680" height="332"> <param name="kernelID" value="1332857158652" /><param name="viewport" value="de.cinderella.ports.EuclideanPort" /><param name="filename" value="Construction.cdy" /><param name="polar" value= "false" /><param name="imagescalemode" value="scalemode.center" /><param name="imagealpha" value="1.0" /><param name="port.background.media" value="" /><param name="show.adjacencymatrix" value="1" /><param name="precision.measure" value="precision.2" /><param name="precision.measure.int" value="2" /><param name="precision.angle" value="precision.1" /><param name="precision.angle.int" value="1" /><param name="anglemodulo" value="modulo.0" /><param name="printscale" value="1:1" /><param name="printscale.int" value="1:1" /><param name="darkenDependent" value="true" /><param name="mesh.rectangular" value="false" /><param name="mesh.triangular" value="false" /><param name="axes.show" value="true" /><param name="snap" value="false" /><param name="mesh.density" value="0" /><param name="euclideanport.scale" value="25.0" /><param name="euclideanport.origin.x" value="226.0" /><param name="euclideanport.origin.y" value="233.0" /><param name="doublebuffer" value= "true" /><param name="cinderella.antialias" value= "true" /><param name="scale" value="25.0" /><param name="originx" value="226.0" /><param name="originy" value= "233.0" /><param name="deltafactor" value= "0" /><param name="mesh" value="false" /><param name="axes" value="true" /><param name="snap" value="false" />Please enable Java for an interactive construction (with Cinderella).</applet><hr><p>Created with <a href="http://www.cinderella.de">Cinderella</a></p></BODY></HTML>')
    #Sage/Python Code
    show(plot(curve, (x,a,b)))
    show(plot_vector_field((F1,F2),(x,a,b), (y,a,b)))
    var ('x, y')
    ff = F1(x=x,y=curve) + F2(x=x,y=curve)*diff(curve,x)
    value = integral(ff, (x, a, b))
    value2= numerical_integral(ff, a, b)
    html('Exact value: %s' %str(value))
    html('Numeric approximation: %s (Error = %s)' %(str(value2[0]), str(value2[1])))
    show(value)
    show(value2)
︡37c1e9dd-0e26-4c51-9d10-d0738d81ac4e︡{"html": ""}︡
︠d249a0ca-5ccd-4618-9388-5ca722c08bc0︠
0
︡0a56e930-13d2-467f-ad0e-cc23b12d57ea︡{"stdout": "0"}︡

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