Ilustrace parciální derivace funkce více proměnných

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x,y,z,t=var('x,y,z,t')
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def par_der(FUN,bod,x_hr,y_hr,z_hr):
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    Gf=plot3d(FUN,(x,x_hr[0],x_hr[1]),(y,y_hr[0],y_hr[1]),opacity=0.4,color='grey')
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    G0=point([bod[0],bod[1],FUN(bod[0],bod[1])],color='yellow',size=10)
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    rovinax=implicit_plot3d(y==bod[1],(x,x_hr[0],x_hr[1]),(y,y_hr[0],y_hr[1]),(z,z_hr[0],z_hr[1]),opacity=0.1,color='blue')
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    prunikx=parametric_plot([t,bod[1],FUN(t,bod[1])],(t,x_hr[0],x_hr[1]),color='red')
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    fx=diff(FUN,x)
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    tex=parametric_plot([t,bod[1],fx(bod[0],bod[1])*(t-bod[0])+FUN(bod[0],bod[1])],(t,x_hr[0],x_hr[1]),color='green')
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    print("\n Parcialni derivace podle x \n")
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    show(Gf+prunikx+G0+tex+rovinax)
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    show(Gf+prunikx+G0+tex)
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    rovinay=implicit_plot3d(x==bod[0],(x,x_hr[0],x_hr[1]),(y,y_hr[0],y_hr[1]),(z,z_hr[0],z_hr[1]),opacity=0.1,color='blue')
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    pruniky=parametric_plot([bod[0],t,FUN(bod[0],t)],(t,y_hr[0],y_hr[1]),color='red')
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    fy=diff(FUN,y)
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    tey=parametric_plot([bod[0],t,fy(bod[0],bod[1])*(t-bod[1])+FUN(bod[0],bod[1])],(t,y_hr[0],y_hr[1]),color='green')
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    print("\n Parcialni derivace podle y \n")
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    show(Gf+pruniky+G0+tey+rovinay)
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    show(Gf+pruniky+G0+tey)
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