︠6c34e676-f3d1-4950-ac84-2fc2f4736137si︠
typeset_mode(True)
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︠3832c541-3121-41f9-a947-caa8824355d9i︠
%md
## Exercice n. 23, section 3.2
On condisère la fonction $f(x) = \frac{2x^2+3xy+4y^2}{3x^2 + 5y^2}$
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︠99a281bc-e5af-463a-8b27-c457ebf113d9s︠
var('x,y')
cm = colormaps.Blues
def f(x,y) :
return (2*x^2 + 3*x*y+4*y^2)/(3*x^2 + 5*y^2)
def c(x,y):
return f(x,y)
S=plot3d(f,(x,-2,2),(y,-2,2),color = (c,cm), opacity=1, mesh=1)
show(S, aspect_ratio = [1,1,3])
C=contour_plot(f, (x,-2, 2), (y,-2, 2), cmap='Blues',linestyles='solid', colorbar=True)
show(C,figsize=4)
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($\\displaystyle x$, $\\displaystyle y$)
"}︡{"file":{"filename":"92ce4d18-16f1-4371-b2aa-4571ea0c93aa.sage3d","uuid":"92ce4d18-16f1-4371-b2aa-4571ea0c93aa"}}︡{"file":{"filename":"/home/user/.sage/temp/project-b317db30-e79c-4087-a881-6ba4c99c270b/144/tmp_GV9C7W.svg","show":true,"text":null,"uuid":"805aaf66-d3cf-4c75-a11c-153a19dcda01"},"once":false}︡{"done":true}︡
︠050f41c7-5294-454a-ad78-c06d0e3e91fb︠
%md
## Exerice n. 42, section 3.2
︡913ff643-c925-40d7-8faa-341414c6570d︡{"done":true,"md":"## Exerice n. 42, section 3.2"}
︠fe80eeeb-5b45-4fb6-b303-2082c8c2f752s︠
var('x,y')
cm = colormaps.Blues
def f(x,y) :
return sin(x^2 + y^2)/(x^2 + y^2)
def c(x,y):
return 0.4+0.8*f(x,y)
S=plot3d(f,(x,-pi, pi), (y,-pi, pi),color = (c,cm), opacity=1, mesh=1)
show(S, aspect_ratio=[1,1,2])
C=contour_plot(f, (x,-3*pi, 3*pi), (y,-3*pi, 3*pi), cmap='Blues',linestyles='solid', colorbar=True)
show(C,figsize=4)
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"}︡{"file":{"filename":"24837d42-19a2-4b4e-8254-22f6730eadf2.sage3d","uuid":"24837d42-19a2-4b4e-8254-22f6730eadf2"}}︡{"file":{"filename":"/home/user/.sage/temp/project-b317db30-e79c-4087-a881-6ba4c99c270b/144/tmp_2Bvw4L.svg","show":true,"text":null,"uuid":"96932034-e279-4374-8220-ed1a35a1b9a8"},"once":false}︡{"done":true}︡
︠05837a4a-3cd3-481d-ba29-338791951208︠