︠73cc504c-6bf5-499f-b79b-c085e3dce4f6i︠
#auto
%hide
html('<applet code="LagrangeMultipliersTwoVariables" archive="http://ocw.mit.edu/ans7870/18/18.02/f07/tools/lagrangeMultipliersTwoVariables.jar, http://ocw.mit.edu/ans7870/18/18.02/f07/tools/mk_lib.jar, http://ocw.mit.edu/ans7870/18/18.02/f07/tools/parser_math.jar, http://ocw.mit.edu/ans7870/18/18.02/f07/tools/jcbwt363.jar" width=760 height=450></applet>')
var('x,y,z,l,m')
@interact
def a(funcion =input_box(default=x*y^2), condiciones=input_box(default=[x^2+y^2-10])):
    cond=False
    if len(condiciones)==2:
        if z in condiciones[1].variables():
            cond=True
    if z in funcion.variables() or z in condiciones[0].variables() or cond:
        if len(condiciones)==2:
            L=funcion+l*condiciones[0]+m*condiciones[1]
            sol=solve([diff(L,x)==0,diff(L,y)==0,diff(L,z)==0,diff(L,l)==0,diff(L,m)==0],[x,y,z,l,m])
        if len(condiciones)==1:
            L=funcion+l*condiciones[0]
            sol=solve([diff(L,x)==0,diff(L,y)==0,diff(L,z)==0,diff(L,l)==0],[x,y,z,l])
    else:
        if len(condiciones)==2:
            L=funcion+l*condiciones[0]+m*condiciones[1]
            sol=solve([diff(L,x)==0,diff(L,y)==0,diff(L,l)==0,diff(L,m)==0],[x,y,l,m])
        if len(condiciones)==1:
            L=funcion+l*condiciones[0]
            sol=solve([diff(L,x)==0,diff(L,y)==0,diff(L,l)==0],[x,y,l])
    for i in range(len(sol)):
        if z in funcion.variables()or z in condiciones[0].variables() or cond:
            show(sol[i][0:3])
        else:
            show(sol[i][0:2])
︡af593f68-c735-4883-b739-9c0aacd51df7︡{"html": "<font color='black'><applet code=\"LagrangeMultipliersTwoVariables\" archive=\"http://ocw.mit.edu/ans7870/18/18.02/f07/tools/lagrangeMultipliersTwoVariables.jar, http://ocw.mit.edu/ans7870/18/18.02/f07/tools/mk_lib.jar, http://ocw.mit.edu/ans7870/18/18.02/f07/tools/parser_math.jar, http://ocw.mit.edu/ans7870/18/18.02/f07/tools/jcbwt363.jar\" width=760 height=450></applet></font>"}︡{"html": "<div padding=6 id=\"div-interact-0\"> <table width=800px height=20px bgcolor=\"#c5c5c5\"\n                 cellpadding=15><tr><td bgcolor=\"#f9f9f9\" valign=top align=left><table>\n<tr><td colspan=3><table><tr><td align=right><font color=\"black\">funcion&nbsp;</font></td><td><input type=\"text\" value=\"x*y^2\" size=80 onchange=\"interact(0, '_interact_.update(\\'0\\', \\'funcion\\', 1, _interact_.standard_b64decode(\\''+encode64(this.value)+'\\'), globals()); _interact_.recompute(\\'0\\');')\"></input></td>\n</tr><tr><td align=right><font color=\"black\">condiciones&nbsp;</font></td><td><input type=\"text\" value=\"[x^2 + y^2 - 10]\" size=80 onchange=\"interact(0, '_interact_.update(\\'0\\', \\'condiciones\\', 2, _interact_.standard_b64decode(\\''+encode64(this.value)+'\\'), globals()); _interact_.recompute(\\'0\\');')\"></input></td>\n</tr></table></td></tr>\n<tr><td></td><td style='width: 100%;'><div id=\"cell-interact-0\"><?__SAGE__START>\n        <table border=0 bgcolor=\"white\" width=100%>\n        <tr><td bgcolor=\"white\" align=left valign=top><pre><?__SAGE__TEXT></pre></td></tr>\n        <tr><td  align=left valign=top><?__SAGE__HTML></td></tr>\n        </table><?__SAGE__END></div></td><td></td></tr>\n<tr><td colspan=3></td></tr>\n</table></td>\n                 </tr></table></div>\n                 "}︡

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