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# solving systems of equations returns [] Redux

I searched the wiki and found the "solve always returns []" question. But it doesn't help me. I will admit that I am a complete neophyte with Sagemath and have been playing with version 7.2 on my windows machine.

I was trying to do something very simple: solve a basic Lagrange Multiplier problem, so I defined the following:

• var('x' ,'y' ,'z', 'lam')
• var('F')
• F = xyz - lam * (xyz-9)
• var('dFx', 'dFy', 'dFz', 'dFlam')
• dFx=diff(F,x)
• dFy=diff(F,y)
• dFz=diff(F,z)
• dFlam=diff(F,lam)
• solve([dFx==0,dFy==0,dFz==0,dFlam==0],x,y,z,lam)

but the solve returns []. It should return something like x==3, y==3, z==3, shouldn't it? Is there an alternative way to approach this?

Thanks.

BobM

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## Comments

To display inline code, surround it within backticks .

To display blocks of code, either indent them with 4 spaces, or select the corresponding lines and click the "code" button (the icon with '101 010').

Can you edit your question to do that?

( 2016-08-29 13:04:46 +0200 )edit

## 2 Answers

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I can not reproduce your problem on 7.4.beta2:

sage: var('x' ,'y' ,'z', 'lam')
(x, y, z, lam)
sage: F = x*y*z - lam * (x*y*z-9)
sage: F
x*y*z - (x*y*z - 9)*lam
sage: dFx=diff(F,x)
sage: dFy=diff(F,y)
sage: dFz=diff(F,z)
sage: dFlam=diff(F,lam)
sage: dFz
-lam*x*y + x*y
sage: solve([dFx==0,dFy==0,dFz==0,dFlam==0],x,y,z,lam)
[[x == 9/(r1*r2), y == r1, z == r2, lam == 1]]

more

## Comments

But what is the latest non-beta version of Sage?

( 2016-08-28 16:05:54 +0200 )edit

This seems to work in Sage 7.3 (the latest public release).

Not sure what change between Sage 7.2 and Sage 7.3 made this work.

One could try to check which ticket is responsible among those merged in Sage 7.3.

http://www.sagemath.org/changelogs/sa...

$sage -v SageMath version 7.3, Release Date: 2016-08-04$ sage -q
sage: x, y, z, lam = var('x' ,'y' ,'z', 'lam')
sage: F = x*y*z - lam * (x*y*z-9); F
x*y*z - (x*y*z - 9)*lam
sage: dFx = diff(F, x)
sage: dFy = diff(F, y)
sage: dFz = diff(F, z)
sage: dFlam = diff(F, lam)
sage: dFx, dFy, dFz, dFlam
(-lam*y*z + y*z, -lam*x*z + x*z, -lam*x*y + x*y, -x*y*z + 9)
sage: solve([dFx == 0, dFy == 0, dFz == 0, dFlam == 0], x, y, z, lam)
[[x == 9/(r1*r2), y == r1, z == r2, lam == 1]]
sage:
`
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Asked: 2016-08-27 10:28:29 +0200

Seen: 283 times

Last updated: Aug 29 '16