seruous solve bug? only when used with simplifying

• To: mathgroup at smc.vnet.net
• Subject: [mg48634] seruous solve bug? only when used with simplifying
• From: sean_incali at yahoo.com (sean kim)
• Date: Wed, 9 Jun 2004 04:16:50 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```hello group,

i think i have a serious Solve[], Simplify[], FullSimplify[] bug...

Take a system of equations as below. (apb is actually (a+b). i defined
it as apb to keep Mathematica crunching away at it)

sys =
{c1[t] == (c*(16*a^4 + 8*a^3*kd + 4*a^2*apb*kd + 2*a*apb^2*kd +
apb^3*kd))/(apb^4*kd),
c2[t] == (2*(8*a^3 + 4*a^2*apb + 2*a*apb^2 + apb^3)*b*c)/(apb^4*d),
c3[t] == (2*(8*a^3 + 4*a^2*apb + 2*a*apb^2 + apb^3)*b*c)/(apb^4*kd)}

sys1 = sys /.{apb -> (a + b)}
sys2 = sys/.{apb -> (a + b)}//Simplify
sys3 = sys/.{apb -> (a + b)}//FullSimplify

and then use

TrueQ[sys1 == sys1]
TrueQ[sys1 == sys2]
TrueQ[sys1 == sys3]
TrueQ[sys2 == sys3]

then it gives,

Out[18]=True
Out[19]=False
Out[20]=False
Out[21]=False

Simplify and FullSimplify changed the system so much that they are not
equal?

Basically, unless I define the (a+b) as a single constant apb, the Mathematica
will do soemthing with it then it messes it up. I think...

Why is this happening? and how do i prevent it from happening again
with other more obsucre systems?  Above I got lucky in finding the
cause (a+b)