# Solving polynomial simultaneous equations

### Solving polynomial simultaneous equations

we assume a,b,c,d are unknown variables,whose solution are either 0 or 1.So a power of a variable equals to itself(e.g,a^(n)=a).Would u please help me find a proper way to sovle the following simultaneous equations whose solutions are either 0 or 1?
-d-c+cd+bd+bc+ac-bcd-acd-abd-2abc+2abcd=0.....(1)
-bd+bc+bcd-ab+abd-2abcd+acd-c=0 .....(3)
ps:Those equations are not Boolean Equations.They are just normal polynomial equations which share the same solution set with the Boolean ones.

Guest

### Re: Solving polynomial simultaneous equations

The easies way is to check all combinations (0,0,0,0), (1, 0, 0, 0) ...
a=0, b=0, c=0, d=0 is not a solution because of this equation:
Guest

### Re: Solving polynomial simultaneous equations

thank u man.but would please tell me your method to sovle it?Is there any effective algerithm except the exhaustive search?
Guest

### Re: Solving polynomial simultaneous equations

So a = 0 or a = 1

Solve the system if a = 0 and then solve the system for a=1

if a = 0
we have:
-d-c+cd+bd+bc-bcd = 0
d-2bd+b+bcd-1=0
-bd+bc+bcd-c=0
-bd-bc+2bcd=0
Guest

### Re: Solving polynomial simultaneous equations

Agreed, look at the cases for 0 and 1.

In the first case where they all equal 0, since all four equations equal zero, you can equate the two sets of equations and use process of elimination. Hopefully that made sense.
olivia

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Joined: Sun Jun 17, 2012 5:27 pm