Hi.
When we write programs, sometimes we obtain some formulas in real or integer moods.
For instance in Integer mood:
formula with integer coefficients: (1 -2x2+1 x2^2+x1 (-2+4 x2-2 x2^2)+x1^2 (1 -2 x2+1 x2^2)).
When we use FullSimplify , we have :
Input: FullSimplify[(1 -2x2+1 x2^2+x1 (-2+4 x2-2 x2^2)+x1^2 (1 -2 x2+1 x2^2))]
Output: (-1+x1)^2 *(-1+x2)^2 .
It works well here. But when we have the formula by real coefficients and use FullSimplify command:
formula with real coefficients: (1. -2. x2+1. x2^2+x1 (-2.+4. x2-2. x2^2)+x1^2 (1. -2. x2+1. x2^2))
Input: FullSimplify[(1 -2x2+1 x2^2+x1 (-2+4 x2-2 x2^2)+x1^2 (1 -2 x2+1 x2^2))]
Output: 1. +x2 (-2.+1. x2)+x1 (-2.+x2 (4. -2. x2))+x1^2 (1. +x2 (-2.+1. x2)).
We obtain a bad form of formula. How to solve this problem so that we can have the simplest form of a formula by real coefficients?
It's a pity, but FullSimplify and real numbers are incompatible.
The reason is very simple: the real number 1.0 only seems similar to 1, in fact it can be stored as 0.99999999999999987 or as 1.000000000000000003.
So 1.x^2 +2.x+1.0 actually looks like this
0.99999999999999987*x^2+2.000000000000000071*x+1.0000000000000003.
Obviously, this expression is not at all equivalent to (1+x)^2
Hi!
You can replace all the real coefficients in your formula by their closest integers
In[12]:= formulaReal = (1. - 2. x2 + 1. x2^2. +
x1 (-2. + 4. x2 - 2. x2^2) + x1^2 (1. - 2. x2 + 1. x2^2.));
In[13]:= formulaInteger = formulaReal /. c_Real -> Round[c]
Out[13]= 1 - 2 x2 + x2^2 + x1 (-2 + 4 x2 - 2 x2^2) +
x1^2 (1 - 2 x2 + x2^2)
In[14]:= FullSimplify[formulaInteger]
Out[14]= (-1 + x1)^2 (-1 + x2)^2
Hi
I copied and pasted your expression, and I am getting this:
In[2]:= FullSimplify[(1. - 2. x2 + 1. x2^2 + x1 (-2. + 4. x2 - 2. x2^2) +
x1^2 (1. - 2. x2 + 1. x2^2))]
Out[2]= (1. + x1 (-2. + 1. x1)) (1. - 1. x2)^2
I don't see a problem.
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