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NumberTheory`Recognize`
This package defines the function Recognize for determining a polynomial with integer coefficients, given an approximate real zero of the polynomial and the degree of the polynomial. The resulting polynomial is normally not unique.
Determining a polynomial from a solution.
This loads the package.
In[1]:= << NumberTheory`Recognize`
This finds a linear polynomial in t with solution 1.7.
In[2]:= Recognize[1.7, 1, t]
Out[2]= 
NSolve gives the numerical solutions of a cubic equation.
In[3]:= NSolve[3 x^3 - 2 x + 5 == 0]
Out[3]= 
Here is the first solution.
In[4]:= sol = First[x /. %]
Out[4]= 
This result is proportional to the original polynomial used in NSolve.
In[5]:= Recognize[sol, 3, t]
Out[5]= 
Here is a quadratic polynomial for which sol is an approximate solution.
In[6]:= Recognize[sol, 2, t]
Out[6]= 
This result is a polynomial of degree 5.
In[7]:= Recognize[N[Sqrt[3^(2/5)]], 5, t]
Out[7]= 
If the penalty is large enough, a lower-order polynomial may be returned.
In[8]:= Recognize[N[Sqrt[3^(2/5)]], 5, t, 10]
Out[8]= 
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | 
