This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 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]=