Sqrt Tip

*To*: mathgroup at smc.vnet.net*Subject*: [mg3032] Sqrt Tip*From*: BobHanlon at aol.com*Date*: Wed, 24 Jan 1996 03:34:42 -0500

Mathematica version 2.2 on a Macintosh does not simplify the product of square roots: In[1]:= Sqrt[x] Sqrt[y] // Simplify Out[1]= Sqrt[x] Sqrt[y] As a result, it overlooks some straightforward simplifications. For example, In[2]:= Sqrt[1-x] Sqrt[1+x]/Sqrt[1 - x^2] // Simplify Out[2]= Sqrt[1 - x] Sqrt[1 + x] ----------------------- 2 Sqrt[1 - x ] One would like to modify the definition of Sqrt to correct this as follows: In[3]:= Unprotect[Sqrt]; Sqrt/: Sqrt[a_] Sqrt[b_] := Sqrt[a b]; Protect[Sqrt]; This generates the error message TagSetDelayed::tagnf: Tag Sqrt not found in Sqrt[a_] Sqrt[b_]. The reason that this failed is apparent if the FullForm of Sqrt is inspected In[6]:= Sqrt[x] // FullForm Out[6]//FullForm= Power[x, Rational[1, 2]] Sqrt is represented internally using Power. Consequently, the modification must be made to Power rather than Sqrt. In[7]:= Unprotect[Power]; Power/: Sqrt[a_] Sqrt[b_] := Sqrt[a b]; Protect[Power]; After, modifying Power we obtain the desired result: In[10]:= Sqrt[1-x] Sqrt[1+x]/Sqrt[1 - x^2] // Simplify Out[10]= 1 _______________ Bob Hanlon bobhanlon at aol.com ==== [MESSAGE SEPARATOR] ====