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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
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