Re: Question about Solve and Reduce (mathematica 8)

*To*: mathgroup at smc.vnet.net*Subject*: [mg114530] Re: Question about Solve and Reduce (mathematica 8)*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 7 Dec 2010 06:44:14 -0500 (EST)

On 6 Dec 2010, at 03:53, olfa wrote: > Hi Mathematica Community, > > 1)now that Solve can handle inequalities in Mathematica 8, what is the > main difference between Solve and Reduce in finding solutions for a > given variable(s)? > 2)is it possible to let Solve give solutions not in terms of rules of > the form x->sol but as it is displayed by Reduce? > > Thank you very much. > There are a number of differences. For example, Solve will return {{}} when the set of solutions is full dimensional: Solve[Sqrt[x+1]<1-Sqrt[3x^3+1],x,Reals] During evaluation of In[423]:== Solve::fulldim: The solution set contains a full-dimensional component; use Reduce for complete solution information. >> {{}} while Reduce will give you the complete solution Reduce[Sqrt[x+1]<1-Sqrt[3x^3+1],x,Reals] Root[3 #1^3+1&,1]<==x<Root[9 #1^6-6 #1^4-6 #1^3+#1^2-2 #1-3&,1] Also, Solve only finds generic solutions, so: Solve[a^2 x^2>==a^2 (x^2+1),x,Reals] {} while Reduce[a^2 x^2>==a^2 (x^2+1),x,Reals] a====0 There are other differences too. On the whole Solve has the advantage in speed, Reduce in the completeness of the solutions it returns. Andrzej Kozlowski