MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Question about Solve and Reduce (mathematica 8)

  • To: mathgroup at
  • Subject: [mg114530] Re: Question about Solve and Reduce (mathematica 8)
  • From: Andrzej Kozlowski <akoz at>
  • 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:

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

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]


Reduce[a^2 x^2>==a^2 (x^2+1),x,Reals]

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

  • Prev by Date: Re: FileName Widget
  • Next by Date: Re: Counting number of numbers in a large list between two valus
  • Previous by thread: Question about Solve and Reduce (mathematica 8)
  • Next by thread: Re: How to get coefficient list from a