Re: Strange result of solve
- To: mathgroup at smc.vnet.net
- Subject: [mg132420] Re: Strange result of solve
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Tue, 11 Mar 2014 03:37:08 -0400 (EDT)
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- References: <20140310084113.E8ECC6A3B@smc.vnet.net>
Reduce is generally more powerful than Solve and indicates that the
expression is True, i.e., valid for all integers, x.
Reduce[5 x==0,x,Modulus->5]
True
In your second example, the result of {{}} does not mean that every x is OK
but rather that there is no solution for x.
Attributes[Solve]
{Protected}
Since Solve does NOT have either the attribute HoldFirst or HoldAll, your
second example is equivalent to
Solve[True,x,Modulus->5]
{{}}
That is, there is no solution for x since x does not appear in the
expression. You can verify this with
Solve[0 x==0,x,Modulus->5]//Trace
{{{0 x,0},0==0,True},{Modulus->5,Modulus->5},Solve[True,x,Modulus->5],{{}}}
Bob Hanlon
On Mon, Mar 10, 2014 at 4:41 AM, Wiel Aerts <wiel.aerts at xs4all.nl> wrote:
>
>
> I cannot really understand the different results of the following:
>
> Solve[ 5 x == 0, x, Modulus-> 5 ]
> result: {{x-> 0}}
>
> and:
>
> Solve[ 0 x == 0, x, Modulus-> 5 ]
> result: {{}}
>
> The last means that every x is OK. Which I think is true. But I would
> expect the same result for the first case.
>
> What am I missing?
>
> Wiel
>
> I'm using MTM v9.
>
>
>
- References:
- Strange result of solve
- From: Wiel Aerts <wiel.aerts@xs4all.nl>
- Strange result of solve