       Re: Eigenvalues, eigenvectors, matrix ranks, determinants, and all that stuff

• To: mathgroup at smc.vnet.net
• Subject: [mg125507] Re: Eigenvalues, eigenvectors, matrix ranks, determinants, and all that stuff
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Fri, 16 Mar 2012 06:32:17 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```On 3/15/12 at 12:31 AM, kparchevsky at gmail.com (Konstantin) wrote:

<snip>

>Very often algebraic manipulations in Mathematica do not produce
>expected result just because we and the program have different
>defaul assumptions about type of variables. So I tried to specify
>EVERYTHING about my variables explicitly ( @ means "belongs to", !=
>means "not equal" )

>\$Assumptions = u@Reals && u!=0 && Bx@Reals && By@Reals && Bz@Reals
>&& Bx!=0 && By!=0 && Bz!=0 && rho>0 && cs>0;

Unless you have re-defined @ (an ill advised thing to do) you
are not repeat not free to use it to do something other than the
built-in definition. That is Mathematica interprets u@Reals as
the function u with argument Reals, i.e:

In:= u@Reals

Out= u(\[DoubleStruckCapitalR])

If you want to declare u to be a real variable use the function
Element that performs exactly this function That is the statement

{u, Bx, By, Bz} \[Element] Reals

defines the list of variables all to be real.

And note,

In:= Reduce[{Element[x, Reals] && x != 0}, x]

Out= x<0\[Or]x>0

That is stating x != 0 is sufficient to declare x to be real
since the comparison of x to 0 is not valid unless x is real

```

• Prev by Date: Re: Clearing a Checkbox
• Next by Date: Re: Using Mathematica to typeset books
• Previous by thread: Eigenvalues, eigenvectors, matrix ranks, determinants, and all that stuff
• Next by thread: Re: Eigenvalues, eigenvectors, matrix ranks, determinants, and all that stuff