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Re: Re: [Help]How to reprensent the result in vector form?

• To: mathgroup at smc.vnet.net
• Subject: [mg51594] Re: [mg51584] Re: [Help]How to reprensent the result in vector form?
• From: DrBob <drbob at bigfoot.com>
• Date: Wed, 27 Oct 2004 01:53:53 -0400 (EDT)
• References: <cl9t1d$7m0$1@smc.vnet.net> <200410230422.AAA26310@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

This won't always work, however.

crossrule = {a3_ b2_ - a2_ b3_, a1_ b3_ - a3_ b1_,
   a2_ b1_ - a1_ b2_} -> myCross[{b1, b2, b3}, {a1, a2, a3}];

Cross[{u1, u2, u3}, {v1, v2, v3}] /. crossrule
myCross[{u1,u2,u3},{v1,v2,v3}]

Fine so far, but these should return cross products too:

Cross[{-u1,u2,u3},{v1,v2,v3}]/.crossrule
{-u3 v2+u2 v3,u3 v1+u1 v3,-u2 v1-u1 v2}

Cross[{u1,-u2,u3},{v1,v2,v3}]/.crossrule
{-u3 v2-u2 v3,u3 v1-u1 v3,u2 v1+u1 v2}

Cross[{u1,u2,-u3},{v1,v2,v3}]/.crossrule
{u3 v2+u2 v3,-u3 v1-u1 v3,-u2 v1+u1 v2}

Besides this problem there are other issues, such as:

(1) EVERY vector is the cross product of two vectors,

and

(2) The vectors are never unique.

Good luck!!

Bobby

On Sat, 23 Oct 2004 00:22:49 -0400 (EDT), Steve Luttrell <steve_usenet at _removemefirst_luttrell.org.uk> wrote:

> You can use a replacement rule to convert your expression into the compact
> form that you want:
>
> Define the replacement rule.
>
> crossrule = {a3_ b2_ -a2_ b3_,a1_ b3_ -a3_ b1_,a2_ b1_ -a1_ b2_} ->
> myCross[{b1,b2,b3},{a1,a2,a3}];
>
> Apply the rule to your expression.
>
> result = {-u3 v2 + u2 v3, u3 v1 - u1 v3, -u2 v1 + u1 v2}/.crossrule
>
> which gives the output
>
> myCross[{u1,u2,u3},{v1,v2,v3}]
>
> You could make the notation more compact by doing this
>
> result /. {{u1,u2,u3} -> u,{v1,v2,v3} -> v}
>
> which gives the output
>
> myCross[u,v]
>
> Another (related but more sophisticated) method is to use the
> Utilities`Notation` package to implement the reformatting of your output
> automatically. This includes a way of defining infix operators so that you
> can get an output that looks like u x v rather than myCross[u,v]
>
> Steve Luttrell
>
> "melon" <sweetmelon at gmail.com> wrote in message
> news:cl9t1d$7m0$1 at smc.vnet.net...
>> I used mathmetica5 to solve a vector equation. Mathmetica expands the
>> result into sub-variable form. But I want to get the vector form. How
>> to do that?
>>
>> ex:
>> Solution:
>> {-u3 v2 + u2 v3, u3 v1 - u1 v3, -u2 v1 + u1 v2}
>> I want mathematica give me {u cross v}
>>
>> p,s,  Could you add me into the forum? Thank you very much. Regards.
>>
>> ShenLei
>>
>
>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net

• References:
  • Re: [Help]How to reprensent the result in vector form?
    • From: "Steve Luttrell" <steve_usenet@_removemefirst_luttrell.org.uk>