kill(all)$

fluid :appendix :  G.grad(G) = grad(G).G
peter.vlasschaert@gmail.com,19/04/2019

website :  : fluid :appendix , vector identity 1,proof,version 1.0a,corrected.
==============================================================

 G.grad(G) = grad(G).G
===================

p1:('diff([G[x],G[y],G[z]],z,1))*G[z]+('diff([G[x],G[y],G[z]],y,1))*G[y]+G[x]*('diff([G[x],G[y],G[z]],x,1));

vector : G
=========

p1a:[G[x],G[y],G[z]];

coef :  { G[x],G[y],G[z]} ?

p2a:coeff(p1,G[x]);
p2b:coeff(p1,G[y]);
p2c:coeff(p1,G[z]);

representation :{p2a,p2b,p2c}

G => [G[x],G[y],G[z]]  , when use 'express' 

p3a:args(p2a);
p3b:args(p2b);
p3c:args(p2c);

combine :{p2a,p2b,p2c} = {p3a,p3b,p3c}
==================================
new : representation 
==================================

p4a:p2a=p3a;
p4b:p2b=p3b;
p4c:p2c=p3c;

rhs  = lhs

rem :
x : list p3a,derivative , number is the order.
y : list p3b,derivative , number is the order.
z : list p3c,derivative , number is the order.

see: document.
fluid :appendix , vector identity 1,proof,version 1.0a,corrected
peter.vlasschaert@gmail.com,19/04/2019

1e row Figure 1 , 'p7c1'
===================

use :  'p3a,p3b,p3c'
----------------

p5a:p3a;
p5b:p3b;
p5c:p3c;

rem : use 'p5a'
[[G[x],G[y],G[z]],x,1]

p6a :p5a[1];
p6b :p5a[2];
p6c :p5a[3];

new : representation,analog 'p4a,p4b,p4c'

p7a:[p1a[1],p5a[2],1] =' diff(p1a[1],p5a[2]);
p7b:[p1a[1],p5b[2],1] =' diff(p1a[1],p5b[2]);
p7c:[p1a[1],p5c[2],1]  =' diff(p1a[1],p5c[2]);

p8a:rhs(p7a)*p1a[1];
p8b:rhs(p7b)*p1a[2];
p8c:rhs(p7c)*p1a[3];

result :  same 'p7c1'
=================

p9:p8a+p8b+p8c;

component : representation : mathematical theory
==========================================

i=1,2,3
------------------------------------------------------------
p7a:[p1a[i],p5a[2],1] =' diff(p1a[i],p5a[2]);
p7b:[p1a[i],p5b[2],1] =' diff(p1a[i],p5b[2]);
p7c:[p1a[i],p5c[2],1]  =' diff(p1a[i],p5c[2]);
-------------------------------------------------------------
'see above,Figure 1'
-------------------------------------------------------------
i=1   = >  'p7c1'
i=2   = >  'p7c2'
i=3   = >  'p7c3'

'------------------------------------------------------------------------------------------------------'