Hello

Consider

alias(x=x(t),y=y(t),phi1=phi1(x(t),y(t)));

phi:=[x,ph1];

I need to calculate the Jacobian of phi in relation to x and y (and finally to t)  but using VectorCalculus[Jacobian] does not work. I guess it is because of the time dependence.   What am I missing?  

Can the Physics package be used?

Many thanks.

Hello

I have a couple of large lists that will be further processed.  One of the steps is to index a list using another list (a list of indices).  A short example will be something like

L:=[2,1,4,3,7,6,8,3,4,5];
ind:=[2,2,3,3,5,6,7,1,4,10];

The solution 

L1:=L[ind]:

does not seem to be a good choice since it takes longer than the following solution

L1:=Threads:-Map(w->L[w],ind):

Since I am not a Maple expert, it is very likely that is a faster solution.   

Many thanks

Hello

I am trying to use Grid:-Seq to speed up some calculations.  To this end, I wrote the following procedure:

fun:=proc(model1::list,model2::list,vars::list,conds::set,tlim::numeric)
description "This function returns models with matching structures":
local ans1,ans2,res:=NULL:
if evalb(expand(model1)<>expand(model2)) then
     (ans1,ans2):=UtilsIORelation:-findMatchingStructures(subs(conds,model1),subs(conds,model2),vars,tlim):
     if nops(ans1) > 1 then
        res:=model1:
     end if:
end if:
return(res):
end proc:

I checked if the procedure works by issuing the following command

aux:=[seq](fun(modelX[i],model,vars,conds,2),i=1..nops(modelX)):

and it did work. The result is what I needed. 

But when I try it using Grid:-Seq instead of seq, I got the following error message:

infolevel[Grid:-Seq]:=3:
Grid:-Set(fun,findMatchingStructures,'model','vars','conds');
aux:=[Grid:-Seq](fun(modelX[i],model,vars,conds,2),i=1..nops(modelX)):

Error, (in fun) findMatchingStructures is not a command in the UtilsIORelation package.

What am I missing?   

Many thanks

Hello 

I need a procedure P that given two lists of sets A and B returns a list of lists L such that L[i] is the list of j such that A[i] subset B[j]. Here is an example:

ans6 := [{alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 8], alpha[3, 6], alpha[3, 9]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 8], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 6], alpha[3, 8]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 3], alpha[3, 8]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 2], alpha[2, 4], alpha[2, 5], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 1], alpha[2, 2], alpha[2, 5], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 0], alpha[2, 2], alpha[2, 5], alpha[3, 3], alpha[3, 6]}, {alpha[1, 5], alpha[2, 8], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 8]}]:

ans7 := [{alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 3], alpha[3, 6], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 7]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 4], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 4], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 9]}]:

and my procedure

SubsetPairs:= (A::list(set), B::list(set))->
    map(z-> [ListTools:-SearchAll](true, map(w-> z subset w, B)), A)
:
SubsetPairs(ans6, ans7);

The result of applying SubsetPairs is:

[[], [], [1], [1], [1], [], [], [], [2, 3, 8, 23], [2, 4, 9, 24], [2, 5, 10, 25], [2, 6, 11, 26], [2, 7, 12, 27], [3, 4, 13, 28], [3, 5, 14, 29], [3, 6, 15, 30], [3, 7, 16], [4, 5, 17], [4, 6, 18], [4, 7, 19]]

When it is used for long lists, it takes a long time to return the results.  I wonder if a more time- and memory-efficient code can be implemented (perhaps Threads or Grid can be used).

In addition to that, how can a diagram (figure, plot, ...) be drawn to show which subset of the first list is linked to which subsets of the second list (including no link as well).  The length of the first list is always smaller than the length of the second list.  

Many thanks

Hello

I am not familiar with the use of notsero in SolveTools:-PolynomialSystem. Is there any special syntax to use it?  In the following example, the trivial solution {x=0,y=0} is to be eliminated.  

SolveTools:-PolynomialSystem({x*(x^2 - 2), y*(y^2 - 2)}, {x, y},explicit=true)

If I issue the command

SolveTools:-PolynomialSystem({x*(x^2 - 2), y*(y^2 - 2)}, {x, y},{x,y},explicit=true)

all roots with either x=0 or y=0 are eliminated.  

Can netzero be used to eliminate only the trivial solution?  

Many thanks