MaplePrimes Questions

restart;
with(GraphTheory);
with(combinat, cartprod);
with(SpecialGraphs);
with(RandomGraphs);

Given any arbitary graph G how many possible paths of length k are possible

G := CartesianProduct(PathGraph(3), PathGraph(3));
s := AllPairsDistance(FLT)

How to find how may possible paths of length say 4 from vertex 1:1 

" for example this CartesianProduct(Path(3),Path(3)) number of possible paths of length 2 are

1:1 - 1:2 -2:2

1:1 -2:1-2:2

1:1-1:2 -1:3

1:1-2:1-3:1

so a total of 2 length paths 

next say how may possible paths of length say 3 from vertex 1:2

similar given a vertex and path length how many possible path of that length are possible from that vertex.

It is not restricted to this graph given any graph G in general , a vertex v and k a path length i should get total number of paths of that length in that graph G

That is function say   F(G::Graph,vertex,k) i should get output of the number of path of length k from that vertex v. 

"Only a idea but I may be wrong 

I had an idea taking a row of a vertex in the graph G in the shortest path matrix and finding the number of possible totals which can get  length k I may be wrong to or correct but I finding to implement this in code neatly too.

That is if (0,1,2,1,3,4,1,2)

The number of possible 2 this are 

0+2=2

0+2=2

1+1=2

1+1=2

1+1=2

So a total of 5 , 2 length path with respect to that vertex moving from left to right

Again if number of 3 length paths 

Moving left to right

0+3=3

1+2=3

1+1+1=3

1+2=3

2+1=3

2+1=3

1+2=3

1+2=3

Total 8 paths of length 3

Until maximum possible length path from that vertex with respect to that graph.

Their is a mistake in the above logic is if the length paths intersection in some edges the path length will decrease so need to be careful so it looks difficult for me.

But I may be wrong in logic need help."

I am trying too

Kind help please your answer will be acknowledged 

Kind help 

Kind help someone please 

I use Int to show some step before evaluating it to become normal int

I'd like to show the following when the integrand is one:

But Int(x) does not work, and Int(,x) gives syntax error. So only choice is to use Int(1,x) which does not look as nice as the above

Is there a trick to use? i.e. when the integrand is one, I want to display it as the first image and not as the second image. This is just to make the Latex look a little nicer only.

I tried few things, but nothing worked so far, as Int needs something there where I want the empty spot to be (There is actually 1 there ofcourse, but I do not want to show the 1).

May be we need a Latex settings for this?  Or interface setting?

Maple 2022.1

Hi,

Please can someone help me with a sample code for bifurcation? You can use parameter values for the parameters. I'm using maple 18. Below is my model:

restart:

f__1 := Delta -(psi + mu)*S(t);

Delta-(psi+mu)*S(t)

(1)

f__2 := psi*S(t) -(delta + mu)*E(t);

psi*S(t)-(delta+mu)*E(t)

(2)

f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);

Delta*E(t)-(gamma+gamma__1+mu)*X(t)

(3)

f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);

gamma__1*X(t)-(eta+xi+mu)*H(t)

(4)

f__5 := xi*H(t) - mu*R(t);

xi*H(t)-mu*R(t)

(5)

f__6 := gamma*X(t)-eta*H(t) - d*D(t);

gamma*X(t)-eta*H(t)-d*D(t)

(6)

f__7 := b*D(t) - b*B(t);

b*D(t)-b*B(t)

(7)

f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);

phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t)

(8)

 

NULL

Download Bifurcation.mw

Please I need your assistance. I want to solve for c__4, c__5, c__6, and c__8  from 4 systems of the equation: See my code below:

Since there 4 equations and 4 unknowns, is it possible to get the result explicitly without setting c__6=c__8 as maple did? The solution is at the end of the maple file.

LSA.mw
 

``

## "Note that I use I(t) = X(t)""  and S^(*),E^(*), I^(*), H^(*), B^(*), D^(*), R^(*), P^(*) = (`S__1`,`E__1`,`I__1`,`H__1`,`B__1`,`D__1`,`R__1`,`P__1`,) thorought the work."

###

###

restart:

f__1 := Delta -(psi + mu)*S(t);

Delta-(psi+mu)*S(t)

(1)

f__2 := psi*S(t) -(delta + mu)*E(t);

psi*S(t)-(delta+mu)*E(t)

(2)

f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);

Delta*E(t)-(gamma+gamma__1+mu)*X(t)

(3)

f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);

gamma__1*X(t)-(eta+xi+mu)*H(t)

(4)

f__5 := xi*H(t) - mu*R(t);

xi*H(t)-mu*R(t)

(5)

f__6 := gamma*X(t)-eta*H(t) - d*D(t);

gamma*X(t)-eta*H(t)-d*D(t)

(6)

f__7 := b*D(t) - b*B(t);

b*D(t)-b*B(t)

(7)

f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);

phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t)

(8)

S__1 := Delta/mu - a__1*E__1/mu: X__1:= delta*E__1/a__2: H__1 := delta*gamma__1*E__1/a__2*a__3: R__1 := delta*gamma__1*xi*E__1/a__2*a__3*mu: B__1 := 1/b*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: D__1 := 1/d*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: P__1 := (1/alpha)*(delta*sigma/a__2 + delta*eta*gamma__1/a__2*a__3 + (d__1/d - b__1/b)*(delta*gamma/a__2 + delta*eta*gamma__1/a__2*a__3))*E__1 + phi__p/alpha:

M__1 := c__1*f__1*(1-S__1/S(t));

c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t))

(9)

M__2 := c__2*f__2*(1-E__1/E(t));

c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t))

(10)

M__3 := c__3*f__3*(1-X__1/X(t));

0

(11)

M__4 :=c__4*f__4*(1-H__1/H(t));

c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)))

(12)

M__5 := c__5*f__5*(1-R__1/R(t));

c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)))

(13)

M__6 := c__6*f__6*(1-D__1/D(t));

c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)))

(14)

M__7 := c__7*f__7*(1-B__1/B(t));

0

(15)

M__8 := c__8*f__8*(1-P__1/P(t));

0

(16)

restart:

u__1 := (psi+mu)*S__1;

(psi+mu)*S__1

(17)

u__2 := psi*S__1;

psi*S__1

(18)

u__3 := delta*E__1;

delta*E__1

(19)

u__4 := gamma__1*X__1;

gamma__1*X__1

(20)

u__5 := xi*H__1;

xi*H__1

(21)

u__6 := gamma*X__1 + eta*H__1;

H__1*eta+X__1*gamma

(22)

u__7 := b*D__1;

b*D__1

(23)

u__8 := phi__p + sigma*X__1+eta__1*H__1 +d__1*D__1+ b__1*B__1;

B__1*b__1+D__1*d__1+H__1*eta__1+X__1*sigma+phi__p

(24)

M__1 := c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t));

c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t))

(25)

M__2 := c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t));

c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t))

(26)

M__3 := c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)));

c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)))

(27)

M__4 := c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)));

c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)))

(28)

M__5 := c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)));

c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)))

(29)

M__6 := c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)));

c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)))

(30)

M__7 := c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)));

c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)))

(31)

M__8 := c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t));

c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t))

(32)

J := M__1 + M__2 + M__3 + M__4 + M__5 + M__6 + M__7 + M__8;

c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t))+c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t))+c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)))+c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)))+c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)))+c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)))+c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)))+c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t))

(33)

##

L__1 := factor(expand(subs(Delta=u__1, M__1)));

-c__1*(psi+mu)*(S(t)-S__1)*(a__1*E__1+S(t)*mu-S__1*mu-psi*S__1)/(S(t)*mu)

(34)

L__2 := expand(subs((delta+mu)*E(t)=u__2, M__2));

c__2*psi*S(t)-c__2*psi*S(t)*E__1/E(t)-c__2*psi*S__1+c__2*psi*S__1*E__1/E(t)

(35)

L__3 := expand(subs((gamma+gamma__1+mu)*X(t)=u__3, M__3));

c__3*Delta*E(t)-c__3*Delta*E(t)*delta*E__1/(a__2*X(t))-c__3*delta*E__1+c__3*delta^2*E__1^2/(a__2*X(t))

(36)

L__4 := expand(subs((eta+xi+mu)*H(t)=u__4, M__4));

c__4*gamma__1*X(t)-c__4*gamma__1^2*X(t)*delta*E__1*a__3/(a__2*H(t))-c__4*gamma__1*X__1+c__4*gamma__1^2*X__1*delta*E__1*a__3/(a__2*H(t))

(37)

L__5 := expand(subs(mu*R(t)=u__5, M__5));

c__5*xi*H(t)-c__5*xi^2*H(t)*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))-c__5*xi*H__1+c__5*xi^2*H__1*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))

(38)

L__6 := expand(subs(d*D(t)=u__6, M__6));

c__6*gamma*X(t)-c__6*gamma^2*X(t)*E__1*delta/(d*D(t)*a__2)-c__6*gamma*X(t)*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__6*eta*H(t)+c__6*eta*H(t)*E__1*gamma*delta/(d*D(t)*a__2)+c__6*eta^2*H(t)*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__6*eta*H__1+c__6*eta*H__1*E__1*gamma*delta/(d*D(t)*a__2)+c__6*eta^2*H__1*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__6*gamma*X__1+c__6*gamma^2*X__1*E__1*delta/(d*D(t)*a__2)+c__6*gamma*X__1*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)

(39)

L__7 := expand(subs(b*B(t)=u__7, M__7));

c__7*b*D(t)-c__7*D(t)*E__1*gamma*delta/(B(t)*a__2)-c__7*D(t)*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)-c__7*b*D__1+c__7*D__1*E__1*gamma*delta/(B(t)*a__2)+c__7*D__1*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)

(40)

L__8 := expand(subs(alpha*P(t)=u__8, M__8));

-c__8*sigma*X(t)*phi__p/(P(t)*alpha)-c__8*eta__1*H(t)*phi__p/(P(t)*alpha)-c__8*d__1*D(t)*phi__p/(P(t)*alpha)-c__8*b__1*B(t)*phi__p/(P(t)*alpha)+c__8*b__1*B__1*phi__p/(P(t)*alpha)-c__8*eta__1*H(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*d__1*D(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*D__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*sigma*X(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*X(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*H(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*d__1*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*D(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*d__1*D__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1*D(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1*D__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*eta__1*H__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*sigma^2*X(t)*E__1*delta/(P(t)*alpha*a__2)+c__8*sigma^2*X__1*E__1*delta/(P(t)*alpha*a__2)-c__8*sigma*X__1-c__8*d__1*D__1-c__8*eta__1*H__1-c__8*b__1*B__1+c__8*sigma*X(t)+c__8*d__1*D(t)+c__8*eta__1*H(t)+c__8*b__1*B(t)-c__8*d__1^2*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*D(t)*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*phi__p/(P(t)*alpha)+c__8*eta__1*H__1*phi__p/(P(t)*alpha)+c__8*sigma*X__1*phi__p/(P(t)*alpha)-c__8*eta__1*H__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*sigma*X__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)

(41)

L := L__1 + L__2 + L__3 + L__4 + L__5 + L__6 + L__7 + L__8;

-c__1*(psi+mu)*(S(t)-S__1)*(a__1*E__1+S(t)*mu-S__1*mu-psi*S__1)/(S(t)*mu)-c__8*sigma*X(t)*phi__p/(P(t)*alpha)-c__8*eta__1*H(t)*phi__p/(P(t)*alpha)-c__8*d__1*D(t)*phi__p/(P(t)*alpha)-c__8*b__1*B(t)*phi__p/(P(t)*alpha)+c__8*b__1*B__1*phi__p/(P(t)*alpha)-c__3*Delta*E(t)*delta*E__1/(a__2*X(t))-c__7*D(t)*E__1*gamma*delta/(B(t)*a__2)+c__7*D__1*E__1*gamma*delta/(B(t)*a__2)+c__6*eta*H(t)*E__1*gamma*delta/(d*D(t)*a__2)+c__6*eta*H__1*E__1*gamma*delta/(d*D(t)*a__2)-c__7*D(t)*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)+c__7*D__1*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)-c__8*eta__1*H(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*d__1*D(t)*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*D__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__5*xi^2*H(t)*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__5*xi^2*H__1*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__6*eta^2*H(t)*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)+c__6*eta^2*H__1*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__6*gamma*X(t)*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)+c__6*gamma*X__1*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__8*sigma*X(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*X(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*H(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*d__1*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*D(t)*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*B(t)*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*d__1*D__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*X(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*eta__1*H(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*H(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1*D(t)*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1*B(t)*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1*D__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*eta__1*H__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__4*gamma__1^2*X(t)*delta*E__1*a__3/(a__2*H(t))+c__4*gamma__1^2*X__1*delta*E__1*a__3/(a__2*H(t))-c__6*gamma^2*X(t)*E__1*delta/(d*D(t)*a__2)+c__6*gamma^2*X__1*E__1*delta/(d*D(t)*a__2)-c__8*sigma^2*X(t)*E__1*delta/(P(t)*alpha*a__2)+c__8*sigma^2*X__1*E__1*delta/(P(t)*alpha*a__2)-c__2*psi*S(t)*E__1/E(t)+c__2*psi*S__1*E__1/E(t)+c__3*delta^2*E__1^2/(a__2*X(t))+c__2*psi*S(t)-c__2*psi*S__1+c__3*Delta*E(t)-c__3*delta*E__1-c__4*gamma__1*X__1+c__4*gamma__1*X(t)+c__5*xi*H(t)-c__5*xi*H__1+c__6*gamma*X(t)-c__6*eta*H(t)-c__6*eta*H__1-c__6*gamma*X__1-c__7*b*D__1+c__7*b*D(t)-c__8*sigma*X__1-c__8*d__1*D__1-c__8*eta__1*H__1-c__8*b__1*B__1+c__8*sigma*X(t)+c__8*d__1*D(t)+c__8*eta__1*H(t)+c__8*b__1*B(t)-c__8*d__1^2*D(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*D(t)*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1^2*B(t)*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1^2*B__1*E__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*phi__p/(P(t)*alpha)+c__8*eta__1*H__1*phi__p/(P(t)*alpha)+c__8*sigma*X__1*phi__p/(P(t)*alpha)-c__8*eta__1*H__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*sigma*X__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)

(42)

## Collecting the coefficients of X, H, D, B and E

k__1 := coeff(L,X(t));

-c__8*sigma*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__6*gamma^2*E__1*delta/(d*D(t)*a__2)-c__8*sigma^2*E__1*delta/(P(t)*alpha*a__2)-c__4*gamma__1^2*delta*E__1*a__3/(a__2*H(t))-c__8*sigma*phi__p/(P(t)*alpha)-c__6*gamma*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__8*sigma*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma+c__4*gamma__1+c__6*gamma

(43)

k__2 := coeff(L,H(t));

-c__5*xi^2*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__6*eta^2*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__8*eta__1*phi__p/(P(t)*alpha)-c__8*eta__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__6*eta+c__5*xi+c__8*eta__1+c__6*eta*E__1*gamma*delta/(d*D(t)*a__2)-c__8*eta__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

(44)

k__3 := coeff(L, D(t));

-c__7*E__1*gamma*delta/(B(t)*a__2)-c__8*d__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*E__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*d__1*phi__p/(P(t)*alpha)-c__8*d__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1+c__7*b-c__7*E__1*delta*eta*gamma__1*a__3/(B(t)*a__2)-c__8*d__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

(45)

k__4 := coeff(L, B(t));

c__8*b__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*b__1^2*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*phi__p/(P(t)*alpha)-c__8*b__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1-c__8*b__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)

(46)

k__5 := coeff(L, E(t));

-c__3*Delta*delta*E__1/(a__2*X(t))+c__3*Delta

(47)

##

## L terms that not coeffiecient X, H, D, B and E

W__12 := coeff(L, X(t), 0):

W__1 := coeff(W__12, H(t), 0):

W__11 := coeff(W__1, D(t), 0):

W__12 := coeff(W__11, B(t), 0):

k__6 := coeff(W__12, E(t), 0);

-c__1*(psi+mu)*(S(t)-S__1)*(a__1*E__1+S(t)*mu-S__1*mu-psi*S__1)/(S(t)*mu)+c__8*b__1*B__1*phi__p/(P(t)*alpha)+c__8*b__1*B__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*D__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__5*xi^2*H__1*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__8*b__1*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*b__1*B__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*d__1*D__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*eta__1*H__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1*B__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1*D__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*eta__1*H__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*eta__1*H__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*sigma^2*X__1*E__1*delta/(P(t)*alpha*a__2)+c__2*psi*S(t)-c__2*psi*S__1-c__3*delta*E__1-c__4*gamma__1*X__1-c__5*xi*H__1-c__6*eta*H__1-c__6*gamma*X__1-c__7*b*D__1-c__8*sigma*X__1-c__8*d__1*D__1-c__8*eta__1*H__1-c__8*b__1*B__1-c__8*b__1^2*B__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*b__1^2*B__1*E__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1^2*D__1*E__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*d__1*D__1*phi__p/(P(t)*alpha)+c__8*eta__1*H__1*phi__p/(P(t)*alpha)+c__8*sigma*X__1*phi__p/(P(t)*alpha)-c__8*eta__1*H__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma*X__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*sigma*X__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*sigma*X__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)

(48)

## from k__5, c__3 = 0 and choose c__1 = c__2 and c__3 =c__7

c__3 := 0:  c__7:=0:

k__1;

-c__8*sigma*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)-c__6*gamma^2*E__1*delta/(d*D(t)*a__2)-c__8*sigma^2*E__1*delta/(P(t)*alpha*a__2)-c__4*gamma__1^2*delta*E__1*a__3/(a__2*H(t))-c__8*sigma*phi__p/(P(t)*alpha)-c__6*gamma*E__1*delta*eta*gamma__1*a__3/(d*D(t)*a__2)-c__8*sigma*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*sigma*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*sigma*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*sigma+c__4*gamma__1+c__6*gamma

(49)

k__2;

-c__5*xi^2*delta*gamma__1*E__1*a__3*mu/(a__2*R(t))+c__6*eta^2*E__1*delta*gamma__1*a__3/(d*D(t)*a__2)-c__8*eta__1*phi__p/(P(t)*alpha)-c__8*eta__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)-c__6*eta+c__5*xi+c__8*eta__1+c__6*eta*E__1*gamma*delta/(d*D(t)*a__2)-c__8*eta__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*eta__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)+c__8*eta__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

(50)

k__3;

-c__8*d__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)-c__8*d__1^2*E__1*gamma*delta/(P(t)*alpha*d*a__2)-c__8*d__1*phi__p/(P(t)*alpha)-c__8*d__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*gamma*delta/(P(t)*alpha*b*a__2)+c__8*d__1-c__8*d__1*E__1*delta*sigma/(P(t)*alpha*a__2)+c__8*d__1*E__1*b__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)

(51)

k__4;

c__8*b__1^2*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*b*a__2)+c__8*b__1^2*E__1*gamma*delta/(P(t)*alpha*b*a__2)-c__8*b__1*phi__p/(P(t)*alpha)-c__8*b__1*E__1*delta*eta*gamma__1*a__3/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*gamma*delta/(P(t)*alpha*d*a__2)+c__8*b__1-c__8*b__1*E__1*delta*sigma/(P(t)*alpha*a__2)-c__8*b__1*E__1*d__1*delta*eta*gamma__1*a__3/(P(t)*alpha*d*a__2)

(52)

## Also choose

sys := solve({k__1=0, k__2 =0, k__3=0, k__4=0}, [c__4,c__5, c__6, c__8]);

[[c__4 = -H(t)*gamma*(E__1*a__3*delta*eta*gamma__1+E__1*gamma*delta-D(t)*a__2*d)*c__6/(D(t)*d*gamma__1*(E__1*a__3*delta*gamma__1-H(t)*a__2)), c__5 = R(t)*eta*(E__1*a__3*delta*eta*gamma__1+E__1*gamma*delta-D(t)*a__2*d)*c__6/(D(t)*d*xi*(E__1*a__3*delta*mu*xi*gamma__1-R(t)*a__2)), c__6 = c__6, c__8 = 0]]

(53)

#

#

``


 

Download LSA.mw

 

How can i see analytical maple calculations?

I recently got introduced to fractional calculus, I saw this image on the internet and went to verify the 3rd block of image i.e fractional differentiation on Maple 2022. But Maple returned answer which does not match the result claimed in the image i.e x. I want to know what I am missing here. But when used fracdiff() the answer matches.I also wanted to know how its done by using showSolution command but didn't get the answer. Can I get the steps? meme.mw


f := diff(x, [`$`(x, 1/2)])

x

(1)

``

evalb(diff(x, [`$`(x, 1/2)]) = x)

true

(2)

evalb(diff(x, [`$`(x, 1/2)]) = 2*sqrt(x/Pi))

false

(3)

ShowSolution(diff(x, x^(1/2)))

Error, invalid input: diff received x^(1/2), which is not valid for its 2nd argument

 

fracdiff(x, x, 1/2)

2*x^(1/2)/Pi^(1/2)

(4)

ShowSolution(fracdiff(x, x, 1/2))

Error, (in Student:-Calculus1:-ShowSolution) input expression does not have any incomplete calculus operations

 

NULL


Download meme.mw

 

Non-Linear.mw

Hi, I have here a interesting non-linear system.

If I attempt to solve it using some specific form of the non-linear equations (form X*Y=Z) of the system, Maple (Verison 18) finds a solution.

But, if I replace some of them by some other forms (like form Y=Z/X), fsolve fails.

I usually use the non-quotient form. But is there any way to guide or configure fsolve to reach a solution?
I set up some of the regular options: placing a seed close to the solution, indicating intervals of possible solutions; but none of that works if I do not set up the non-quotient form of the equations. In some cases, fsolve does not reach a solution at all, no matter the form of the equations.

In the file, the equations that are causing the isssue are the last 3, those who start with the variable f1,f2 and f3.
I ran the system twice with both cases: non-quotient form and quotient form.

Thanks for your attention! 

Consider the following integral, shown below in this image.

>> Link to the Maple sheet: example.mw <<

Why does Maple provide erroneous results? Is there a bug in the software? I use Maple 2021.

I am curious to know steps of integration for e^(t^3)*(cos(t))^3 as Maple found the answer correctly. So I wanted to know how it got to that solution. I applied the commands shown in document but unable to get steps. I want to know the reason for this and is it possible to get it work.
 

``

exp(t^2)*cos(t)^3

int(exp(t^2)*cos(t)^3, t)

-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t+3/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t+1/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t-1/2)-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t-3/2)

(1)

Student[Calculus1][IntTutor]()

eval(-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t+3/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t+1/2)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(I*t-1/2)-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(I*t-3/2), [t = 1])

-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2+I)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2+I)+((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2-I)+((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2-I)

(2)

evalf[10](-((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2+I)-((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2+I)+((3/16)*I)*Pi^(1/2)*exp(1/4)*erf(1/2-I)+((1/16)*I)*Pi^(1/2)*exp(9/4)*erf(3/2-I))

.8154967124+0.*I

(3)

        
with(Student:-Calculus1):

 

 

Understand(Int, constant, constantmultiple, sum, difference)

ShowSolution(Int(exp(t^2)*cos(t)^3, t), maxsteps = 1000)

Error, (in Student:-Calculus1:-ShowSolution) unable to compute solution steps

 

NULL


 

Download e.mwe.mw

 

Derar All

I'm trying ot adapt some old Maple V code to a new Maple 2022 Module/Package and have an issue understanding if the "ModuleLoad" process does really run automatically with the "> with(TST); " command ?
the "> restart;" runs the ModuleUnload though, but for me the ModuleLoad does not seem to run when I expect it to !?

Sincerely

Ivar

Any comment appreciated ?
the test code :

====================

Tst := module()
  local ModuleLoad, ModuleUnload;
  export MyProc;
  global AAA;
  option package;
  ModuleLoad := proc()
      global AAA;
      AAA := 1;
      print("Hello Module");
  end proc;
  ModuleUnload := proc()
      print("Bye Module");
  end proc;
  MyProc := proc()
      print("Hello from Core");
  end proc;
end module ;

When was ?define, forall stripped from Maple?
Define used to accept all of these: Group, Linear, forall, antisymmetric, associative, binary, commutative, identity, inverse, symmetric, type, unary, zero. Was this function moved to another package?

How can I define an arbitrary signature of a space-time metric?

I want to define the signature of the form `++--`.

Multibody exports from MapleSim to Maple convert a symbolic expression to a rational quotient:

The parameters (parameter "a" above) disappear in the exported equations. How can I prevent this (conversion of sqrt3 and disapprence of "a")?

MB_exports_with_rational_quotients_instead_of_symbols.msim

 

Given

restart;
eq:=A=(1/2+x+y)^(3);
the_rhs:=solve(eq,A);

I asked solve to solve the above equation for A, expecting to get back (1/2+x+y)^(3), but it returns instead this

I looked at solve options, and tried number of them, but no change. I was looking for option to tell Maple not to simplify as it solves.

I also tried to see if the solution returned can be put back to the original form, and could not so far find a way, tried simplify and some options. But I did not try every possible method as there are do many.

Compare to Mathematica, which keeps the solution the same, as what one would expect. I see no reason to change it

ClearAll[A,x,y]
eq=A==(1/2+x+y)^3
Solve[eq,A]

The reason I am asking, is that it now makes parsing a little harder as I am looking for something in the form (expression)^power   as the solution.  i.e. the type to be `^`.    Now the type shows up as `*` because Maple for some reason changed it. 

It will easier if Maple did not do that, or if there is a way to change the expression back to the way it was. If all this fails, I have to just make the parsing handle this extra case form if needed.

Any suggestions?

Maple 2022.1

Update

Found a way after lots of trials and errors

simplify(the_rhs,[power,symbolic]);

 

But it would have been better if Maple did not do the simplification in the first place. But I could not find an option to tell it to do that while solving.

 

Unit_vectors_from_different_coordinate_systems.mw
 

restart

NULLNULL

with(Physics)``

with(Vectors)

NULL

It's common in mathematical physics to use cartesian unit vectors to describe the position of a point in space.

 

r_(t) = x(t)*_i+y(t)*_j

r_(t) = x(t)*_i+y(t)*_j

(1)

Sometimes it neccessary to convert a position vector like `#mover(mi("r"),mo("&rarr;"))`(t) to another cartensian coordinate system with different unit vectors, I call the primed system. In the primed system the position vector looks like:

"(r')(t)=x'(t) (i')+y'(t) (j')"

When using Physics[Vectors] and the unit vector hat notations to define vectors in cartesian space, can I define more than one cartesian space such as:

`#mover(mi("r"),mo("&rarr;"))`(t) = x(t)*`#mover(mi("i"),mo("&and;"))`+y(t)*`#mover(mi("j"),mo("&and;"))`

NULL

and

  "(r')(t)=x'(t) (i')+y'(t) (j')"?

Another way to ask the same thing: Can I define the position vector in different coordinates, each system having a distinct pair of orthogonal unit vectors?

 

The short answer I think is no. Given the current implementation it's not clear how one would go about defining the relationships between unit vectors from different coordinate systems. See below.

 

In 2D the transformation corresponds to a rotation of a vector the plane. The tranformation is characterized by the rotation angle α.

 

 

 

The unit vectors from different systems are related through scalar products.

 

"(i)*i' =(|i|)*|i'|*cos(alpha)=cos(alpha)"``NULL

NULL

"(j)*(j)' =(|j|)*|(j)'|*cos(alpha)=cos(alpha)"NULLNULL

``

"(j)*(i)' =(|j|)*|(i)'|*cos(3 alpha)=cos(3 alpha)"``NULL

 

Is there a way to implement scalar products of vectors from different coordinate systems using the Physics Tensors package? Here I create three different coordinate systems. I don't know whether the unit vectors systems X and Y have the same (i, j, k) unit vectors or does each system have its own triplet?

NULL

Setup(coordinates = cartesian, metric = Euclidean, dimension = 3, spacetimeindices = lowercaselatin, geometricdifferentiation = true)

[coordinatesystems = {X}, dimension = 3, geometricdifferentiation = true, metric = {(1, 1) = 1, (2, 2) = 1, (3, 3) = 1}, spacetimeindices = lowercaselatin]
````

(2)

Coordinates(Y, Z, Z = cylindrical)

{X, Y, Z}

(3)

NULL

NULL


 

Download Unit_vectors_from_different_coordinate_systems.mw

 

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