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What's the simplest way to partially substitute for expressions that contain operators from the Physics package? 
(hopefully my worksheet below shows what I mean)
Thanks

restart:

with(Physics):

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1092 and is the same as the version installed in this computer, created 2021, October 18, 14:11 hours Pacific Time.`

(1)

Setup(quantumoperators = {sigma__x, sigma__y, sigma__z, rho, H, comm}, mathematicalnotation = true);

[mathematicalnotation = true, quantumoperators = {H, comm, rho, sigma__x, sigma__y, sigma__z}]

(2)

we could just use Physics:-Psigma, etc... but here let's define these manually:

Setup(algebrarules={
%Commutator(sigma__x, sigma__y) = 2*I*sigma__z,
%Commutator(sigma__y, sigma__z) = 2*I*sigma__x,
%Commutator(sigma__z, sigma__x) = 2*I*sigma__y
}
);

[algebrarules = {%Commutator(sigma__x, sigma__y) = (2*I)*sigma__z, %Commutator(sigma__y, sigma__z) = (2*I)*sigma__x, %Commutator(sigma__z, sigma__x) = (2*I)*sigma__y}]

(3)

some expression (normally long and complicated that contains many operators):

expr:=(sigma__y*sigma__x*rho - sigma__y*rho*sigma__x);

Physics:-`*`(sigma__y, sigma__x, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

(4)

say want to make this type of substitution:

subs_vars:=sigma__y*sigma__x=H;

Physics:-`*`(sigma__y, sigma__x) = H

(5)

this doesn't work

algsubs(subs_vars, expr);

Physics:-`*`(sigma__y, sigma__x, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

(6)

this also doesn't work:

subs(subs_vars, expr);

Physics:-`*`(sigma__y, sigma__x, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

(7)

this works (here we explicitly specify the whole thing, that includes rho)

subs(sigma__y*sigma__x*rho=H*rho, expr);

Physics:-`*`(H, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

(8)

but I would like for the substitution to also work for *parts* of the expression, as in the normal case, when not using operators.

 

 

 

Download maple_1.mw

I need to declare a whole set of variables as local. The variable names are generates algorithmically using assign. Like so:

seq(seq(assign(cat(S,i,j)=Vector(datatype=float)),i=1..9),j=1..9);

Stand-alone, this works and creates all these Vectors for later use. But this:

local seq(seq(assign(cat(S,i,j)=Vector(datatype=float)),i=1..9),j=1..9);

does not work; I get an "error; '(' unexpected".

I really do not want to type all these by hand... on the other hand, if I do not declare these as local I get 99 warnings about implicit local declaration; not nice.

Is there a way to do this?

Thanks,

M.D.

PS: I do not upload as the one line really is all that is needed. At the lowest level one does not get the implicit-declaration warning, but with "local" it still fails.

My forced spring mass system is 4x"+4x'+3x=sin(wt). I calculated my w=w* value that maximizes the amplitude (0.5) and my initial conditions are x(0)=x'(0)=0. I need to graph x(t) when w= w* and when w=w*/2. How am I supposed to input this information into maple to create a graph? 

I drew a polygon using some point coordinates combined with the pointplot.

c1 := <0, -2>:
c2 := <1, 2>:
c3 := <2, 2>:
c4 := <0.5, 6>:
c5:=<1, 4>:
with(plots):
p1:=pointplot([c1, c2, c3, c4,c5, c1], color = red, connect = true);

I ‘d like to add  label  of endpoints to polygons, although I did this via textplot, but it didn't feel very neat. I hope when the polygon is drawn, labels of  every endpoints appear . These labels are the names of the assignment variable for the coordinates of the endpoints.

c1 := <0, -2>:
c2 := <1, 2>:
c3 := <2, 2>:
c4 := <0.5, 6>:
c5:=<1, 4>:
with(plots):

t1 :=textplot([0, -2, 'typeset'("c1")], 'align' = 'above'):
t2 :=textplot([1, 2, 'typeset'("c2")], 'align' = 'above'):
t3 :=textplot([2, 2, 'typeset'("c3")], 'align' = 'above'):
t4 :=textplot([0.5, 6, 'typeset'("c4")], 'align' = 'above'):
t5 :=textplot([1, 4, 'typeset'("c5")], 'align' = 'above'):
p1:=pointplot([c1, c2, c3, c4,c5, c1], color = red, connect = true):
display({p1, t1,t2,t3,t4,t5});

 

I think  DrawGraph command  in graph theory package  is very good to achieve this in a sense. 

Hello everyone.

Please help me solve this equation for u using Maple.

Div(u) = d(ru)/(dr)*1/r = 2*a = const; u = u(r);

``

Divergence(u) = d(ru)/(r*dr) and d(ru)/(r*dr) = 2*a and 2*a = const

u = u(r)


Thanks in advance for your help.

Hi all,
i'm working with the confluent Heun function (Maple 2019).
Since for the case of an integer coefficient delta or gamma there are two integer Frobenius roots at the regular singularities 0 or 1, there is a logarithmic term in the Frobenius solution at these singularities. So, my question is the following:
When moving around this singularity in the complex plane, the value of the logarithmic term might depend on the choice of the complex logarithm's branch cuts. So, does anybody know just about how HeunC is implemented? Is there sth like a power series solution, which value would in my oppinion depend on this choice of a branch cut?
Or is there another implementation that preserves us from this ambiguity in the case of logarithmic singularities (i.e. integer coefficients in the confluent Heun equation)?

Many thanks,

integration_doubt.mw
Hello all,

I am trying to solve for the first-order derivative of a function f2 w.r.t variable a when it is equated to 0. the function f2 is a summation of two integrals as shown in the file. Kindly help me if there is any way to obtain solutions without numerical settings. Can functionalities like the Leibnitz rule be done in MAPLE? Thanks for your advice/help. 

Could you please give an example of a code where I can add outputs from a loop to a list. I am using the break command to end the loop so I don't have the number of elements in advance.

Thank you for your time.

How do I find with maple's help  for which parameter m does the equation:

x^2+2*m*x-6*x=m^3 have one of its roots equal to the square of the other root?

Thanks!

I wrote the following orders

With(GeM):
gem_decl_vars(indeps=[t,x], deps=[u(t,x)]);
gem_decl_eqs([diff(u(t,x),t,t)+a∗diff(u(t,x),x,x)+b∗
u(t,x)+c∗(u(t,x))^3=0],solve_for=[diff(u(t,x),t,t)])

det_eqs:=gem_conslaw_det_eqs([t,x,u(t,x),diff(u(t,x),
t),diff(u(t,x),x)]):
CL_multipliers:=gem_conslaw_multipliers();
simplified_eqs:=DEtools[rifsimp](det_eqs,
CL_multipliers, mindim=1)

in maple 17, but the program cannot calculate and gives me an error. Does anyone help me to solve this problem.


 

.

BTW "recusant" is an old word, religious in origin, for someone who refuses to do what they're told, or believe what they're told to believe.

Here's my problem:

phi := (1+sqrt(5))/2;

plots[pointplot]([seq([n, sin(n*phi)], n = 1000 .. 2000)], symbol = point, axes = boxed, labels = [n, typeset('sin(n*phi)')], labeldirections = [horizontal, vertical])

produces a label sin( n phi ).  I want it to say sin( phi n ). 

I've tried the noncommuting times &*  (which prints &*) and the matrix product . (which prints as a function call).

Is there a way to typeset this product in the order that I want?  Here "n" is the variable and "phi" is the constant (yes that looks weird, but so does the graph).  I suspect that there is; I think "typeset" is probably much more powerful than I have been kludging it as.  Help?

screenshot:

I have this function : r(theta) = sec[t(theta)] = sec * (theta - (Pi/2) * (2/Pi *(theta + Pi/4))).

Since this function is in terms of (theta,r(theta)) ... how would I graph this in terms of Cartesian Co-ordinates instead of Polar ? 

Hi, I have animated plot visualizing the moving of point from location a to location b. I need line to be plotted in trace of moved point in area. Please see the code that I implement below. Many Thanks

restart:
with(plots):
with(Statistics):
L:=[[0],[34,7],[39,8,6], [45,2,3,7]]:
animate(( PointPlot, [L[trunc(t)]], t=1..3, frames=50), symbol=solidcircle,symbolsize=40);

Sorry for this simple question but I am new to Maple and need to do just this one thing...

Lets say I have a function fp(x) which draws out some envelope when I change p. I wanted to calculate this euqation by hand but this does not seem possible, since f is too complex. How can I use Maple to find the area under any Enevelope? Or maybe a bit simpler: How can I just find the envelope and save it to use it later?

I am sorry,since I don't know anything about Maple and I need that fast...

Hi,
I want to solve the following equation and, assuming x=x_r+Ix_i where x_r and x_i are real and imaginary part of x,  plot x_r and x_i versus y . How can I do in Maple?

x^6+x^4*(1.02-0.50e-2*y)+x^2*(-0.4950e-2*y+0.625e-5*y^2)+0.625e-5*y^2=0

Thanks

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