Maple Questions and Posts

These are Posts and Questions associated with the product, Maple
 

Download test.mw
Udp: document attached.

Q__gr := Typesetting[delayDotProduct](Vector[row](8, {(1) = 0, (2) = 5, (3) = 10, (4) = 15, (5) = 20, (6) = 25, (7) = 30, (8) = 35}), Unit('m'^3/'day'), true)

Vector[row](%id = 18446746861178193550)

(1)

`η__gr` := Vector[row](8, {(1) = 0, (2) = 9.324, (3) = 17, (4) = 23.232, (5) = 27.192, (6) = 29.6, (7) = 29.516, (8) = 24.592})

Vector[row](%id = 18446746861214593262)

(2)

`pointsη` := [seq([Q__gr[i], `η__gr`[i]], i = 1 .. 8)]

[[0, 0], [5*Units:-Unit(m^3/d), 9.324], [10*Units:-Unit(m^3/d), 17], [15*Units:-Unit(m^3/d), 23.232], [20*Units:-Unit(m^3/d), 27.192], [25*Units:-Unit(m^3/d), 29.6], [30*Units:-Unit(m^3/d), 29.516], [35*Units:-Unit(m^3/d), 24.592]]

(3)

CurveFitting[PolynomialInterpolation](`pointsη`, q)

0.2348698413e-7*q^7/Units:-Unit(m^3/d)^7-0.2980622223e-5*q^6/Units:-Unit(m^3/d)^6+0.1482222222e-3*q^5/Units:-Unit(m^3/d)^5-0.3663955556e-2*q^4/Units:-Unit(m^3/d)^4+0.4666528890e-1*q^3/Units:-Unit(m^3/d)^3-.3165382223*q^2/Units:-Unit(m^3/d)^2+2.655161905*q/Units:-Unit(m^3/d)

(4)

eta := proc (q) options operator, arrow; 0.2348698413e-7*q^7/Units:-Unit(m^3/d)^7-0.2980622223e-5*q^6/Units:-Unit(m^3/d)^6+0.1482222222e-3*q^5/Units:-Unit(m^3/d)^5-0.3663955556e-2*q^4/Units:-Unit(m^3/d)^4+0.4666528890e-1*q^3/Units:-Unit(m^3/d)^3-.3165382223*q^2/Units:-Unit(m^3/d)^2+2.655161905*q/Units:-Unit(m^3/d) end proc

proc (q) options operator, arrow; 0.2348698413e-7*q^7/Units:-Unit(m^3/d)^7-0.2980622223e-5*q^6/Units:-Unit(m^3/d)^6+0.1482222222e-3*q^5/Units:-Unit(m^3/d)^5-0.3663955556e-2*q^4/Units:-Unit(m^3/d)^4+0.4666528890e-1*q^3/Units:-Unit(m^3/d)^3-.3165382223*q^2/Units:-Unit(m^3/d)^2+2.655161905*q/Units:-Unit(m^3/d) end proc

(5)

eta(12*Unit('m'^3/'day'))

.8415811058*Units:-Unit(m^3/d)^7/Units:-Unit(m^3/d)^7-8.900090268*Units:-Unit(m^3/d)^6/Units:-Unit(m^3/d)^6+36.88243199*Units:-Unit(m^3/d)^5/Units:-Unit(m^3/d)^5-75.97578241*Units:-Unit(m^3/d)^4/Units:-Unit(m^3/d)^4+80.63761922*Units:-Unit(m^3/d)^3/Units:-Unit(m^3/d)^3-45.58150401*Units:-Unit(m^3/d)^2/Units:-Unit(m^3/d)^2+31.86194286*Units:-Unit(m^3/d)/Units:-Unit(m^3/d)

(6)

simplify(19.76619849)

Error, (in Units:-Standard:-+) the units `m^21/s^7` and `m^18/s^6` have incompatible dimensions

 

``


 

Download test.mw

 

Hi!

I got a function (from CurveFitting), that produce a polynomial with the some units inside:

 

As i can see, it can be easy simplified, but i get:


 

Is where any trick to do it, without stripping units with convert(unit_free) or something?

Thank you!

 

Letter_L_rotate.mws

The attached program is of the letter L rotating.  about an axis which is the outer side of the 'upright' of the L.  I want to give the illusion that the letter L is rotating about a y-axis, where the x, y axes are in the plane of the screen, with the x-axis going from left to right.  The program at present 'works', in the sense that the letter L is rotating about an axis.  ...but it's not quite what I want.  My eventual aim is to plot the letters A and L side by side, AL, and as the letter L rotates the leg of the L would bump into the A,  so I want the A to rise in sync with movement of the letter L.   ...but that's a long way off!  For the moment I just want to know how to orientate the letter L, so that it is in its usual L state

   I think I have two options: either to change the coordinate positions of L, (long and tedious..) or quicker might be to change the axis of rotation.  Any suggestions on making the animation smoother would also be appreciated.

Thanks, David

 .

I wanted to use MAPLE to preform symbolic quantum computations. The role
of quantum operators and their tensor product is very important in simplying
the understating of such new calculus at least for the beginners. For instance,
(using "o" for the tensor product and "." for the scalar product, H being the Hadamard
operator on a qubit, I the identity operator, and CNOT the 2 qubit controled not
operator)
1) generating the Bells states |Bxy> two stages of operators are needed
     (CNOT) .  (H o  I)  . |x> o |y>

2) performing quantum teleportation of |psi>
     (H o I o I) . (CNOT o I ) . |psi>o |B00>
    followed by a measurements on the first two qubits for driving the application of
    quantum gates to the third qubit.

All these tensor products of operators can be easily written in MAPLE.

Here is a first version of the ExpandQop procedure that will be usefull the purpose of
expanding correctly the tensor product of two quantum operator expressed in Dirac notation.

I hope this is usefull.

LL 

 

######################################################################
# Author: Louis Lamarche                                             #
#         Institute of Research of Hydro-Quebec (IREQ)               #
#         Science des données et haute performance                   #
#         2018/02/20                                                 #
#                                                                    #
#         Function name: ExpandQop (x)                               #
#               Purpose: Compute the tensor product of two quantum   #
#                        operators in Dirac notations                #
#              Argument: x - a simple quantum operator               #
#   Future improvements: Manage all +, -, *, /, ^, mod  operations   #
#                        in the argument                             #
#               Version: 1.0                                         #
######################################################################
restart;

with(Physics):
interface(imaginaryunit=i):
Setup(mathematicalnotation=true);

[mathematicalnotation = true]

(1)

Setup(quantumoperators={A,B,C,Cn});
Setup(noncommutativeprefix={a,b});

[quantumoperators = {A, B, C, Cn}]

 

[noncommutativeprefix = {a, b}]

(2)

ExpandQop:=proc(x)
    local ret,j,lkb,cbk,rkb,no;
    ret:=1; lkb:=0; cbk:=0; rkb:=0; no:=nops(x);
    if (no > 3 ) then
        for j from 1 to no do
            if (j>1) then
                 if(lkb=0) then
                     if( type(op(j-1,x),Ket) and
                         type(op(j,x),Bra) ) then lkb:=j-1; fi;
                 else
                     if( type(op(j-1,x),Ket) and
                         type(op(j,x),Bra) ) then rkb:=j;   fi;
                 fi;
                 if( type(op(j-1,x),Bra) and type(op(j,x),Ket) )
                                             then cbk:=j;   fi;
            fi;
        end do;
        if ( (lkb < cbk) and (cbk<rkb) ) then
            for j from 1     to lkb   do ret := ret*op(j,x); end do;
            for j from cbk   to no    do ret := ret*op(j,x); end do;
            for j from lkb+1 to cbk-1 do ret := ret*op(j,x); end do;
        else
            ret:=x;
        fi;
    else
        ret:=x;
    fi;
    return ret;
end proc:

# Let A be an operator in a first Hilbert space of dimension n
#  using the associated orthonormal ket and bra vectors
#
#
kets1:=Ket(a1)*Ket(a2)*Ket(a3)*Ket(a4)*Ket(a5):
A:=kets1*Dagger(kets1);


# Let B be an operator in a second Hilbert (Ketspace of dimension m
#  using the associated orthonormal ket and bra vectors
#
#
kets2:=Ket(b1)*Ket(b2)*Ket(b3):
B:=kets2*Dagger(kets2);


# The tensor product of the two operators acts on a n+m third
# Hilbert space   unsing the appropriately ordered ket
# and bra  vectors of the two preceding spaces. The rule for
# building this operator in Dirac notation is as follows,
#
#


print("Maple do not compute the tensor product of operators,");
print("C=A*B gives:");
C:=A*B;

print("ExpandQop(C) gives the expected result:");
Cn:=ExpandQop(C);

Physics:-`*`(Physics:-Ket(a1), Physics:-Ket(a2), Physics:-Ket(a3), Physics:-Ket(a4), Physics:-Ket(a5), Physics:-Bra(a5), Physics:-Bra(a4), Physics:-Bra(a3), Physics:-Bra(a2), Physics:-Bra(a1))

 

Physics:-`*`(Physics:-Ket(b1), Physics:-Ket(b2), Physics:-Ket(b3), Physics:-Bra(b3), Physics:-Bra(b2), Physics:-Bra(b1))

 

"Maple do not compute the tensor product of operators,"

 

"C=A*B gives:"

 

Physics:-`*`(Physics:-Ket(a1), Physics:-Ket(a2), Physics:-Ket(a3), Physics:-Ket(a4), Physics:-Ket(a5), Physics:-Bra(a5), Physics:-Bra(a4), Physics:-Bra(a3), Physics:-Bra(a2), Physics:-Bra(a1), Physics:-Ket(b1), Physics:-Ket(b2), Physics:-Ket(b3), Physics:-Bra(b3), Physics:-Bra(b2), Physics:-Bra(b1))

 

"ExpandQop(C) gives the expected result:"

 

Physics:-`*`(Physics:-Ket(a1), Physics:-Ket(a2), Physics:-Ket(a3), Physics:-Ket(a4), Physics:-Ket(a5), Physics:-Ket(b1), Physics:-Ket(b2), Physics:-Ket(b3), Physics:-Bra(b3), Physics:-Bra(b2), Physics:-Bra(b1), Physics:-Bra(a5), Physics:-Bra(a4), Physics:-Bra(a3), Physics:-Bra(a2), Physics:-Bra(a1))

(3)

kets3:=kets1*kets2;
bras3:=Dagger(kets3);
print("Matrix element computed with C appears curious");
'bras3.C. kets3'="...";
bras3.C.kets3;
print("Matrix element computed with Cn as expected");
'bras3.Cn.kets3'=bras3.Cn.kets3;

Physics:-`*`(Physics:-Ket(a1), Physics:-Ket(a2), Physics:-Ket(a3), Physics:-Ket(a4), Physics:-Ket(a5), Physics:-Ket(b1), Physics:-Ket(b2), Physics:-Ket(b3))

 

Physics:-`*`(Physics:-Bra(b3), Physics:-Bra(b2), Physics:-Bra(b1), Physics:-Bra(a5), Physics:-Bra(a4), Physics:-Bra(a3), Physics:-Bra(a2), Physics:-Bra(a1))

 

"Matrix element computed with C"

 

Physics:-`.`(bras3, C, kets3) = "..."

 

Physics:-Bracket(Physics:-Bra(b1), Physics:-Ket(a1))*Physics:-Bracket(Physics:-Bra(b2), Physics:-Ket(a2))*Physics:-Bracket(Physics:-Bra(b3), Physics:-Ket(a3))*Physics:-Bracket(Physics:-Bra(a1), Physics:-Ket(b1))*Physics:-Bracket(Physics:-Bra(a2), Physics:-Ket(b2))*Physics:-Bracket(Physics:-Bra(a3), Physics:-Ket(b3))*Physics:-Bracket(Physics:-Bra(a4), Physics:-Ket(a4))^2*Physics:-Bracket(Physics:-Bra(a5), Physics:-Ket(a5))^2*Physics:-Bracket(Physics:-Bra(a1), Physics:-Ket(a1))*Physics:-Bracket(Physics:-Bra(a2), Physics:-Ket(a2))*Physics:-Bracket(Physics:-Bra(a3), Physics:-Ket(a3))*Physics:-Bracket(Physics:-Bra(b1), Physics:-Ket(b1))*Physics:-Bracket(Physics:-Bra(b2), Physics:-Ket(b2))*Physics:-Bracket(Physics:-Bra(b3), Physics:-Ket(b3))

 

"Matrix element computed with Cn as expected"

 

Physics:-`.`(bras3, Cn, kets3) = Physics:-Bracket(Physics:-Bra(a1), Physics:-Ket(a1))^2*Physics:-Bracket(Physics:-Bra(a2), Physics:-Ket(a2))^2*Physics:-Bracket(Physics:-Bra(a3), Physics:-Ket(a3))^2*Physics:-Bracket(Physics:-Bra(a4), Physics:-Ket(a4))^2*Physics:-Bracket(Physics:-Bra(a5), Physics:-Ket(a5))^2*Physics:-Bracket(Physics:-Bra(b1), Physics:-Ket(b1))^2*Physics:-Bracket(Physics:-Bra(b2), Physics:-Ket(b2))^2*Physics:-Bracket(Physics:-Bra(b3), Physics:-Ket(b3))^2

(4)

 


 

Download ExpandQop.mw

 

 

In the fraction 3^665/2^x=y, where y is more than 1 and less than 2, I want to know the value of x. What input should I write, please?

  1. (k-2)*(k^2+5)*(k^3-k^2+7*k+8)/(6*k*(k^2-3*k+8))
  2. (k+2)*(k^2+5)*(k^3-5*k^2+13*k-8)/(6*k*(k^2-3*k+8))
  3. k^3+3*k^2+11*k-3
  4. k^2+2*k+9

Lesson_on_functions.mws

As the title says, a lesson on functions:  eg the -> operator, f(2), eval, evalf etc 

How to draw the following function containing an imaginary number
 

NULL

u := proc (x, t) options operator, arrow; 1/2+I*sqrt(2)/(exp(x-t)+2*exp(-x+t))+(1/2)*(exp(x-t)-2*exp(-x+t))/(exp(x-t)+2*exp(-x+t)) end proc

proc (x, t) options operator, arrow; 1/2+I*sqrt(2)/(exp(x-t)+2*exp(-x+t))+(1/2)*(exp(x-t)-2*exp(-x+t))/(exp(x-t)+2*exp(-x+t)) end proc

 

``

 

 

 

``

 

 

 

 

 

 

``

 

 

``

NULL


 

Download plot33.mwDownload plot33.mw

I'm attempting to solve the complex-valued differential equation

restart:
assume(t::real):

pde := diff(A(t),t) - I * conjugate(A(t))*A(t)^2 = 0:
dsolve(pde);

However, it seems Maple attempts to solve it using separation of variables and gives

t-Intat(-I/conjugate(_a)/_a^2,_a = A(t))+_C1 = 0

Unless I'm mistaken, a complex integral such as this isn't even defined without a contour.

Working the integral out by hand, I know the solution to be

_C1*exp(I*abs(_C1)*t)

Is there a trick I'm missing to get Maple to find this solution? Or is this outside the scope of what Maple can handle on it's own?

Thanks!

I believe I am having memory issues which is causing the MAPLE kernal to terminate.  If I assign m a value then it seems to work, but I would like to leave m unassigned so that S1 can later be evaluated for any arbitrary m.  Is there a way around this?


 

T := M*tau;

`assuming`([simplify(expand(combine(S1)))], [m::integer])

``


 

Download MAPLE_crashing.mw

Hello everybody

I am currently having trouble 'manually simplifying' an equation that I differentiated using maple. Basically, the equation that I get involves hessian-matrices. Since the resulting equation is rather long, I would like to replace every such matrix by a sign, say H.
This is easy to do for non-matrix equations, i.e.

subs(sin(x)sin(y) = z, sin(x)sin(y) + xy)

will give me z + xy, which looks a bit easier.

However, I couldn't figure out how to do a similar thing with matrices. For example, the following code

subs(Matrix(3, 3, [[x, y, z], [y, z, x], [z, x, y]]) = A, Matrix(3, 3, [[x, y, z], [y, z, x], [z, x, y]])+B)

 will not work.
I already thought about converting the matrices first into lists (because for some reason it works for lists). However, I would also like to do the same as above for for functions of matrices, i.e. set F(A) = G, where A is a matrix (this also fails, probably for the same reason).

Also, the same thing seems to fail for vectors and general arrays, so I guess the actual problem might be the array type.

I also tried alternative ways, such as eval or algsubs, but the later even gives an error since it cannot handle matrices at all.

This feels a bit like a noob question, but I spent almost 2 days now searching for an answer or a workaround, so my apologies if I missed something trivial.

All the best
Adrian

 

 

Hi, I try to solve the below integral. when I press enter key maple dosen't show answer and show the integral again.

int(r*r[bc]*r[tc], r = r[bc] .. r[tc]);

but when I write intgral this way and use " i " as subscript ,maple solve it.

int(r[i]*r[bc]*r[tc], r[i] = r[bc] .. r[tc]);

I just want to know why?

what is difference between first and second integral?

and also is there any way (or any packages) to solve these integrals?

(I read https://www.maplesoft.com/applications/view.aspx?SID=6846&view=html article befor)

thanks.

Good day everyone,

I'm relatively new to Maple, and I study engineering (not maths), so maybe my problem is related to a bad approach of the equations.

The problem is that I'm asking Maple to do a double integral of a "complex" expression and it only solve the first integral, but not the second.

Here is the code:

https://www.dropbox.com/home/C%C3%81LCULO%20FUERZAS

Thanks.

Dears!

Hope everyone should be fine. I am face to import excel sheet in maple. I saved execl sheet with name "Employees.xlsx" at desktop. When I use the following command
S := Import("Employees.xlsx", 1, "A1:B101");

I got the following error. 

"Error, (in ExcelTools:-Import) Could not open the file"

Please help me to fix this problem. I am waiting positive response. 

Special request to:

@Carl Love
@Preben Alsholm
@acer

  1. (2*k^3-6*k^2+7*k+15-k*sqrt(k^6-12*k^5+64*k^4-198*k^3+448*k^2-636*k+369))/(-k^4+2*k^3-2*k^2+10*k+15)
  2. (k^3+5*k+(-k^2+k)*sqrt(k^4-10*k^3+37*k^2-60*k+180)+30)/(-k^4+k^3+k^2+5*k+30)

Please I am trying to get a compact result for this code in particular the lines assigne "a" and "b" respectively. I am sure the result shoud not be more than two lines. Can someone be of help? 

restart:
P:=a[0]+(a[1]*x)/(1+(a[2]*x)/(1+(a[3]*x))):
Q:=diff(P,x):
T:=diff(P,x,x):
e1:=simplify(eval(P, x=q))=y[n]:
e2:=simplify(eval(Q,x=q))=f[n]:
e3:=simplify(eval(Q,x=q+h))=f[n+1]:
e4:=simplify(eval(T,x=q+h))=g[n+1]:
var:=seq(a[i], i=0..3):
M:=e||(1..4):
Cc:=eval(<var>, solve(eval({M}),{var}) ):
for i from 1 to 4 do
	a[i-1]:=Cc[i]:
end do:
Cf:=P:
a:=y[n+1]=collect(simplify(eval(Cf, x=q+h)),[y[n], f[n], f[n+1],g[n+1]], recursive):
b:=map(eval@allvalues, [a]);

 

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