Maple Questions and Posts

Using maple to evaluate lengthy expressions...

Asked by: aliboyo 0

March 09 2018

0 1

First time maple user here,

I have a set of equations, as follows

u_o = u-(diff(v(x), x)) . y-(diff(w(x), x)) . z

v__o = v-phi . z

w__o = w+phi . y

where u,v,w are all differentiable w.r.t. x,y,z. I want to evaluate the partial derivative of each of these three expressions w.r.t. x,y,z.

For example, epsilon = Diff(u__o,x) (this is supposed to be a partial derivative)

When I try epsilon = diff(uo, x), i get this epsilon = -(diff(v(x), x, x)) . y-(diff(w(x), x, x)) . z

which is evaluating u as a constant but not giving me Diff(u,x)

when I try using convert((D(uo))(x), diff), I get diff(u(x), x)-(diff(diff((v(x))(x), x), x)) . y(x)-(diff((v(x))(x), x)) . (diff(y(x), x))-(diff(diff((w(x))(x), x), x)) . z(x)-(diff((w(x))(x), x)) . (diff(z(x), x))

which doesn't know that Diff(y,x)=0

How can I evaluate these expressions appropriately?

Any help will be greatly appreciated!

logplot with unwanted y-axis tickmarks!...

Asked by: shadi1386 35

March 09 2018

1 3

Dear all,

I am saving a logplot as :

plotsetup(jpeg, plotoutput = "/Users/test.jpg", plotoptions = "quality=200,height=1100, width=1500"); display(logplot(x^2-3, x = 0 .. 100), legendstyle = [font = [bold, "TimesNewRoman", 30], location = right], thickness = 4, font = [bold, "TimesNewRoman", 30]); plotsetup("inline", plotoutput = "terminal", plotoptions = "quality=100,height=1000, width=1500")

and the output is the plot attached.

test.jpg

This is my problem: I do not want the y-axis tickmarks to be shown as .1 e2, .1e3, ...

I would like them to be 10^2, 10^3, ...

Please remember that I need them to be saved like this because the quality is much better than when you export the plot directly.

Can someone help me, please?

isolve for inequalites...

Asked by: Gonzalo Garcia 155

March 09 2018

0 4

Hi!

Looking the Maple's help, I see that the command "isolve" tries to solve an equations over the integers. Then, given m>1 and t in the interval [0,1], How can used this command to find an integer j>=1 such that (j-1)/m<=t<j/m. That is, fin j such that t belongs to the interval [(j-1)/m,j/m].

Thanks in advance for your comments and help.

pvalue of TwoSampleTTest...

Asked by: mweisbr 30

March 09 2018

1 2

Hello,

I have to compare a lot of sample pairs with the TwoSampleTTest. I need only the pvalue for a cross table. It is possible to extract the pvalue of the TwoSampleTTest?

Many thanks!

¿How I change the output function to my ODE or PDE...

Asked by: ricardo25050 0

March 08 2018

0 2

This is an example, the program gave me functions _F as outputs and i want to see what F is.

This is an example.

Thanks.

Quantum Teleportation in Dirac notation with...

by: Louis Lamarche 105 Product: Maple

March 08 2018

4 4

This is an application of the previous posts
https://www.mapleprimes.com/posts/209057-Procedure-For-Expanding-Tensor-Product

I have a fourth version of the ExpandQop that will expand automaticaly the power of
quantum tensor product. This is just a minor change to the procedure.

Now here is an application for all this that will help understanding a little about
quantum computing. This is the classical concept of quantum teleportation.

You will need to run the above mentionned file and uncomment the save line in the file
before running the example.

LL

>

######################################################################
# NOTICE                                                             #
# Author: Louis Lamarche                                             #
#         Institute of Research of Hydro-Quebec (IREQ)               #
#         Science des données et haute performance                   #
#         2018, March 7                                              #
#                                                                    #
# Function name: ExpandQop (x)                                       #
#       Purpose: Compute the tensor product of two quantum           #
#                operators in Dirac notations                        #
#      Argument: x: a quantum operator                               #
# Improvements: Manage all +, -, *, /, ^, mod operations           #
#                in the argument. Manages multiple tensor products   #
#                like A*B*C*F                                        #
#       Version: 3                                                   #
#                                                                    #
# Copyrigth(c) Hydro-Quebec.                                        #
#        Note 1: Permission to use this softwate is granted if you   #
#                acknowledge its author and copyright                #
#        Note 2: Permission to copy this softwate is granted if you #
#                leave this 21 lines notice intact. Thank you.       #
######################################################################
restart;

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

(1)

>	Setup(unitaryoperators={I,U,X,Y,Z,H,HI,CNOT,CnotI}); Setup(noncommutativeprefix={q,beta,psi});

(2)

>	Setup(bracketrules= { %Bracket(%Bra(q0), %Ket(q0))=1, %Bracket(%Bra(q1), %Ket(q1))=1, %Bracket(%Bra(q1), %Ket(q0))=0, %Bracket(%Bra(q0), %Ket(q1))=0 });

(3)

>

####################################################################################
# Load the procedure and set the required global variables
#
read "ExpandQop.m": optp:=op(0,Ket(q0)*Ket(q1)): optpx:= op(0,(Ket(q0)+Ket(q1))^2):
#
####################################################################################

>

#
# Pauli operators
#
print("Pauli gates");
I:=Ket(q0)*Bra(q0)+Ket(q1)*Bra(q1);        # = sigma[0]
X:=Ket(q1)*Bra(q0)+Ket(q0)*Bra(q1);        # = sigma[1] = sigma[x]
Y:=-i*Ket(q1)*Bra(q0)+i*Ket(q0)*Bra(q1);   # = sigma[2] = sigma[y]
Z:=Ket(q0)*Bra(q0)-Ket(q1)*Bra(q1);        # = sigma[3] = sigma[z]

(4)

>	############################## # Defining the Hadamard gate # ############################## print("Hadamard gate"); H:= Ket(q0)Bra(q0)/sqrt(2)+Ket(q0)Bra(q1)/sqrt(2)+Ket(q1)Bra(q0)/sqrt(2)-Ket(q1)Bra(q1)/sqrt(2);

(5)

>

# This is usefull to represent a 2 qubits system
# A more general approach is needed for a n qubit system.
DefineStates:=proc()
    Ket(q00):=Ket(q0)*Ket(q0); Ket(q01):=Ket(q0)*Ket(q1);
    Ket(q10):=Ket(q1)*Ket(q0); Ket(q11):=Ket(q1)*Ket(q1);
    Bra(q00):=Dagger(Ket(q00)); Bra(q01):=Dagger(Ket(q01));
    Bra(q10):=Dagger(Ket(q10)); Bra(q11):=Dagger(Ket(q11));
    return;
    end proc:
UndefineStates:=proc()
    Ket(q00):='Ket(q00)'; Ket(q01):='Ket(q01)';
    Ket(q10):='Ket(q10)'; Ket(q11):='Ket(q11)';
    Bra(q00):='Bra(q00)'; Bra(q01):='Bra(q01)';
    Bra(q10):='Bra(q10)'; Bra(q11):='Bra(q11)';
    return;
    end proc:

>	#################################### # Defining the CNOT gate (2 qubits) #################################### print("CNOT gate"); CNOT:=Ket(q00)Bra(q00)+ Ket(q01)Bra(q01)+ Ket(q11)Bra(q10)+Ket(q10)Bra(q11); DefineStates(); 'CNOT'=CNOT;

(6)

>

###########################
# Defining the Bell states
###########################
Ket(beta,x,y)='CNOT.(((H.Ket(x)))*Ket(y))';
Ket(beta00):=CNOT.(Expand((H.Ket(q0)))*Ket(q0));
Ket(beta01):=CNOT.(Expand((H.Ket(q0)))*Ket(q1));
Ket(beta10):=CNOT.(Expand((H.Ket(q1)))*Ket(q0));
Ket(beta11):=CNOT.(Expand((H.Ket(q1)))*Ket(q1));

(7)

>

##########################################################
# Quantum teleportation
# Reference: Quantum Computation and Quantum Information
#            10th Anniversary Edition
#            Michael A. Nielsen & Isaac L. Chuang
#            Cambridge University Press, Cambridge 2010
#            pp 25-28
##########################################################
print("State to be teleported");
Ket(psi) := a*Ket(q0)+b*Ket(q1);
print("Step 1: Compute the tensor product of the state to be teleported with ", 'Ket(beta00)');
Ket(psi[0])='Ket(psi)'*'Ket(beta00)';
Ket(psi[0]):=Expand(Ket(psi)*Ket(beta00));
print("This is a 3 qubits state");
#######
print("Step 2: Pass these 3 qubits through a CNOT*I operator");
'CnotI'='CNOT*I';
CnotI:=ExpandQop(Expand(CNOT*I)):
#
# To see what the CNOTI operator looks like
#
# print("CNOTI=");
# print(op(1,CNOTI)+op(2,CNOTI)+op(3,CNOTI)+op(4,CNOTI));
# print(op(5,CNOTI)+op(6,CNOTI)+op(7,CNOTI)+op(8,CNOTI));
'Ket(psi[1])'='CnotI.Ket(psi[0])';
Ket(psi[1]):=Expand(CnotI.Ket(psi[0]));
#######
print("Step 3: Pass these 3 qubits through an Haldamard*I operator");
'HalI'='H*I';
HalI:=ExpandQop(Expand(H*I)):
#
# To see what the Haldamard*I operator looks like
#
# print("HalI=");
# print(op(1,HalI)+op(2,HalI)+op(3,HalI)+op(4,HalI));
# print(op(5,HalI)+op(6,HalI)+op(7,HalI)+op(8,HalI));
'Ket(psi[2])'='HalI.Ket(psi[1])';
Ket(psi[2]):=Expand(HalI.Ket(psi[1]));

(8)

>

UndefineStates();
print("Using contracted names for the first two qubits");
Ket(q00)*Bra(q0)*Bra(q0)='I';
Ket(q01)*Bra(q0)*Bra(q1)='I';
Ket(q10)*Bra(q1)*Bra(q0)='I';
Ket(q11)*Bra(q1)*Bra(q1)='I';
'Ket(psi[2])'=Ket(q00)*Bra(q0)*Bra(q0).Ket(psi[2])+
              Ket(q01)*Bra(q0)*Bra(q1).Ket(psi[2])+
              Ket(q10)*Bra(q1)*Bra(q0).Ket(psi[2])+
              Ket(q11)*Bra(q1)*Bra(q1).Ket(psi[2]);

(9)

>	print("Rewriting this result by hand"); 'Ket(psi[2])'=(Ket(q00)(aKet(q0)+bKet(q1))+ Ket(q01)(aKet(q0)-bKet(q1))+ Ket(q10)(aKet(q1)+bKet(q0))+ Ket(q11)(aKet(q1)-bKet(q0)))/2;

Physics:-Ket(psi[2]) = (1/2)*Physics:-`*`(Physics:-Ket(q00), a*Physics:-Ket(q0)+b*Physics:-Ket(q1))+(1/2)*Physics:-`*`(Physics:-Ket(q01), a*Physics:-Ket(q0)-b*Physics:-Ket(q1))+(1/2)*Physics:-`*`(Physics:-Ket(q10), a*Physics:-Ket(q1)+b*Physics:-Ket(q0))+(1/2)*Physics:-`*`(Physics:-Ket(q11), a*Physics:-Ket(q1)-b*Physics:-Ket(q0))

(10)

>

DefineStates();
print("If Alice measures 00 Bob does noting");
''I'.   '2*Bra(q00).Ket(psi[2])'' = I.   2*Bra(q00).Ket(psi[2]);
print("If Alice measures 01 Bob applies the X gate");
''X'.   '2*Bra(q01).Ket(psi[2])'' = X.   2*Bra(q01).Ket(psi[2]);
print("If Alice measures 10 Bob applies the Z gate");
''Z'.   '2*Bra(q10).Ket(psi[2])'' = Z.   2*Bra(q10).Ket(psi[2]);
print("If Alice measures 11 Bob applies the X gate and then the Z gate");
''Z'.'X'. '2*Bra(q11).Ket(psi[2])'' = Z.X. 2*Bra(q11).Ket(psi[2]);

(11)

>

Download QuantumTeleportation.mw

I want to solve the nonlinear system...

Asked by: Jameel123 20

March 08 2018

0 5

>

(1)

>

alpha := 1; 1; beta := 1; 1; N := 2; 1; M := 2; 1; L := 1; 1; X := 2*x/L-1; 1; T := 2*t/L-1; 1; `ϰ` := 3; 1; epsilon := 4; 1; delta := 2; 1; tau := 5; 1; B := 1; 1; c := 1; 1; sigma := 1

(2)

>

u := expand(sum(sum(a[s, k]*P(s, T)*P(k, X), k = 0 .. M), s = 0 .. N));

(3)

>

v := expand(sum(sum(b[s, k]*P(s, T)*P(k, X), k = 0 .. M), s = 0 .. N));

(4)

>

(5)

>

eq2 := diff(v, t)-epsilon*v*(-(tau+delta*B*v)/(1+B*v)+u/(v+u))-sigma*(diff(v, x, x))

(6)

>

4*a[1, 1]*t-12*a[1, 2]*t+12*a[2, 1]*t^2-12*a[2, 1]*t-36*a[2, 2]*t^2+36*a[2, 2]*t+2*a[0, 1]-6*a[0, 2]-2*a[1, 1]+6*a[1, 2]+2*a[2, 1]-6*a[2, 2]

(7)

>

4*a[1, 1]*t+12*a[1, 2]*t+12*a[2, 1]*t^2-12*a[2, 1]*t+36*a[2, 2]*t^2-36*a[2, 2]*t+2*a[0, 1]+6*a[0, 2]-2*a[1, 1]-6*a[1, 2]+2*a[2, 1]+6*a[2, 2]

(8)

>

4*b[1, 1]*t+2*b[0, 1]-6*b[0, 2]-2*b[1, 1]+6*b[1, 2]+2*b[2, 1]-6*b[2, 2]-12*b[1, 2]*t+12*b[2, 1]*t^2+36*b[2, 2]*t-36*b[2, 2]*t^2-12*b[2, 1]*t

(9)

>

4*b[1, 1]*t+12*b[1, 2]*t+2*b[0, 1]+6*b[0, 2]-2*b[1, 1]-6*b[1, 2]+2*b[2, 1]+6*b[2, 2]+36*b[2, 2]*t^2+12*b[2, 1]*t^2-36*b[2, 2]*t-12*b[2, 1]*t

(10)

>

a[0, 0]-a[0, 1]+a[0, 2]-a[1, 0]+a[1, 1]-a[1, 2]+a[2, 0]-a[2, 1]+a[2, 2]+2*a[0, 1]*x+6*a[0, 2]*x^2-6*a[0, 2]*x-2*a[1, 1]*x-6*a[1, 2]*x^2+6*a[1, 2]*x+2*a[2, 1]*x+6*a[2, 2]*x^2-6*a[2, 2]*x

(11)

>

2*b[0, 1]*x+6*b[0, 2]*x^2-6*b[0, 2]*x-2*b[1, 1]*x-6*b[1, 2]*x^2+6*b[1, 2]*x+2*b[2, 1]*x+6*b[2, 2]*x^2-6*b[2, 2]*x+b[0, 0]-b[0, 1]+b[0, 2]-b[1, 0]+b[1, 1]-b[1, 2]+b[2, 0]-b[2, 1]+b[2, 2]

(12)

>

(13)

>

(14)

>

4*a[1, 1]*t[j]-12*a[1, 2]*t[j]+12*a[2, 1]*t[j]^2-12*a[2, 1]*t[j]-36*a[2, 2]*t[j]^2+36*a[2, 2]*t[j]+2*a[0, 1]-6*a[0, 2]-2*a[1, 1]+6*a[1, 2]+2*a[2, 1]-6*a[2, 2]

(15)

>

4*a[1, 1]*t[j]+12*a[1, 2]*t[j]+12*a[2, 1]*t[j]^2-12*a[2, 1]*t[j]+36*a[2, 2]*t[j]^2-36*a[2, 2]*t[j]+2*a[0, 1]+6*a[0, 2]-2*a[1, 1]-6*a[1, 2]+2*a[2, 1]+6*a[2, 2]

(16)

>

4*b[1, 1]*t[j]+2*b[0, 1]-6*b[0, 2]-2*b[1, 1]+6*b[1, 2]+2*b[2, 1]-6*b[2, 2]-12*b[1, 2]*t[j]+12*b[2, 1]*t[j]^2+36*b[2, 2]*t[j]-36*b[2, 2]*t[j]^2-12*b[2, 1]*t[j]

(17)

>

4*b[1, 1]*t[j]+12*b[1, 2]*t[j]+2*b[0, 1]+6*b[0, 2]-2*b[1, 1]-6*b[1, 2]+2*b[2, 1]+6*b[2, 2]+36*b[2, 2]*t[j]^2+12*b[2, 1]*t[j]^2-36*b[2, 2]*t[j]-12*b[2, 1]*t[j]

(18)

>

a[0, 0]-a[0, 1]+a[0, 2]-a[1, 0]+a[1, 1]-a[1, 2]+a[2, 0]-a[2, 1]+a[2, 2]+2*a[0, 1]*x[i]+6*a[0, 2]*x[i]^2-6*a[0, 2]*x[i]-2*a[1, 1]*x[i]-6*a[1, 2]*x[i]^2+6*a[1, 2]*x[i]+2*a[2, 1]*x[i]+6*a[2, 2]*x[i]^2-6*a[2, 2]*x[i]

(19)

>

2*b[0, 1]*x[i]+6*b[0, 2]*x[i]^2-6*b[0, 2]*x[i]-2*b[1, 1]*x[i]-6*b[1, 2]*x[i]^2+6*b[1, 2]*x[i]+2*b[2, 1]*x[i]+6*b[2, 2]*x[i]^2-6*b[2, 2]*x[i]+b[0, 0]-b[0, 1]+b[0, 2]-b[1, 0]+b[1, 1]-b[1, 2]+b[2, 0]-b[2, 1]+b[2, 2]

(20)

>

X1 := evalf(fsolve((1-(2*x-1)^2)*(diff(P(N, X), x)))):

(21)

>

T1 := evalf(fsolve(P(M, T))):

(22)

>

(23)

(24)

>

for i to M-1 do for j from 0 to N-1 do s[i, j] := simplify(evalf(eq11)) end do end do;

(25)

(26)

>

for i to M-1 do for j from 0 to N-1 do w[i, j] := simplify(evalf(eq22)) end do end do;

(27)

>

for j from 0 to N-1 do s[j] := simplify(evalf(eq33)) end do;

-1.154700538*a[1, 1]+3.464101615*a[1, 2]-0.1000000000e-8*a[2, 2]+2.*a[0, 1]-6.*a[0, 2]

(28)

>

for j from 0 to N-1 do w[j] := simplify(evalf(eq44)) end do

-1.154700538*a[1, 1]-3.464101615*a[1, 2]+0.1000000000e-8*a[2, 2]+2.*a[0, 1]+6.*a[0, 2]

1.154700538*a[1, 1]+3.464101615*a[1, 2]-0.1000000000e-7*a[2, 2]+2.*a[0, 1]+6.*a[0, 2]

(29)

>

for j from 0 to N-1 do ww[j] := simplify(evalf(eq55)) end do

-1.154700538*b[1, 1]+2.*b[0, 1]-6.*b[0, 2]+3.464101615*b[1, 2]-0.1000000000e-9*b[2, 1]-0.1000000000e-8*b[2, 2]

1.154700538*b[1, 1]+2.*b[0, 1]-6.*b[0, 2]-3.464101615*b[1, 2]+0.1000000000e-7*b[2, 2]

(30)

>

for j from 0 to N-1 do www[j] := simplify(evalf(eq66)) end do

-1.154700538*b[1, 1]-3.464101615*b[1, 2]+2.*b[0, 1]+6.*b[0, 2]-0.1000000000e-9*b[2, 1]+0.1000000000e-8*b[2, 2]

1.154700538*b[1, 1]+3.464101615*b[1, 2]+2.*b[0, 1]+6.*b[0, 2]-0.1000000000e-7*b[2, 2]

(31)

>

for i from 0 to M do www1[i] := simplify(evalf(eq77)) end do

a[0, 0]-.5000000000*a[0, 2]-1.*a[1, 0]+.5000000000*a[1, 2]+a[2, 0]-.5000000000*a[2, 2]

(32)

>

for i from 0 to M do ww1[i] := simplify(evalf(eq88)) end do

-.5000000000*b[0, 2]+.5000000000*b[1, 2]-.5000000000*b[2, 2]+b[0, 0]-1.*b[1, 0]+b[2, 0]

(33)

>

fsolve({s[0] = 0, s[1] = 0, s[1, 0] = 0, s[1, 1] = 0, w[0] = 0, w[1] = 0, w[1, 0] = 0, w[1, 1] = 0, ww[0] = 0, ww[1] = 0, ww1[0] = 0, ww1[1] = 0, ww1[2] = 0, www[0] = 0, www[1] = 0, www1[0] = 0, www1[1] = 0, www1[2] = 0}, {a[0, 0], a[0, 1], a[0, 2], a[1, 0], a[1, 1], a[1, 2], a[2, 0], a[2, 1], a[2, 2], b[0, 0], b[0, 1], b[0, 2], b[1, 0], b[1, 1], b[1, 2], b[2, 0], b[2, 1], b[2, 2]})

(34)

>

Download aisha.mw

Procedure for expanding tensor product of quantum...

by: Louis Lamarche 105 Product: Maple

March 08 2018

1 1

Version 2 do not enable to expand multiple product like A*A*B*E
Version 3 will now do that.
I just forgot to add this feature.

LL.

>

######################################################################
# NOTICE                                                             #
# Author: Louis Lamarche                                             #
#         Institute of Research of Hydro-Quebec (IREQ)               #
#         Science des données et haute performance                   #
#         2018, March 7                                              #
#                                                                    #
# Function name: ExpandQop (x)                                       #
#       Purpose: Compute the tensor product of two quantum           #
#                operators in Dirac notations                        #
#      Argument: x: a quantum operator                               #
# Improvements: Manage all +, -, *, /, ^, mod operations           #
#                in the argument. Manages multiple tensor products   #
#                like A*B*C*F                                        #
#       Version: 3                                                   #
#                                                                    #
# Copyrigth(c) Hydro-Quebec.                                        #
#        Note 1: Permission to use this softwate is granted if you   #
#                acknowledge its author and copyright                #
#        Note 2: Permission to copy this softwate is granted if you #
#                leave this 21 lines notice intact. Thank you.       #
######################################################################
restart;

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

(1)

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

(2)

>

opexp:= op(0,10^x):            # exponentiation id
opnp := op(0,10*x):            # normal product id
optp := op(0,Ket(q0)*Ket(q1)): # tensor product id
opdiv:= `Fraction`:            # fraction       id
opsym:= op(0,x):               # symbol         id
opint:= op(0,10):              # integer        id
opflt:= op(0,10.0):            # float          id
opcpx:= op(0,i):               # complex        id
opbra:= op(0,Bra(q)):          # bra            id
opket:= op(0,Ket(q)):          # ket            id
opmod:= op(0, a mod b):        # mod            id
ExpandQop:=proc(x)
    local nx,ret,j,lkb,cbk,rkb,no,lop,success;
    lop:=op(0,x);
    no:=nops(x);
    if lop = opsym or lop = opint or lop = opflt or
       lop = opbra or lop = opket or lop = opcpx then
         ret:=x;
    else
    if lop = opexp then
        ret:=x;
    else
    if lop = opnp then
        ret:=1;
        for j from 1 to no do
            ret:=ret*ExpandQop(op(j,x));
        end do;
    else
    if lop = `+` then
        ret:=0;
        for j from 1 to no do
            ret:=ret+ExpandQop(op(j,x));
        end do;
    else
    if lop = `-` then
        ret:=0;
        for j from 1 to no do
            ret:=ret-ExpandQop(op(j,x));
        end do;
    else
    if lop = opdiv then
       ret:=1;
       for j from 1 to no do
           ret:=ret/ExpandQop(op(j,x));
       end do;
    else
    if lop = opmod then
       ret:=x;
    else
    if lop = optp then
       if (no > 3 ) then
           success:=false;
           nx:=x;
           while not success do
             lkb:=0; cbk:=0; rkb:=0;ret:=1;
             for j from 1 to no do
                 if (j>1) then
                      if(lkb=0) then
                          if( type(op(j-1,nx),Ket) and
                              type(op(j,nx),Bra) ) then lkb:=j-1; fi;
                      else
                          if( type(op(j-1,nx),Ket) and
                              type(op(j,nx),Bra) ) then rkb:=j;   fi;
                      fi;
                      if( type(op(j-1,nx),Bra) and type(op(j,nx),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,nx); end do;
                 for j from cbk   to no    do ret := ret*op(j,nx); end do;
                 for j from lkb+1 to cbk-1 do ret := ret*op(j,nx); end do;
             else
               ret:=nx;
             fi;

             if nx = ret then
                success := true;
             else
                nx := ret;
             fi
           end do;
       else
           ret:=x;
       fi;
    else ret:=x;
    fi; # optp
    fi; # opmod
    fi; # opdiv
    fi; # `-`
    fi; # `+`
    fi; # `opnp
    fi; # `opexp`
    fi; # opsym, opint, opflt, opbra, opket, opcpx

    return ret;
end proc:

# For saving
# save opexp,opnp,optp,opdiv,opint,opflt,opcpx,opbra,opket,opmod, ExpandQop,"ExpandQop.m"

>

# 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);

(3)

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

(4)

>	print("Example"); En:=ExpandQop(10(1-x+y+z)i(1/sqrt(2))A*B);

(5)

>	print("Another example"); 'F'='AB/sqrt(2)+BA/sqrt(2)'; F:=AB/sqrt(2)+BA/sqrt(2): 'op(1,F)'=op(1,F); 'op(2,F)'=op(2,F); 'Fn'='ExpandQop(F)'; Fn:=ExpandQop(F): 'op(1,Fn)'=op(1,Fn); 'op(2,Fn)'=op(2,Fn);

(6)

>	print("Final example, multiple products"); G:=BBB; 'G'=ExpandQop(G);

(7)

>

Download ExpandQopV3.mw

fractional Adams-Bashforth-Moulton method...

Asked by: torabi 90

March 08 2018

3 27

Dear all

Is there any one can help me to find the Maple code to solve these fractioanal equations using fractional Adams-Bashforth-Moulton method

Doc229.pdf

Thank you very much for helping me.

How do I plot the solutions to my differential equ...

Asked by: shrey183 45

March 08 2018

0 5

I have the following ode:

ode1 := diff(x(t), t, t) = (5*9.80665)*sin((1/6)*Pi)-(10*(10-sqrt(x(t)^2+25)))*x(t)/sqrt(x(t)^2+25)-(diff(x(t), t))

I tried the following code:

DEplot(ode, x(t), t = -2 .. 2, [`$`([x(0) = (1/4)*k], k = -20 .. 20)], x = -8 .. 8, color = blue, stepsize = 0.5e-1, linecolour = red, arrows = MEDIUM)

But I get the following error:

Error, (in DEtools/DEplot/CheckInitial) too few initial conditions: [x(0) = -5]

Any help in plotting this differential equation will be much appreciated.

easy way (w/o programming) to calculate a special ...

Asked by: maple_user_2017 20

March 08 2018

0 4

Hi,

I'm searching for an easier way to execute the following computation using only matrix calculations
(meaning no programming, no loops):

> restart:with(linalg):
> S:=matrix(3,3,[s11,s12,s13,s21,s22,s23,s31,s32,s33]):
> X:=matrix(3,1,[x1,x2,x3]):
> A:=array(1..3,1..3):
> for j from 1 to 3 do
>   for i from 1 to 3 do
>     A[i,j]:=S[i,j]/X[j,1]
>   od;
> od;
> op(A);

So far, I've got the following ideas:

A)
> S:=matrix(3,3,[s11,s12,s13,s21,s22,s23,s31,s32,s33]):
> X:=matrix(3,1,[x1,x2,x3]):
> h:=matrix(1,3,[1,1,1]):
> Xm:=evalm(transpose(h)&*transpose(X)):
## memberwise division: S / Xm

How can I do a memberwise division?

B)
>S:=matrix(3,3,[s11,s12,s13,s21,s22,s23,s31,s32,s33]):
>X:=matrix(3,1,[x1,x2,x3]):
## make X the diagonal of a square matrix
> Xd:=matrix(3,3,[x1,0,0,0,x2,0,0,0,x3]):
> A:=evalm(S&*inverse(Xd));

How can I make a vector X the diagonal of a square matrix (without retyping the values)?

Thanks in advance
Ben

Physics[Vectors} divergence of r^-2 should be D...

Asked by: dglevitt 120

March 08 2018

2 1

with(Physics[Vectors]);

This should equal Dirac delta function

I know this must have been addressed somewhere previously. However I have searched extensively and not been able to find an answer. Sorry for asking again.

Open Newton-Cotes Integrations...

Asked by: AmirHosein Sadeghimanesh 225

March 08 2018

1 1

In the package Student[Calculus1], the NewTon-Cotes closed formulas are implemented. But I was thinking if there is any other package of Maple having the open Newton-Cotes Fromulas. I searched and I just saw in Student[NumericalAnalysis] for Quadratures.

Navie quesion: for all item in a vector....

Asked by: weidade37211 110

March 08 2018

1 3

I have a vector P_X

I want to use it in the constraint of Maple optimization, that all item in P_X is smaller than 1. I am looking for some expression looks like: all(P_X[i]<1,i=1..10)

Thanks.

Change Values of a Matrix...

Asked by: mweisbr 30

March 08 2018

0 3

Hello,

I want to change some values of a matrix.

For example: I have a matrix with measured data, but some of these values get the number 1.0 (because maple cannot import these expression correctly). Is it possible to change all "1.0" with an other expression?

Thanks a lot!
Martin

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