Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

how I can sort differential equation [q] in terms of u(x,y,z,t) and its derivatives.

In other words, we should find three relations including L11(u) ,L12 (v), and L13(w). 

For instance in L13{w) only w(x,y,z,t) and its derivatives would appear...

For example;

sort.mw


 

q := h*(A11*(diff(u(x, y, z, t), x, x)-(diff(w(x, y, z, t), x))/R+(diff(w(x, y, z, t), x))*(diff(w(x, y, z, t), x, x)))+A12*(diff(v(x, y, z, t), x, y)-(diff(w(x, y, z, t), x))/a+(diff(w(x, y, z, t), y))*(diff(w(x, y, z, t), x, y))))+h^2*(-B11*(diff(w(x, y, z, t), x, x, x))+B12*(-(diff(w(x, y, z, t), x, y, y))-(diff(v(x, y, z, t), x, y))/a))+B66*h^2*(-2*(diff(w(x, y, z, t), x, y, y))-(diff(v(x, y, z, t), x, y))/a)+A66*h*(diff(u(x, y, z, t), y, y)+diff(v(x, y, z, t), x, y)+(diff(w(x, y, z, t), y, y))*(diff(w(x, y, z, t), x))+(diff(w(x, y, z, t), y))*(diff(w(x, y, z, t), x, y))) = rho*(diff(u(x, y, z, t), t, t))-e0^2*a^2*(rho*(diff(u(x, y, z, t), t, t, x, x))+rho*(diff(u(x, y, z, t), t, t, y, y)))

h*(A11*(diff(diff(u(x, y, z, t), x), x)-(diff(w(x, y, z, t), x))/R+(diff(w(x, y, z, t), x))*(diff(diff(w(x, y, z, t), x), x)))+A12*(diff(diff(v(x, y, z, t), x), y)-(diff(w(x, y, z, t), x))/a+(diff(w(x, y, z, t), y))*(diff(diff(w(x, y, z, t), x), y))))+h^2*(-B11*(diff(diff(diff(w(x, y, z, t), x), x), x))+B12*(-(diff(diff(diff(w(x, y, z, t), x), y), y))-(diff(diff(v(x, y, z, t), x), y))/a))+B66*h^2*(-2*(diff(diff(diff(w(x, y, z, t), x), y), y))-(diff(diff(v(x, y, z, t), x), y))/a)+A66*h*(diff(diff(u(x, y, z, t), y), y)+diff(diff(v(x, y, z, t), x), y)+(diff(diff(w(x, y, z, t), y), y))*(diff(w(x, y, z, t), x))+(diff(w(x, y, z, t), y))*(diff(diff(w(x, y, z, t), x), y))) = rho*(diff(diff(u(x, y, z, t), t), t))-e0^2*a^2*(rho*(diff(diff(diff(diff(u(x, y, z, t), t), t), x), x))+rho*(diff(diff(diff(diff(u(x, y, z, t), t), t), y), y)))

(1)

``


 

Download sort.mw

 

Why won't Maple solve any of these inequalities for Q?

At first I tried solving the system of equations, but then I tried solving the inequalities individually for Q, and those too could not be solved by Maple.  What am I doing wrong?
 

restart

 

assume(R1, real, R2, real, RL, real, XC1, real, XC2, real, XL1, real)

additionally(R1 > 0, R2 > 0, RL > 0, XC1 > 0, XC2 > 0, XL1 > 0)

 

 

eq3 := R1*(4*Q^2+1)-RL > 0

0 < R1*(4*Q^2+1)-RL

(1)

eq4 := 4*Q^2*R1*RL-(R1-RL)^2 >= 0

0 <= 4*Q^2*R1*RL-(R1-RL)^2

(2)

eq5 := Rs^2*(RL-R1)/Q^2+R1^2*RL > 0

0 < Rs^2*(RL-R1)/Q^2+RL*R1^2

(3)

 

``

sys1 := {eq3, eq4, eq5}

`assuming`([solve(sys1, {Q})], [R1 > RL])

`assuming`([solve(sys1, {Q})], [R1 < RL])

solve(sys1, {Q})

Warning, solutions may have been lost

 

solve(eq3, Q)

Warning, solutions may have been lost

 

solve(eq4, Q)

Warning, solutions may have been lost

 

solve(eq5, Q)

Warning, solutions may have been lost

 

``


 

Download pi-filter_anal_copy.mw

How can I get Maple to simplify expressions into more meaningful forms?

For example, 

xc1 := -(2*Q*R1 + sqrt(4*Q^2*R1*RL - R1^2 + 2*R1*RL - RL^2))*R1/(4*Q^2*R1 + R1 - RL)

 

The numerator, under the radical, is more meaningful as sqrt(4 Q^2 R1 RL-(R1-RL)^2).

 

Similarly, the denominator can be simplified to Rs(4 Q^2+1)-RL.  

 

How do I get Maple to get me there?

I actually want to numerically solve Karhunen-Loeve Decomposition, which is reduced to homogenous Fredholm integral equation second kind when the kernel is the function of correlation of variables, by using any procedures (Galerkin is better if it is availabe). FYI, with "intsolve" I just got f(x)=0. 

I have Maple solve a system of equations.  I then want to assign the result to the different variables for use later in the worksheet.  How do I do this?
 

 

{C1 = .6666666670*Ceq, C2 = 2.000000002*Ceq, L1 = 0.1377592863e-15/Ceq, R1 = 0.8802817643e-8/Ceq}

(24)

c1 := sol3[1]

C1 = .6666666670*Ceq

(25)

l1 := sol3[2]

C2 = 2.000000002*Ceq

(26)

r1 := sol3[3]

L1 = 0.1377592863e-15/Ceq

(27)

Solutions, C2=10pf

Ceqsol := 20*e-12

20*e-12

(28)

C1sol := subs(Ceq = Ceqsol, c1)

C1 = 13.33333334*e-8.000000004

(29)
 

 

 


First, all I want to do is assign the solution value for C1 to C1.  Not being able to do this, I try to assign C1 to "different" variable c1, but the assignment is C1~=.66667* Ceq, instead of just the value of C1.  Later, I then try to substitute the value of Ceq, to get the solution for c1, and instead of just getting the value, I get  that C1= 13.33x10^-8 is assigned to C1sol, again instead of just the value, 13.33x10^-8.  How do I just assign the values to these variables instead of the expressions?

 

Thank you.

Download new_filter_solution.mw

How do I get Maple to simplify:

 

Io := I Cp Vin L1/(M sqrt(Cp L1))

 

to :  I sqrt(L1 CP) Vin/ M  ?

 

Furthermore, if  w = 1/sqrt(L1 *CP),  how do I get Maple to display the solution or the simplification as:

I*Vin/(w M) ?

I've t ried multiple substitutions and simplifications to no avail.

 

Thank you.

Jorge

 

I*Cp*RL*Vin*L1/(M*(Cp*L1)^(1/2))

(4)

simplify(I*Cp*RL*Vin*L1/(M*(L1*Cp)^(1/2)), 'symbolic')

I*Cp^(1/2)*RL*Vin*L1^(1/2)/M

(5)

 

NULL

Io := Vores/RL

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(6)

simplify(I*Cp*Vin*L1/(M*(L1*Cp)^(1/2)))

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(7)

simplify(I*Cp*Vin*L1/(M*(L1*Cp)^(1/2)), 'assume = real')

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(8)

combine(Vores/RL, power)

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(9)

factor(I*Cp*Vin*L1/(M*(L1*Cp)^(1/2)))

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(10)

combine(I*Cp*Vin*L1/(M*(L1*Cp)^(1/2)), radical)

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(11)

I*Cp*Vin*L1/(M*(L1*Cp)^(1/2))

cancel(I*Cp*Vin*L1/(M*(Cp*L1)^(1/2)))

(12)

simplify(cancel(I*Cp*Vin*L1/(M*(L1*Cp)^(1/2))), 'assume = real')

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(13)

simplify(I*Cp*Vin*L1/(M*(L1*Cp)^(1/2)), 'radical')

I*Cp*Vin*L1/(M*(Cp*L1)^(1/2))

(14)

simplify(I*Cp*Vin*L1/(M*(L1*Cp)^(1/2)), 'symbolic')

I*Cp^(1/2)*Vin*L1^(1/2)/M

(15)

``


 

Download Resonant_xformer.mw

 

Hello there, 

Would you tell me how to check if the two expressions presented below are the same?

My simple attempt (at the end of the worksheet below) failed. 

This page might be helpful to check the equality: https://www.myphysicslab.com/springs/trig-identity-en.html
 

restart;

subexpx := Ls*cos(omega*t + phi__l + theta)*omega + sin(omega*t + phi__l + theta)*Rs;

Ls*cos(omega*t+phi__l+theta)*omega+sin(omega*t+phi__l+theta)*Rs

(1)

subexpx2 := sqrt((omega*Ls)^2+Rs^2)*sin(omega*t + phi__l + theta + arctan(omega*Ls/Rs));

(Ls^2*omega^2+Rs^2)^(1/2)*sin(omega*t+phi__l+theta+arctan(omega*Ls/Rs))

(2)

is(subexpx - subexpx2 = 0) assuming omega::positive, Ls::positive, Rs::positive;

false

(3)

 

 


Thank you,

Download Q20201108.mw

Hello, I'm new to Maple, transitioning over from Mathematica.  I have a system of equations I'm trying to solve, but am trying to substitute values for some of the variables.  I don't think I'm doing it right, because I don't see the value in place of the variable when it echos the expression. Here are my equations, and how I'm trying to solve them:

wres := sqrt(C1+C2)/sqrt)C1*C2*L1)

vores := -C1/C2*vin

z3 = (C1^2 *R1- j*sqrt(C1*C2*L1*(C1+C2)))/C2^2

sys :={wres=13.56e6*2*pi, C1=C2, z3=40,abs(vores/vin)>=1}

solve(sys, {C1, C2, L1, R1})

 

(I apologize; I coulnd't figure out how to enter the Maple code here, directly).

 

When I try this, solve returns nothing.  I then try forcing R1 to be 2000, for ex.  I tried modifying sys to be

 

sys:={wres=13.56e6*2*pi, C1=C2, R1=2000,  z3=40,abs(vores/vin)>=1}, but this does't work.

then I tried, R1:=2000, exepcting to see R1 substituted with 2000 in the echo from sys, but it stills shows R1....

 

How do I do this?  

Also, how do I go about investigating why solve is having trouble solving a system of equations?

 

Thanks

Hello

Without any success, I've been trying to hide the input/code, such that only the output (moment and shear) diagram is shown. I've tried guides with Document Blocks method but all seem outdated, since they're referring to commands which don't seem to exist i.e. "collapse document block". I can't understand that there isn't some neat and user-friendly way to something as simple as show/hide the input, to make it more document-reader friendly? It seems the only way is to just hightlight the input and color it white, which isn't too viable long term. 

I hope you can help, it would be alot of help to me and my classmates. 
Kind regards and thanks for your time.

 

PS. Here's a picture of the input and diagram.

Hi:

Every once-in-a-while Maple crashes due to a bug in numerical integration that I reported ages ago, but was never fixed (or if it was, I was never told). Anyway, this time, in addition to crashing, it wiped out my worksheet, and froze the machine. When I recovered, Maple had lost all memory of my preferences, recent files, etc - it was as if I had a clean installation.

I restored the link to the usual style file I use, but it still refuses to give me back the style I want - that is - the classical worksheet. Every command I enter now requires F5 or I will get 2D input which I hate. Does anyone know where the preferences, probably an .INI file, are kept, so I can restore it from an older version of Maple.

Thank you

Hi, i am using solve and solve command to find the root but when i used fsolve command to separate only real root, could separate all roots, can anyone correct me, please


 

restart

f := 9.765625000*10^(-6)*(-6671.221362*(x^2+2)^5*sqrt(2)*arctan((1/2)*x*sqrt(2))*x-555.9351135*(x^2+2)^6/((1/2)*x^2+1)-10479.13001*(x^2+2)^5*sqrt(2)*x-(374220*(0.297116730e-1*x^9+.269385824*x^7+.99643086*x^5+5.18951288*x^3+4.42867382*x))*x-1111.870227*x^10-12601.19538*x^8-62147.39274*x^6-485504.8775*x^4-828649.1585*x^2-788850.2769)/(x^2+2)^6-(0.1171875000e-3*(-555.9351135*(x^2+2)^6*sqrt(2)*arctan((1/2)*x*sqrt(2))-873.2608343*(x^2+2)^6*sqrt(2)-(374220*(0.29711673e-2*x^10+0.33673228e-1*x^8+.16607181*x^6+1.29737822*x^4+2.21433691*x^2+2.107985348))*x))*x/(x^2+2)^7+(3.484800000*sqrt(2)*(x^2+2)*arctan((1/2)*x*sqrt(2))*x+.8712000000*(x^2+2)^2/((1/2)*x^2+1)+(5.473911040*(x^2+2))*sqrt(2)*x+5.227200000*x^2-22.99200001)/(16*(x^2+2)^2)-(.8712000000*sqrt(2)*(x^2+2)^2*arctan((1/2)*x*sqrt(2))+1.368477760*sqrt(2)*(x^2+2)^2-36*x*(-0.484000000e-1*x^2+.638666667))*x/(4*(x^2+2)^3)

0.9765625000e-5*(-6671.221362*(x^2+2)^5*2^(1/2)*arctan((1/2)*x*2^(1/2))*x-555.9351135*(x^2+2)^6/((1/2)*x^2+1)-10479.13001*(x^2+2)^5*2^(1/2)*x-374220*(0.297116730e-1*x^9+.269385824*x^7+.99643086*x^5+5.18951288*x^3+4.42867382*x)*x-1111.870227*x^10-12601.19538*x^8-62147.39274*x^6-485504.8775*x^4-828649.1585*x^2-788850.2769)/(x^2+2)^6-0.1171875000e-3*(-555.9351135*(x^2+2)^6*2^(1/2)*arctan((1/2)*x*2^(1/2))-873.2608343*(x^2+2)^6*2^(1/2)-374220*(0.29711673e-2*x^10+0.33673228e-1*x^8+.16607181*x^6+1.29737822*x^4+2.21433691*x^2+2.107985348)*x)*x/(x^2+2)^7+(1/16)*(3.484800000*2^(1/2)*(x^2+2)*arctan((1/2)*x*2^(1/2))*x+.8712000000*(x^2+2)^2/((1/2)*x^2+1)+5.473911040*(x^2+2)*2^(1/2)*x+5.227200000*x^2-22.99200001)/(x^2+2)^2-(1/4)*(.8712000000*2^(1/2)*(x^2+2)^2*arctan((1/2)*x*2^(1/2))+1.368477760*2^(1/2)*(x^2+2)^2-36*x*(-0.484000000e-1*x^2+.638666667))*x/(x^2+2)^3

(1)

ip := solve(f = 0, x)

.6540411301, 3126.002498+5414.398621*I, .4137989369+1.038962897*I, .6364817315+1.870977651*I, -.6364817315+1.870977651*I, -.4137989369+1.038962897*I, -.6540411301, -6252.010299, -.4137989369-1.038962897*I, -.6364817315-1.870977651*I, .6364817315-1.870977651*I, .4137989369-1.038962897*I, 3126.002498-5414.398621*I

(2)

cp := fsolve(numer(f) = 0, x)

.6540411302

(3)

``


 

Download help_fsolve_real_root.mw

Hello! I would like to ask a short question about particularsol function. Could someone please explain to me, why the function interprets the cosinus term as particular solution, even though it is homogeneous solution? Is it a bug in Maple or I unterstand something wrong?

As the title states, I want to have an equation f(x), and f(x) = 0 if x < 0, f(x) = x if x >= 0. How could I accomplish this?

I'm actually trying to generating a differential equation something like y'(x) + k*h(y) = sin(x) where h(y) is what I described above. Is there any convenient way to do this?

Hi,

I'm new to Maple and was wondering if anyone could help me with how to put a discrete distribution such as Pr(X=1)=0.25, Pr(X=2)=0.65, Pr(X=3)=0.1, into Maple.

Thanks.

To solve this, I got this far but am not sure where to go next?

 

f2 := x^2 - 3;
f2d := diff(f2, x);
                              2    
                             x  - 3
                              2 x

set value for x0, number precision

x0 := 3;
eps := 0.1*10^(-5);
                               3
                            0.000001
 

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