MaplePrimes Questions

How I can change this solution or remove the RootOf, because i have to show variables and params in this solutions.
 

restart

with(linalg)

f1 := alpha*x*(1-x/N)-beta[1]*sqrt(x)*y1/(1+h[1]*beta[1]*sqrt(x))-beta[2]*sqrt(x)*y2/(1+h[2]*beta[2]*sqrt(x))-d*E*x

f2 := -omega[1]*y1+Mu[1]*beta[1]*sqrt(x)*y1*(1-y1/(beta[1]*sqrt(x)))/(1+h[1]*beta[1]*sqrt(x))

f3 := -omega[2]*y2+Mu[2]*beta[2]*sqrt(x)*y2*(1-y2/(beta[2]*sqrt(x)))/(1+h[2]*beta[2]*sqrt(x))

T := solve({f1, f2, f3}, [x, y1, y2])

[[x = -N*(E*d-alpha)/alpha, y1 = 0, y2 = 0], [x = RootOf(alpha*beta[2]*Mu[2]*h[2]*_Z^4+alpha*Mu[2]*_Z^3+(E*N*d*Mu[2]*beta[2]*h[2]-N*alpha*Mu[2]*beta[2]*h[2])*_Z^2+(-N*beta[2]^2*h[2]*omega[2]+E*N*d*Mu[2]+N*Mu[2]*beta[2]^2-N*alpha*Mu[2])*_Z-N*omega[2]*beta[2])^2, y1 = 0, y2 = -(RootOf(alpha*beta[2]*Mu[2]*h[2]*_Z^4+alpha*Mu[2]*_Z^3+(E*N*d*Mu[2]*beta[2]*h[2]-N*alpha*Mu[2]*beta[2]*h[2])*_Z^2+(-N*beta[2]^2*h[2]*omega[2]+E*N*d*Mu[2]+N*Mu[2]*beta[2]^2-N*alpha*Mu[2])*_Z-N*omega[2]*beta[2])*omega[2]*beta[2]*h[2]-RootOf(alpha*beta[2]*Mu[2]*h[2]*_Z^4+alpha*Mu[2]*_Z^3+(E*N*d*Mu[2]*beta[2]*h[2]-N*alpha*Mu[2]*beta[2]*h[2])*_Z^2+(-N*beta[2]^2*h[2]*omega[2]+E*N*d*Mu[2]+N*Mu[2]*beta[2]^2-N*alpha*Mu[2])*_Z-N*omega[2]*beta[2])*beta[2]*Mu[2]+omega[2])/Mu[2]], [x = RootOf(alpha*beta[1]*Mu[1]*h[1]*_Z^4+alpha*Mu[1]*_Z^3+(E*N*d*Mu[1]*beta[1]*h[1]-N*alpha*Mu[1]*beta[1]*h[1])*_Z^2+(-N*beta[1]^2*h[1]*omega[1]+E*N*d*Mu[1]+N*Mu[1]*beta[1]^2-N*alpha*Mu[1])*_Z-N*omega[1]*beta[1])^2, y1 = -(RootOf(alpha*beta[1]*Mu[1]*h[1]*_Z^4+alpha*Mu[1]*_Z^3+(E*N*d*Mu[1]*beta[1]*h[1]-N*alpha*Mu[1]*beta[1]*h[1])*_Z^2+(-N*beta[1]^2*h[1]*omega[1]+E*N*d*Mu[1]+N*Mu[1]*beta[1]^2-N*alpha*Mu[1])*_Z-N*omega[1]*beta[1])*omega[1]*beta[1]*h[1]-RootOf(alpha*beta[1]*Mu[1]*h[1]*_Z^4+alpha*Mu[1]*_Z^3+(E*N*d*Mu[1]*beta[1]*h[1]-N*alpha*Mu[1]*beta[1]*h[1])*_Z^2+(-N*beta[1]^2*h[1]*omega[1]+E*N*d*Mu[1]+N*Mu[1]*beta[1]^2-N*alpha*Mu[1])*_Z-N*omega[1]*beta[1])*beta[1]*Mu[1]+omega[1])/Mu[1], y2 = 0], [x = RootOf(alpha*beta[2]*beta[1]*Mu[2]*Mu[1]*h[2]*h[1]*_Z^5+(alpha*Mu[1]*Mu[2]*beta[1]*h[1]+alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^4+(E*N*d*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]-N*alpha*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]+alpha*Mu[1]*Mu[2])*_Z^3+(-N*Mu[1]*beta[1]*beta[2]^2*h[1]*h[2]*omega[2]-N*Mu[2]*beta[1]^2*beta[2]*h[1]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]*beta[1]*h[1]+E*N*d*Mu[1]*Mu[2]*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]^2*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]*beta[2]^2*h[1]-N*alpha*Mu[1]*Mu[2]*beta[1]*h[1]-N*alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^2+(-N*Mu[1]*beta[1]*beta[2]*h[1]*omega[2]-N*Mu[1]*beta[2]^2*h[2]*omega[2]-N*Mu[2]*beta[1]^2*h[1]*omega[1]-N*Mu[2]*beta[1]*beta[2]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]+N*Mu[1]*Mu[2]*beta[1]^2+N*Mu[1]*Mu[2]*beta[2]^2-N*alpha*Mu[1]*Mu[2])*_Z-N*omega[2]*beta[2]*Mu[1]-N*omega[1]*beta[1]*Mu[2])^2, y1 = (-RootOf(alpha*beta[2]*beta[1]*Mu[2]*Mu[1]*h[2]*h[1]*_Z^5+(alpha*Mu[1]*Mu[2]*beta[1]*h[1]+alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^4+(E*N*d*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]-N*alpha*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]+alpha*Mu[1]*Mu[2])*_Z^3+(-N*Mu[1]*beta[1]*beta[2]^2*h[1]*h[2]*omega[2]-N*Mu[2]*beta[1]^2*beta[2]*h[1]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]*beta[1]*h[1]+E*N*d*Mu[1]*Mu[2]*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]^2*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]*beta[2]^2*h[1]-N*alpha*Mu[1]*Mu[2]*beta[1]*h[1]-N*alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^2+(-N*Mu[1]*beta[1]*beta[2]*h[1]*omega[2]-N*Mu[1]*beta[2]^2*h[2]*omega[2]-N*Mu[2]*beta[1]^2*h[1]*omega[1]-N*Mu[2]*beta[1]*beta[2]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]+N*Mu[1]*Mu[2]*beta[1]^2+N*Mu[1]*Mu[2]*beta[2]^2-N*alpha*Mu[1]*Mu[2])*_Z-N*omega[2]*beta[2]*Mu[1]-N*omega[1]*beta[1]*Mu[2])*omega[1]*beta[1]*h[1]+RootOf(alpha*beta[2]*beta[1]*Mu[2]*Mu[1]*h[2]*h[1]*_Z^5+(alpha*Mu[1]*Mu[2]*beta[1]*h[1]+alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^4+(E*N*d*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]-N*alpha*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]+alpha*Mu[1]*Mu[2])*_Z^3+(-N*Mu[1]*beta[1]*beta[2]^2*h[1]*h[2]*omega[2]-N*Mu[2]*beta[1]^2*beta[2]*h[1]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]*beta[1]*h[1]+E*N*d*Mu[1]*Mu[2]*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]^2*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]*beta[2]^2*h[1]-N*alpha*Mu[1]*Mu[2]*beta[1]*h[1]-N*alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^2+(-N*Mu[1]*beta[1]*beta[2]*h[1]*omega[2]-N*Mu[1]*beta[2]^2*h[2]*omega[2]-N*Mu[2]*beta[1]^2*h[1]*omega[1]-N*Mu[2]*beta[1]*beta[2]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]+N*Mu[1]*Mu[2]*beta[1]^2+N*Mu[1]*Mu[2]*beta[2]^2-N*alpha*Mu[1]*Mu[2])*_Z-N*omega[2]*beta[2]*Mu[1]-N*omega[1]*beta[1]*Mu[2])*beta[1]*Mu[1]-omega[1])/Mu[1], y2 = (-RootOf(alpha*beta[2]*beta[1]*Mu[2]*Mu[1]*h[2]*h[1]*_Z^5+(alpha*Mu[1]*Mu[2]*beta[1]*h[1]+alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^4+(E*N*d*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]-N*alpha*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]+alpha*Mu[1]*Mu[2])*_Z^3+(-N*Mu[1]*beta[1]*beta[2]^2*h[1]*h[2]*omega[2]-N*Mu[2]*beta[1]^2*beta[2]*h[1]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]*beta[1]*h[1]+E*N*d*Mu[1]*Mu[2]*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]^2*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]*beta[2]^2*h[1]-N*alpha*Mu[1]*Mu[2]*beta[1]*h[1]-N*alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^2+(-N*Mu[1]*beta[1]*beta[2]*h[1]*omega[2]-N*Mu[1]*beta[2]^2*h[2]*omega[2]-N*Mu[2]*beta[1]^2*h[1]*omega[1]-N*Mu[2]*beta[1]*beta[2]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]+N*Mu[1]*Mu[2]*beta[1]^2+N*Mu[1]*Mu[2]*beta[2]^2-N*alpha*Mu[1]*Mu[2])*_Z-N*omega[2]*beta[2]*Mu[1]-N*omega[1]*beta[1]*Mu[2])*omega[2]*beta[2]*h[2]+RootOf(alpha*beta[2]*beta[1]*Mu[2]*Mu[1]*h[2]*h[1]*_Z^5+(alpha*Mu[1]*Mu[2]*beta[1]*h[1]+alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^4+(E*N*d*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]-N*alpha*Mu[1]*Mu[2]*beta[1]*beta[2]*h[1]*h[2]+alpha*Mu[1]*Mu[2])*_Z^3+(-N*Mu[1]*beta[1]*beta[2]^2*h[1]*h[2]*omega[2]-N*Mu[2]*beta[1]^2*beta[2]*h[1]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]*beta[1]*h[1]+E*N*d*Mu[1]*Mu[2]*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]^2*beta[2]*h[2]+N*Mu[1]*Mu[2]*beta[1]*beta[2]^2*h[1]-N*alpha*Mu[1]*Mu[2]*beta[1]*h[1]-N*alpha*Mu[1]*Mu[2]*beta[2]*h[2])*_Z^2+(-N*Mu[1]*beta[1]*beta[2]*h[1]*omega[2]-N*Mu[1]*beta[2]^2*h[2]*omega[2]-N*Mu[2]*beta[1]^2*h[1]*omega[1]-N*Mu[2]*beta[1]*beta[2]*h[2]*omega[1]+E*N*d*Mu[1]*Mu[2]+N*Mu[1]*Mu[2]*beta[1]^2+N*Mu[1]*Mu[2]*beta[2]^2-N*alpha*Mu[1]*Mu[2])*_Z-N*omega[2]*beta[2]*Mu[1]-N*omega[1]*beta[1]*Mu[2])*beta[2]*Mu[2]-omega[2])/Mu[2]]]

(1)

NULL

NULL


 

Download titikkesetimbangan.mw

Theoretically, if the multiplication sign  is missed Maple needs to give reminders or warnings.But the following is not the case, why?I am surprised its output. 

x:=1
                             x := 1
x(2+1)Actually, I want to enter x*(2+1)

                               1
x(sin(y))Actually, I want to enter x*(sin(y))
                               1

I am a little confused by why this error occurs in the second line and not the first, as well as the weird details specified in it. I don't know if the commands that are being called are inbuilt or not, but it is a safe bet that they will be. thankyou.


 

MAX := max({[seq(seq(n-(n^k-floor(n^(1/k))^(k-1)*igcd(floor(ithprime(n)^k/n^k), floor(n^(1/k))))^(1/k), n = 2 .. 100), k = 2 .. 100)][]}):

seq(seq(piecewise(radnormal(n-(n^k-floor(n^(1/k))^(k-1)*igcd(floor(ithprime(n)^k/n^k), floor(n^(1/k))))^(1/k)) = MAX, [n, k], NULL), n = 2 .. 100), k = 2 .. 100)

Error, (in radnormal/rational/nthpower) cannot determine if this expression is true or false: iroot(646162507019111437893207695980096110233782566593779/(_c27_37*_c25_38), [_c25_38, 1]) < 0

 

``


 

Download ASKMAPLE000.mw

In preparing to sample problems, I came across this difference in an output depending upon the input type: 2d Input vs. Maple Input. Is there a typo on my part?


 

restart; kernelopts(version); Digits

`Maple 2020.1, X86 64 WINDOWS, Jun 10 2020, Build ID 1474787`

 

10

(1)

Very happy with the output of the following line:

x := evalf[30](3.0^1.2)

3.73719281884655197790004100992

(2)

 

But I'm confused about the output of the next line. Is it a limit to the calculation or a display problem?

a := evalf[30](3.0^(1.2))

3.737192819

(3)

 

and yet this next output looks fine:

b := evalf[30]( exp( 1.2 * ln(3)))

3.73719281884655197790004100989

(4)

 

Fortunately, there appears to be no difference between x and b:

evalf[30](x-b)

0.3e-28

(5)

 

But these next  lines suggest there is an actual limit in the calculation of a.

evalf[30](a-b)

0.15344802209995899011e-9

(6)

evalf[30](a - b);

0.15344802209995899011e-9

(7)

Note - when Digits is set to 30, the calculation difference between x and a disappears.

``


 

Download 2020_evalf_digits.mw

Hi,

How do I solve numerically this set of equations with the following ICs to plot U1(x), phi(x),diff(phi(x),x) versus x:

diff(U1(x),x)=-diff(phi(x),x)/(U1(x)-T/U1(x));
diff(phi(x),x$2)=(1+A1*phi(x)+A2*phi(x)**(3/2)+A3*phi(x)**2)-(M1/U1(x));
where

A1:=(2*k-1)/(2*k-3);
A2:=8*sqrt(2/pi)*(beta-1)*k*Gamma(k)/(3*Gamma(k-0.5)*(2*k-3)**(3/2));
A3:=(4*k**2-1)/(2*(2*k-3)**2);
M1=0.1+sqrt(T+(1/A1));
(Gamma is gamma function)

assume, for example, T=0.1, pi=3.14, beta=0.6, k=3.5

ICs:

U1(x=0)=M1, phi(x=0)=0, diff(phi(x=0),x)=0.001.

Thanks.

I know we can use Maple LPSolver for linear programming problem (eg. https://www.maplesoft.com/support/help/Maple/view.aspx?path=Optimization/LPSolveMatrixForm), while I am wondering if we can use maple to solve a LP problem symbolically when some of the constants in those examples are unknow parameters.

If no, any suggestions of other solutions?I guess I have to do the simplex method manually? Thanks.

From help, it says

coulditbe routine returns true if there is a possible value of x1 that satisfies prop1

my question is, how to find out this condition/possible values that Maple found?  This infomration is very useful, but now I do not see how to obtain it. All what coulditbe retuirn is true or false.

Context of why I am asking:  Sometimes odetest do not verify its own solutions. And coulditbe can help in finding under what conditions the solution can satisfy the ode. Here is an example

restart;
ode:=diff(y(x),x) = abs(y(x))+1;
solExplicit:=dsolve(ode);
offset := odetest~([solExplicit],ode)

gives

[exp(-x)/_C1 - abs((-exp(-x) + _C1)/_C1) - 1, exp(x)*_C1 - abs(exp(x)*_C1 - 1) - 1]

Both solution fail odetest. 

coulditbe~(offset,0)

gives true

So there are assumptions/conditions which makes the solution satisfy the ODE. In this case, by inspection one can see what these conditions are. They are, for one solution:

(-exp(-x) + _C1)/_C1  >0

and for the other, the condition is

exp(x)*_C1 - 1 >0

Under these assumptions, odetest would have given 0 for each odetest.

And it is this information I wanted to obtain automatically from coulditbe.

In Mathematica, Reduce is used for this. Reduce gives conditions under which something is satisfied. For example, 

Reduce[ C[1] Exp[x] - Abs[C[1] Exp[x] - 1] - 1 == 0, {x, C[1]}, Reals]

Gives

C[1] >= Exp[-x]


While the above in  Maple

coulditbe( C[1]*exp(x)- abs( C[1]*exp(x)-1)-1 = 0)

gives true  only, but without the important information, true under what conditions.

Is there a different command in Maple which could give this information?

Hello, dear forum users!

Does anyone use the method of homotopy analysis (HAM) and the NOPH package in their work. (moderator: link)
 


It seems to me that only HAM can help.

I ask for help if someone has already mastered.

There are no developments, as I do not own the NOPH package.

Could anyone help me with: How to start a command-line terminal for Maple in Linux Ubuntu? Thanks a lot

Hi there.

I need to calculate multiplcations of huge polynoms with reducing in GF(2^m) with m>1000.

For example, modpol(a*a,f_t,t,2^N) with N=4007, degree(a)=8008 and degree(f_t)=8009.

Standard modpol calculates this in 4-5 sec on my computer.

Maybe there is an easy way to speed up this calculation?

Thank you.

ex.mw

nn.txt

Hi all,

I am new to maplesim and trying to learn it.

While simulation of the battery operated 4 wheeled driven electric vehicle 

it tells can't find solution.

 

 

Same time if i connect a fixed reference all four wheels are running (same place) but not moving since the frame fixed.

 

HELP ME TO SOLVE THIS.

 

thank you..

 

Hi everyone,

I am trying to integrate this function, however, it did not generate any results. Is there any chance to make this run?
 

I0 := 1/sqrt(1-C2OverC1*cos(t))^3

1/(1-C2OverC1*cos(t))^(3/2)

(1)

`assuming`([int(I0, t = 0 .. 2*Pi)], [C2OverC1 > -1, C2OverC1 < 1])

``

``

``


 

Download ellipticIntegral.mw

Hello all, 

Would you please tell me how to rewrite the expression 'Is_square' like 'Is_square2'?

The way how the first expression is re-written is that both numerator and denominator were divided by 'sigma^2*omega[rK]^2': 

One attempt I made was to use 'algsub' command using the subexpression ''sigma^2*omega[rK]'', but somehow it missed the term in the denominator. 


 

restart;

Is_square := M[dmax]*(sigma^2*omega[rK]^2 + omega[r]^2)*L[sigma]/(3*p*omega[r]*omega[rK]*L[mu]^2*sigma^2);

(1/3)*M[dmax]*(sigma^2*omega[rK]^2+omega[r]^2)*L[sigma]/(p*omega[r]*omega[rK]*L[mu]^2*sigma^2)

(1)

Is_square2 := M[dmax]*(1 + omega[r]^2/(sigma^2*omega[rK]^2))*L[sigma]/(3*p*omega[r]*L[mu]^2/omega[rK]);

(1/3)*M[dmax]*(1+omega[r]^2/(sigma^2*omega[rK]^2))*L[sigma]*omega[rK]/(p*omega[r]*L[mu]^2)

(2)

algsubs(omega[rK]*sigma^2=tt, Is_square);

(1/3)*M[dmax]*L[sigma]*(tt*omega[rK]+omega[r]^2)/(p*omega[r]*L[mu]^2*omega[rK]*sigma^2)

(3)

 


 

Download Qprime_20200621.mw

 

Suppose I have

with(GraphTheory):
vertices:=["M","P","C"]:
edge_weights:={[{"M","P"},3],[{"M","C"},1]}:

G1:=Graph(vertices,edge_weights)

EigenvectorCentrality(G1)
                                                  

Is it right to say the EigenvalueCentrality values correspond to the names in the vertices correspondingly?  ie M corresponds to 0.4415.. P corresponds to  0.4188.. and C corresponds to 0.1396... ?

 

restart;
sub:=x/C;
expr:=1/2*x*(p^2+a)/p;

And now

subs(p = sub, expr)

But

algsubs(p = sub,expr)

Notice one "p" is still not replaced. 

This is very annoying. I looked at help and did not see anything about this. I could have missed it. It looks like it does not replace "p" when it is in denominator:

algsubs(p = x,1/p)

Remains 1/p but 

subs(p = x,1/p)

gives 1/x as expected.

May be this is documented somewhere? But why it does this?

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