Maple 13 Questions and Posts

These are Posts and Questions associated with the product, Maple 13

Good evening!!!

Let me briefly describe the problem I've faced recently.

The program (attached) deals with a rather complicated function f depending on parametrs eps1, eps2, eps3, eps4 and variable w. The aim is to expand the function f(w1) into Taylor series with respect to all parametrs (eps1, eps2, eps3, eps4) in order to study its asymptotic behavior as function depending only on k; 0<k<1.

I decided to use mtaylor-function for that problem, which (as I've understood) is the only one to be applied in such cases, but the result was rather unsatisfactory, an error: 

Error, (in gcd/LinZip) input must be polynomials over the integers

Programm code: (1)-(12) only announcing functions....(((, see below
 

f := proc (w) options operator, arrow; -B1+(A1-C1)*w+(B1-D1)*w^2-A1*w^3 end proc

proc (w) options operator, arrow; -B1+(A1-C1)*w+(B1-D1)*w^2-A1*w^3 end proc

(1)

f1 := proc (w) options operator, arrow; A1-C1+(2*B1-2*D1)*w-3*A1*w^2 end proc

proc (w) options operator, arrow; A1-C1+(2*B1-2*D1)*w-3*A1*w^2 end proc

(2)

w1 := (B1-D1+sqrt((B1-D1)^2+3*A1*(A1-C1)))/(3*A1)

(1/3)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))/A1

(3)

f(w1)

-B1+(1/3)*(A1-C1)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))/A1+(1/9)*(B1-D1)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))^2/A1^2-(1/27)*(B1-D1+(B1^2-2*B1*D1+D1^2+3*A1^2-3*A1*C1)^(1/2))^3/A1^2

(4)

s := eps4*sin(l*tau)+(4*(l*sqrt(k/(1-k))+l*eps3)+2*l*((1-2*k)/sqrt(k*(1-k))+eps1))/l^2

eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2

(5)

A1 := (2*(l*sqrt(k/(1-k))+l*eps3)+l*((1-2*k)/sqrt(k*(1-k))+eps1))/s

(2*l*(k/(1-k))^(1/2)+2*l*eps3+l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)

(6)

A1 := (2*(l*sqrt(k/(1-k))+l*eps3)+l*((1-2*k)/sqrt(k*(1-k))+eps1))/s

(2*l*(k/(1-k))^(1/2)+2*l*eps3+l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)

(7)

B1 := 4/s^2

4/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)^2

(8)

C1 := (((1-2*k)/sqrt(k*(1-k))+eps1)^2+(-(1-2*k)/sqrt(k*(1-k))+eps2)^2)/s^2

(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)^2

(9)

D1 := (2*((1-2*k)/sqrt(k*(1-k))+eps1))*(-(1-2*k)/sqrt(k*(1-k))+eps2)/s^2

2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(l*tau)+(4*l*(k/(1-k))^(1/2)+4*l*eps3+2*l*((1-2*k)/(k*(1-k))^(1/2)+eps1))/l^2)^2

(10)

l := 1

1

(11)

f(w1)

-4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(1/3)*((2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)-(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2)*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(16/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4-16*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+4*((1-2*k)/(k*(1-k))^(1/2)+eps1)^2*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)*(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^3)^(1/2))*(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)/(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)+(1/9)*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2)*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(16/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4-16*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+4*((1-2*k)/(k*(1-k))^(1/2)+eps1)^2*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)*(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^3)^(1/2))^2*(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2/(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2-(1/27)*(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2*(4/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-2*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2+(16/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4-16*((1-2*k)/(k*(1-k))^(1/2)+eps1)*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+4*((1-2*k)/(k*(1-k))^(1/2)+eps1)^2*(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^4+3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^2-3*(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)*(((1-2*k)/(k*(1-k))^(1/2)+eps1)^2+(-(1-2*k)/(k*(1-k))^(1/2)+eps2)^2)/(eps4*sin(tau)+4*(k/(1-k))^(1/2)+4*eps3+2*(1-2*k)/(k*(1-k))^(1/2)+2*eps1)^3)^(1/2))^3/(2*(k/(1-k))^(1/2)+2*eps3+(1-2*k)/(k*(1-k))^(1/2)+eps1)^2

(12)

assume(0 < k and k < 1)

mtaylor(f(w1), [eps1, eps2, eps3, eps4], 2)

Error, (in gcd/LinZip) input must be polynomials over the integers

 

``


Wish you could give some advice on how to improve the situation.

Thanks a lot in advance.

Download res2.mw

 

 

How can I run Maple Script ,hold it and continue to run it ?
Somethink like Matlab pause statment

 

Tank you

I have this maple code:
I want to change

back to α. How can i do it ? (it don't work with unprotect)

 

 

I do the numerical simulation with

lp:=dsolve(....,type = numeric, range = ta .. te)

The simulation stop at t=te .

I want to stop the simulation when e.g. x(t) < 0

How can i do it ?

 

I use
lp1=dsolve(...,numeric)
p1 := odeplot(lp1,....)

new parameter

lp2=dsolve(...,numeric)
p2 := odeplot(lp2,....)

display([p1, p2], legend = ["step", "impulse"])

anf get the error

 

Error, (in plots:-display) display does not accept the legend option

 

 

 

 


In the following file when p is a fraction other than 1/2 the integral is not evaluated. Please help

INTEGRAL2.mw
 

 

 

restart; Digits := 7; r := 2.5; Q := proc (n) options operator, arrow; int(simplify(1/(x*r^2*cos(x-y)+z*r^2*sin(z-y))^n, symbolic), y = 0 .. Pi) end proc; HH := eval(Q(5))

int(0.1048576e-3/(x^5*cos(x-1.*y)^5-5.*x^4*cos(x-1.*y)^4*z*sin(-1.*z+y)+10.*x^3*cos(x-1.*y)^3*z^2-10.*x^3*cos(x-1.*y)^3*z^2*cos(-1.*z+y)^2-10.*x^2*cos(x-1.*y)^2*z^3*sin(-1.*z+y)+10.*x^2*cos(x-1.*y)^2*z^3*sin(-1.*z+y)*cos(-1.*z+y)^2+5.*x*cos(x-1.*y)*z^4-10.*x*cos(x-1.*y)*z^4*cos(-1.*z+y)^2+5.*x*cos(x-1.*y)*z^4*cos(-1.*z+y)^4-1.*z^5*sin(-1.*z+y)+2.*z^5*sin(-1.*z+y)*cos(-1.*z+y)^2-1.*z^5*sin(-1.*z+y)*cos(-1.*z+y)^4), y = 0 .. Pi)

(1)

``


 

Download integral_unknown.mw

 

Can any one help to find the value of sigma(r,z) and theta(r,z) from the differential equations analytically, 

ODEs:= <
      diff(theta(r),r$2) = -(1/r)*diff(theta(r),r) - diff(sigma(r),r)*diff(theta(r),r)-diff(theta(r),r)^2,  
   diff(sigma(r),r$2) = -(1/r)*diff(sigma(r),r) -diff(theta(r),r$2)-(1/r)*diff(theta(r),r)>;
boundary conditions

'diff((theta),r)=0','diff((sigma),r)=0'; # at r=0
and theta=0, sigma=0; #at r=h(z) 

help required to find the value of u analytically

 

restart:
ode:=-diff(y(x),x,x)+(1/4)*y(x)-4*exp(-x)=0:
init:=y(0)=0,y(1)=0:
exact:=dsolve({ode,init},y(x)):
N:=8:
trial:=sum(c[i]*x^i,i=1..N):
residual:=lhs(subs(y(x)=trial,ode)):
R:=simplify(residual):
sys:=[]:
for i from 1 to N  do sys:=[op(sys),int(R*x^i,x=0..1)=0];    
od:
sys:
vars:=seq(c[i],i=1..N):
A,b:=LinearAlgebra[GenerateMatrix](sys,[vars]):
sol:=solve({op(sys)},{vars}):
assign(sol):
trial:

# if i am plotting the graph exact and trial i am getting the error, separately if i am plotting the graph of exact i am getting the plot, similarly exact - trial error
trial_fun:=unapply(trial,x):
exact_fun:=unapply(rhs(exact),x):
evalf(trial_fun(1)-exact_fun(1)):
plot(exact,trial,x=0..1):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
plot(trial,x=0..1,legend['trial']):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct



#error calculation

plot(exact-trial,x=0..1):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct


restart:

restart:

Eqn:=-diff(y(x),x,x)+(1/4)*y(x)-4*exp(-x)=0:
BCs:=y(0)=0,y(1)=0:
dsolve({Eqn,BCs},y(x)):
assign(%):y:=unapply(y(x),x):
plot(y(x),x=0..1);
 

 

 

 

Dear sir

 I am facing the problem with executing the program with Maple13. The software problem is maple13 is not executing the programs and showing the dialogue box as waiting for the kernel. Actually, what is this kernel, which is not understanding me? So please can anyone do a favor in this regard? How to connect to the kernel? 

I need some help. I'm trying to solve this system of equations, but maple says the solutions may have been lost.

I don't know why. Here are the equations:

I have four equations,very unknown variables in the equation.

I am trying to solve for any 4 unknowns ,not must had be Zoo1.Zoo2.th1.th2,it can be Za1.Za2.Zb1.Zb2.  

Any help  would be greatly appreciated.

Пример02.mws

for example,i have already got the odeplot of function m(t),n(t).  And now i want to use the value of m(t) to calculate function x(t),y(t).

eq1:=diff(x(t),t)=m(t)*cos(y(t))-n(t)*sin(y(t));  #The function of x(t):

eq2:=diff(y(t),t)=m(t)*sin(y(t))+n(t)*cos(y(t));  #The function y(t):

inc:=x(0)=1;y(0)=2;

dsolve({eq1,eq2,inc},[x(t),y(t)],numeric);

but i got an Error

Error, (in dsolve/numeric/process_input) unknown m present in ODE system is not a specified dependent variable or evaluatable procedure.

But before this i have already got the odeplot of function m(t) and n(t),how can i solve this problem?

Can anyone tell me why the following command

restart; with(plots): with(Statistics):  with(numapprox):

 create an error of this type?

Error, Got internal error in Typesetting:-Parse : "cannot determine if this expression is true or false: membertype(specfunc(Typesetting:-mspace),Typesetting:-mempty(Typesetting:-mspace(depth = "0.0ex",height = "0.0ex",width = "0.0em",linebreak = "newline")))"
 

Hello everyone!

Please help me to resolve following error appeared in PDEs.

I have following system of partial differential equation and tried to solve with numerical method

pde1:=diff(U, t)-(diff(U, x, x))-2*U*(diff(U, x))+diff(U*V, x)

> pde2 := diff(V, t)-(diff(V, x, x))-2*V*(diff(V, x))+diff(U*V, x);
> ics := { U(x, 0) = sin(x),  V(x, 0) = sin(x)};

sol:=pdsolve(pde1,pde2,ics,numeric,time=t, range=1..20)

I am get following error

Error, (in pdsolve) invalid input: `pdsolve/numeric` expects its 2nd argument, IBCs, to be of type {set, list}, but received 0
 

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