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I assume that I'm not providing the correct input to the simplify command to get the simplification that I want.  In particular, for the following code:

assume(n, positive);
simplify(3^(-(1/2)*n)*2^((1/6)*n)-2^((2/3)*n)*6^(-(1/2)*n));
simplify(log(3^(-(1/2)*n)*2^((1/6)*n))-log(2^((2/3)*n)*6^(-(1/2)*n))); 

The expression should evaluate to 0.  However, the first expression does not simplify to 0 (it does not simplify at all in Maple) while the second expression simplifies to 0.

The simplification is fairly easy for the first expression by factoring 6 and combining terms; it seems like I'm not entering the command to simplify in this way.

After manually working out answer for problem 4-4 in Mathews & Walker's Mathematical Methods of Physics , I tried to check my solution with maple2015. Briefly the problem involves inputs periodic with period T, being transformed into outputs, through a kernal G.  The net result is that all input frequencies omega periodic in T are multiplied by (omega_0/omega)^2, except for constant frequency which transforms to zero.  The problem asks to evaluate the kernal G.

Maple2015 correctly evaluated the integral for a constant input, a cosine input, and a sine input, but gave undefined when I tried an exponential(i*x) input which is just a linear combination of the two previous inputs.  I found this interesting because the integral is finite, well defined, and only has an absolute function (in the kernal), which may cause Maple problems, as it correctly evaluated integral when I split it into two regions.  Interestingly if instead of working with a period of T, I used 2*pi, and redfined my G function accordingly, Maple evaluated the exp input integral without any problems.  So the problem appears to be with the T variable, but I correctly used assumptions of T>0, and 0<t<T, so I am not sure why it would work correctly when I use T=2*pi, but failed when using a general period T.  Any help would be welcome.

 

 

restart

assume(T > 0)

assume(0 < t and t < T)

about(T)

Originally T, renamed T~:

  Involved in the following expressions with properties
    T-t assumed RealRange(Open(0),infinity)
  is assumed to be: real
  also used in the following assumed objects
  [T-t] assumed RealRange(Open(0),infinity)

 

about(t)

Originally t, renamed t~:

  Involved in the following expressions with properties
    T-t assumed RealRange(Open(0),infinity)
  is assumed to be: RealRange(Open(0),infinity)
  also used in the following assumed objects
  [T-t] assumed RealRange(Open(0),infinity)

 

assume(n::integer, n > 0)

about(n)

Originally n, renamed n~:

  is assumed to be: AndProp(integer,RealRange(1,infinity))

 

G := proc (x) options operator, arrow; (1/2)*omega0^2*T^2*((1/6)*Pi^2-(1/2)*Pi*abs(2*Pi*x/T)+Pi^2*x^2/T^2)/Pi^2 end proc

proc (x) options operator, arrow; (1/2)*omega0^2*T^2*((1/6)*Pi^2-(1/2)*Pi*abs(2*Pi*x/T)+Pi^2*x^2/T^2)/Pi^2 end proc

(1)

(int(G(t-tp), tp = 0 .. T))/T

0

(2)

(int(G(t-tp)*sin(2*Pi*n*tp/T), tp = 0 .. T))/T

(1/2)*T^2*omega0^2*cos(t*Pi*n/T)*sin(t*Pi*n/T)/(Pi^2*n^2)

(3)

(int(G(t-tp)*cos(2*Pi*n*tp/T), tp = 0 .. T))/T

(1/4)*T^2*omega0^2*(2*cos(t*Pi*n/T)^2-1)/(Pi^2*n^2)

(4)

(int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = 0 .. T))/T

undefined/T

(5)

(int(G(t-tp)*(cos(2*Pi*n*tp/T)+I*sin(2*Pi*n*tp/T)), tp = 0 .. T))/T

undefined/T

(6)

simplify((int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = 0 .. t))/T+(int(G(t-tp)*exp((I*2)*Pi*n*tp/T), tp = t .. T))/T)

(1/4)*omega0^2*exp((2*I)*t*Pi*n/T)*T^2/(Pi^2*n^2)

(7)

assume(0 < t and t < 2*Pi)

G2 := proc (x) options operator, arrow; 2*omega0^2*((1/6)*Pi^2-(1/2)*Pi*abs(x)+(1/4)*x^2) end proc

proc (x) options operator, arrow; 2*omega0^2*((1/6)*Pi^2-(1/2)*Pi*abs(x)+(1/4)*x^2) end proc

(8)

(int(G2(t-tp)*exp(I*n*tp), tp = 0 .. 2*Pi))/(2*Pi)

omega0^2*exp(I*n*t)/n^2

(9)

 

Download MathewsWalkerProblem4-4.mwMathewsWalkerProblem4-4.mw

 

 

Hello! Hope every is fine. I want to expand the following expression

exp(2*c*t+2*d*n-d)*alpha*c*a[0]*b[1]^2-exp(2*c*t+2*d*n-d)*alpha*c*a[1]*b[0]*b[1]-exp(2*c*t+2*d*n-d)*alpha*a[0]*a[1]*b[1]+exp(2*c*t+2*d*n-d)*alpha*a[1]^2*b[0]+exp(2*c*t+2*d*n)*alpha*a[0]*a[1]*b[1]-exp(2*c*t+2*d*n)*alpha*a[1]^2*b[0]+exp(c*t+d*n)*alpha*c*a[0]*b[0]*b[1]-exp(c*t+d*n)*alpha*c*a[1]*b[0]^2-exp(2*c*t+2*d*n-d)*a[0]*b[1]^2+exp(2*c*t+2*d*n-d)*a[1]*b[0]*b[1]-exp(c*t+d*n-d)*alpha*a[0]^2*b[1]+exp(c*t+d*n-d)*alpha*a[0]*a[1]*b[0]+exp(2*c*t+2*d*n)*a[0]*b[1]^2-exp(2*c*t+2*d*n)*a[1]*b[0]*b[1]+exp(c*t+d*n)*alpha*a[0]^2*b[1]-exp(c*t+d*n)*alpha*a[0]*a[1]*b[0]-exp(c*t+d*n-d)*a[0]*b[0]*b[1]+exp(c*t+d*n-d)*a[1]*b[0]^2+exp(c*t+d*n)*a[0]*b[0]*b[1]-exp(c*t+d*n)*a[1]*b[0]^2

 

like this 

exp(2*c*t+2*d*n)*exp(-d)*alpha*c*a[0]*b[1]^2-exp(2*c*t+2*d*n)*exp(-d)*alpha*c*a[1]*b[0]*b[1]-exp(2*c*t+2*d*n)*exp(-d)*alpha*a[0]*a[1]*b[1]+exp(2*c*t+2*d*n)*exp(-d)*alpha*a[1]^2*b[0]+exp(2*c*t+2*d*n)*alpha*a[0]*a[1]*b[1]-exp(2*c*t+2*d*n)*alpha*a[1]^2*b[0]+exp(c*t+d*n)*alpha*c*a[0]*b[0]*b[1]-exp(c*t+d*n)*alpha*c*a[1]*b[0]^2-exp(2*c*t+2*d*n)*exp(-d)*a[0]*b[1]^2+exp(2*c*t+2*d*n)*exp(-d)*a[1]*b[0]*b[1]-exp(c*t+d*n)*exp(-d)*alpha*a[0]^2*b[1]+exp(c*t+d*n)*exp(-d)*alpha*a[0]*a[1]*b[0]+exp(2*c*t+2*d*n)*a[0]*b[1]^2-exp(2*c*t+2*d*n)*a[1]*b[0]*b[1]+exp(c*t+d*n)*alpha*a[0]^2*b[1]-exp(c*t+d*n)*alpha*a[0]*a[1]*b[0]-exp(c*t+d*n)*exp(-d)*a[0]*b[0]*b[1]+exp(c*t+d*n)*exp(-d)*a[1]*b[0]^2+exp(c*t+d*n)*a[0]*b[0]*b[1]-exp(c*t+d*n)*a[1]*b[0]^2

i.e., expand exp(2*c*t+2*d*n-d) into exp(2*c*t+2*d*n)*exp(-d) 

waiting your kind response 

M := 10^2; plot(exp(M), t);

When we execute the above code we get graph in output naturally. But when execute the following code  , there is no graph in output, why?

M := 10^3; plot(exp(M), t);

Thanks in advance for any suggestion.

I am trying to integrate product of exp(t+s) and a piecewise polynomial but the result can not be read and not usefull. also I used numerical integration function "Quadrature" but the result did not change.

error.mwerror.mw

Hi,

I got the Real and Imaginary of an expression J1 

assume(d,real):

Gamma:=0.04:tau:=10*Pi:j:=0:

J1:=(exp((1-I*d)*Gamma*tau)-1)/((1-I*d));

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): (I works here this amont is real)

################

but when I change the expression  for J1 to be

J1:=((2*e^(-2^(-j-1)*(1-I*d))-e^(-2^(-j)*(1-I*d))-1)*exp((1-I*d)*Gamma*tau)-1)/((1-I*d)):

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): 

J1mod here is complex(I dont know why? it doesnt separate the real and the im )

Any comments will help

Thanks

It seems a frequent issue that exported 3d plots are not shown as wished. I experience the same problem. Although I exported in the .eps format into a .tex latex-file the resulting .pdf-file shows a somewhat pixelated image of my 3d plot as if it was created in "Paint". Is there a solution for this in Maple13?

I'm trying to get the RHL of exp1:=(2/(1+e^(-1/x)) as x->0+

and have l2:=limit(exp1,x=0,right) but that isn't giving me a value. How do I correct this? 

 

Hi all.

I try to get the real part from the complex expression. But it turns out to not be the simplest result:

A:=I*sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*exp(-I*k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b)

convert(exp(-I*k[0]*h), sin);

simplify(Re(A));

Maple results in:

Re(sin(k*Pi*(-x+h*cos(theta))/a)*sin(l*Pi*(-y+h*sin(theta))/b)*exp(-I*k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b))

while the simplified result should be:

sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*sin(k*Pi*x/a)*sin(l*Pi*y/b)*sin(k[0]*h)

 

I wander how to get the simplifyed result in maple. Thanks

AOA... How are you all. I need the answer of the following question.

 

input in Maple: expand(exp(a+b)+exp(c+b))

output:  exp(a)*exp(b)+exp(c)*exp(b)

and

input in Maple: expand(exp(2a+b)+exp(3c+b))

output:  (exp(a))^2*exp(b)+(exp(c))^3*exp(b)

but i need exp(2a)*exp(b)+exp(3c)*exp(b)

 

PhD (Scholar)
Department of Mathematics

how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation

 

is there a faster way to calculate exp(x) than with the x^k/k! series

 

thanks

 

 

 

 

 

 

 

 

Hi

Is it possible to plot WKB solutions such as exp(-I*f(x)*x)/sqrt(f(x); where f(x) is any generic function of x e.g. sin^2x ? I have been trying in maple but can't get it to give me a plot.

How to solve the inequality 3^((x+3)/(5*x-2))-4 >= 5*3^((9*x-7)/(5*x-2)) with Maple?
An exact and explicit solution is required.

testing.mw

Hi all,

Basically, I want to substitute everthing in m using the s .

More or less, I am doing a reparameterization.

I have looked into subs command, but it does not quite does what I want.

It seems to me the Maple wont be substituting exp(-mu) to s1 ( or exp(mu) to 1/s1 ) if the exp has some other powers in it, such as exp(mu+tau).

Any ideas?

Thanks.

Casper

Hi, anyone can show me how to expand this formula with Maple:

                            (x+1)^n

where n is an unknown integer. My expectation is x^n +n*x^(n-1)+...

 

Thank you and regards,

Bhm

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