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Dear all

 

If its possible in  Maple to change the integral of the sum to  the sum of integrals when I calucle the integral of a function series

 

Thank you

I would prefer that all the polynomials generated in my workbook by MAPLE were in expanded form.  For instance, it the elements of a matrix are polynomials, I want to see the expanded form for all of them.  What do I type into a workbook to make this happen.  (I am a new user of MAPLE.) 

Hello! Hope every is fine. I want to expand all expression of exp of the attached file like this

exp(c[1]*t+d[1]*n-d) = exp(c[1]*t+d[1]*n)*exp(-d)

waiting your kind response.

Help.mw

 

 

Mob #: 0086-13001903838

 

hey guys Im new client in maple and today I was about check out the resualt of my mathematic quastion with maple.

I need a step by step solution and exact command to give me true resualts 

for example 

how can I expand a factorization like (x^2-y^2) to (x-y)(x+y)

in a little more  complicated form (cd-1)^2-(c-d)^2/(d^2)(c-1)=5 the value of c=?

for solve this problem I need to expand (cd-1)^2-(c-d)^2 than other expands & in the end value of c

I dont have anymore time for my mathemathic exam so know that how maple works in basic and intermadiate mathematic level is important to me

thank you guys

 

How do I multiply the 4x into the summation to get  (Sum(4*n*a[n]*x^(n), n = 0 .. infinity))  and same idea for the 3rd third?

Also, how do I go from   Sum(a[n-2]*x^(n-2), n = 2 .. infinity)  to  Sum(a[n]*x^(n), n = 0 .. infinity)  by manipulating the indices?

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 

It's my first post on this forum so Hi everyone from Poland!

I have the following question.

Is it possible to force the Maple to obtain a result in a particular form? For example instead (a+b)3 I wan to have the result of the form: a3+3a2b+3ab2+b3. And I want to multiply the red brackets to receive a quadratic forms.

Below is a sample result that I get and I want it in a different form.

http://i65.tinypic.com/28k29hk.png

[IMG]http://i65.tinypic.com/28k29hk.png[/IMG]

Hi,

Wondered if anyone could help with the query below.

Consider f(x,y) defined as:
f := proc (x, y) options operator, arrow; x*y/(x+y) end proc

 

Then f(A, B); becomes:
(A * B )/(A + B)

 

now consider the polynomial:(poly2)

poly2:=(A*B+A*X+B*X)*(Y+X)/((A+B)*X*(2*Y+X))

 

This polynomial is just the expansion of the polynomial below (lets call it poly1) which MAPLE does not recognize.

(A*B/(A+B)+X)/(X+Y*X/(Y+X))

Here you can see that A,B on top and X,Y on the bottom are clearly of the form f(x,y).

 

Is there a way you can get MAPLE to recognize certain algebraic forms such that the polynomial poly2 could be written either as poly1 (already shown above) or as poly3 below:

poly3:=(f(A, B)+X)/(X+f(Y, X))

 

I have tried using simplify in the following form but not much luck. It doesn't seem to recognize anything other than the obvious.

simplify(poly2, {A*B/(A+B) = F1}, tdeg(A, B))

 

(I am still a bit new to the MAPLE syntax and procedures so apologies if I have missed something obvious function that can do this.)

 

Thanks.

 

Why does the collect command work for some expressions and not for others. Here is a screen shot

I assume the collect command is supposed to rewrite the expression in terms of the variable descending order.

p := expand((a^2+2*x)*(a^2+2*x));
                        4      2        2   2
                       a  + 4 a  x + 4 x

collect(p, x);
                        4      2        2   2
                       a  + 4 a  x + 4 x

Does not work.

But if you look at the screenshot , it works for other expressions.

hi  for example to calculate the following

residue((Psi(-z)+Eulergamma)^2*h(z), z = 2)

gives

3*h(2)+(D(h))(2)

but it possible to write 

as( Psi(2)+Eulergamma(z))*h(2)+(D(h))(2)

so that 

and Psi(z)+Eulergamma== harmonicNumber(z-1)

the result must be

harmonicNumber(2)*h(2)+(D(h))(2)

it is possible that Maple gives explit form of the values function avoid to calculate automatic.

thanks

I am trying to expand out the terms  of equation 13.  The expand command causes the lhs to be zero?


Initialize the metric and tetrad

 

restart; with(Physics); with(Tetrads); with(PDETools)

0, "%1 is not a command in the %2 package", Tetrads, Physics

(1.1)

X = [zetabar, zeta, v, u]

X = [zetabar, zeta, v, u]

(1.2)

ds2 := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(zetabar, zeta, v, u)), (du+Physics:-`*`(Ybar(zetabar, zeta, v, u), dzeta)+Physics:-`*`(Y(zetabar, zeta, v, u), dzetabar)-Physics:-`*`(Physics:-`*`(Y(zetabar, zeta, v, u), Ybar(zetabar, zeta, v, u)), dv))^2)

2*dzeta*dzetabar+2*du*dv+2*H(zetabar, zeta, v, u)*(du+Ybar(zetabar, zeta, v, u)*dzeta+Y(zetabar, zeta, v, u)*dzetabar-Y(zetabar, zeta, v, u)*Ybar(zetabar, zeta, v, u)*dv)^2

(1.3)

declare(ds2)

Ybar(zetabar, zeta, v, u)*`will now be displayed as`*Ybar

(1.4)

NULL

vierbien = Matrix([[1, 0, -Ybar(zetabar, zeta, v, u), 0], [0, 1, -Y(zetabar, zeta, v, u), 0], [Physics:-`*`(H(zetabar, zeta, v, u), Y(zetabar, zeta, v, u)), Physics:-`*`(H(zetabar, zeta, v, u), Ybar(zetabar, zeta, v, u)), 1-Physics:-`*`(Physics:-`*`(H(zetabar, zeta, v, u), Y(zetabar, zeta, v, u)), Ybar(zetabar, zeta, v, u)), H(zetabar, zeta, v, u)], [Y(zetabar, zeta, v, u), Ybar(zetabar, zeta, v, u), -Physics:-`*`(Y(zetabar, zeta, v, u), Ybar(zetabar, zeta, v, u)), 1]])

vierbien = (Matrix(4, 4, {(1, 1) = 1, (1, 2) = 0, (1, 3) = -Ybar(zetabar, Zeta, v, u), (1, 4) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = -Y(zetabar, Zeta, v, u), (2, 4) = 0, (3, 1) = H(zetabar, Zeta, v, u)*Y(zetabar, Zeta, v, u), (3, 2) = H(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (3, 3) = 1-H(zetabar, Zeta, v, u)*Y(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (3, 4) = H(zetabar, Zeta, v, u), (4, 1) = Y(zetabar, Zeta, v, u), (4, 2) = Ybar(zetabar, Zeta, v, u), (4, 3) = -Y(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (4, 4) = 1}))

(1.5)

``

NULL

Setup(tetrad = rhs(vierbien = Matrix(%id = 18446744078213056502)), metric = ds2, mathematicalnotation = true, automaticsimplification = true, coordinatesystems = (X = [zetabar, zeta, v, u]), signature = "+++-")

[automaticsimplification = true, coordinatesystems = {X}, mathematicalnotation = true, metric = {(1, 1) = 2*H(X)*Y(X)^2, (1, 2) = 1+2*H(X)*Y(X)*Ybar(X), (1, 3) = -2*H(X)*Y(X)^2*Ybar(X), (1, 4) = 2*H(X)*Y(X), (2, 2) = 2*H(X)*Ybar(X)^2, (2, 3) = -2*H(X)*Ybar(X)^2*Y(X), (2, 4) = 2*H(X)*Ybar(X), (3, 3) = 2*H(X)*Y(X)^2*Ybar(X)^2, (3, 4) = 1-2*H(X)*Y(X)*Ybar(X), (4, 4) = 2*H(X)}, signature = `+ + + -`, tetrad = {(1, 1) = 1, (1, 3) = -Ybar(X), (2, 2) = 1, (2, 3) = -Y(X), (3, 1) = H(X)*Y(X), (3, 2) = H(X)*Ybar(X), (3, 3) = 1-H(X)*Y(X)*Ybar(X), (3, 4) = H(X), (4, 1) = Y(X), (4, 2) = Ybar(X), (4, 3) = -Y(X)*Ybar(X), (4, 4) = 1}]

(1.6)

gamma_[4, 1, 1] = 0

diff(Ybar(X), zeta)-(diff(Ybar(X), u))*Ybar(X) = 0

(1)

gamma_[4, 2, 2] = 0

diff(Y(X), zetabar)-(diff(Y(X), u))*Y(X) = 0

(2)

gamma_[1, 4, 4] = 0

(diff(Ybar(X), u))*Y(X)*Ybar(X)-Y(X)*(diff(Ybar(X), zeta))-Ybar(X)*(diff(Ybar(X), zetabar))-(diff(Ybar(X), v)) = 0

(3)

gamma_[2, 4, 4] = 0

(diff(Y(X), u))*Y(X)*Ybar(X)-Y(X)*(diff(Y(X), zeta))-(diff(Y(X), zetabar))*Ybar(X)-(diff(Y(X), v)) = 0

(4)

gamma_[3, 4, 4] = 0

0 = 0

(5)

gamma_[4, 4, 4] = 0

0 = 0

(6)

shearconditions := {diff(Y(X), zetabar)-(diff(Y(X), u))*Y(X) = 0, diff(Ybar(X), zeta)-(diff(Ybar(X), u))*Ybar(X) = 0, (diff(Y(X), u))*Y(X)*Ybar(X)-Y(X)*(diff(Y(X), zeta))-(diff(Y(X), zetabar))*Ybar(X)-(diff(Y(X), v)) = 0, (diff(Ybar(X), u))*Y(X)*Ybar(X)-Y(X)*(diff(Ybar(X), zeta))-Ybar(X)*(diff(Ybar(X), zetabar))-(diff(Ybar(X), v)) = 0}:

 

 

RicciT := proc (a, b) options operator, arrow; SumOverRepeatedIndices(Ricci[mu, nu]*e_[a, `~mu`]*e_[b, `~nu`]) end proc

proc (a, b) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-`*`(Physics:-`*`(Physics:-Ricci[mu, nu], Physics:-Tetrads:-e_[a, `~mu`]), Physics:-Tetrads:-e_[b, `~nu`])) end proc

(7)

SlashD := proc (f, a) options operator, arrow; SumOverRepeatedIndices(D_[b](f)*e_[a, `~b`]) end proc

proc (f, a) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-`*`(Physics:-D_[b](f), Physics:-Tetrads:-e_[a, `~b`])) end proc

(8)

SlashD(f(X), 1)

diff(f(X), zeta)-Ybar(X)*(diff(f(X), u))

(9)

SlashD(f(X), 2)

diff(f(X), zetabar)-Y(X)*(diff(f(X), u))

(10)

SlashD(f(X), 3)

(1+H(X)*Y(X)*Ybar(X))*(diff(f(X), u))-H(X)*((diff(f(X), zeta))*Y(X)+Ybar(X)*(diff(f(X), zetabar))+diff(f(X), v))

(11)

SlashD(f(X), 4)

-Y(X)*Ybar(X)*(diff(f(X), u))+Ybar(X)*(diff(f(X), zetabar))+(diff(f(X), zeta))*Y(X)+diff(f(X), v)

(12)

NULL

  simplify(RicciT(1, 2), shearconditions) = 0

H(X)*(diff(diff(Y(X), zeta), zetabar))*Ybar(X)-H(X)*Ybar(X)*Y(X)*(diff(diff(Ybar(X), u), zetabar))-H(X)*Ybar(X)^2*(diff(diff(Y(X), u), zetabar))-H(X)*Y(X)^2*(diff(diff(Ybar(X), u), zeta))-2*H(X)*Y(X)*Ybar(X)*(diff(diff(Y(X), u), zeta))+H(X)*Y(X)^2*Ybar(X)*(diff(diff(Ybar(X), u), u))-H(X)*Y(X)*(diff(diff(Ybar(X), u), v))+H(X)*Y(X)*Ybar(X)^2*(diff(diff(Y(X), u), u))-H(X)*(diff(diff(Y(X), u), v))*Ybar(X)+H(X)*(diff(Ybar(X), zetabar))^2+(-3*H(X)*Y(X)*(diff(Ybar(X), u))-(diff(H(X), u))*Y(X)*Ybar(X)+(diff(H(X), zeta))*Y(X)+(diff(H(X), zetabar))*Ybar(X)+diff(H(X), v))*(diff(Ybar(X), zetabar))+H(X)*(diff(Y(X), zeta))^2+(-4*H(X)*(diff(Y(X), u))*Ybar(X)-(diff(H(X), u))*Y(X)*Ybar(X)+(diff(H(X), zeta))*Y(X)+(diff(H(X), zetabar))*Ybar(X)+diff(H(X), v))*(diff(Y(X), zeta))+2*H(X)*Y(X)^2*(diff(Ybar(X), u))^2-Y(X)*(-(diff(H(X), u))*Y(X)*Ybar(X)+(diff(H(X), zeta))*Y(X)+(diff(H(X), zetabar))*Ybar(X)+diff(H(X), v))*(diff(Ybar(X), u))+2*(diff(Y(X), u))*Ybar(X)*(H(X)*(diff(Y(X), u))*Ybar(X)+(1/2)*(diff(H(X), u))*Y(X)*Ybar(X)-(1/2)*(diff(H(X), zeta))*Y(X)-(1/2)*(diff(H(X), zetabar))*Ybar(X)-(1/2)*(diff(H(X), v))) = 0

(13)

``

0 = 0

0 = 0

(14)

``

Why does the expand command cause the lhs to be zero?

NULL


Download Question_R12.mw

When I write in maple the following:

x*(x+y)

 

What do I need to write to make maple make the operation that will evaluate the expression and show the following?

 

x^2+x*y

 

simplify(%) or evaluate(%) only shows it the same way it was inputted to start with.

I am trying separation of variables in Maple. I get an equation that has the form   

And now I want to tell Maple to assign the terms with 1/R in them to one variable, say eq21, and the term with 1/Z to second variable, say eq22 The idea is that I can later more easily work with each separate ode. 

I do not know to separate those apart. I could offcourse copy and paste by hand, but I want to automate this.

I tried match() and patmatch() but I am not seeing the way. Here is the code:

restart;
T:=  (r,z)-> Z(z)*R(r);
eq1:= diff(T(r,z),r$2)+1/r*diff(T(r,z),r)+diff(T(r,z),z$2);
eq2:=expand(eq1/(Z(z)*R(r)));

#need now way to break the above into 2 different variables.

ps. I know I can do this:

restart;
T:=  (r,z)-> Z(z)*R(r);
eq1:= diff(T(r,z),r$2)+1/r*diff(T(r,z),r)+diff(T(r,z),z$2);
eq2:=expand(eq1/(Z(z)*R(r)));
eq3:=collect(eq2,1/R(r));
eq21:=op(1,eq3);
eq22:=op(2,eq3);

But this for me is not the right way to do it. I think there should be more algebraic way.

 

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

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