Items tagged with expand

Hello people in mapleprimes,


To the following expression, I want to apply applyop so that I want to change its denominator expanded ,

but I don't know how to do it.

So, I am writing now hoping someone  teach me it.

m:= 2*p/(p^2+1)^2;


op(m) brings the result of 2, p, 1/(p^2+1)^2,

And, op(1,m) is 2, op(2,m) is p and op(3,m) is 1/(p^2+1)^2, and

op([3,1],m) is p^2+1 and op([3,2],m) is -2.

So, the tree is `*`{2,p, 1/(p^2+1)^2}, and the tree of 1/(p^2+1)^2 is `^`{p^2+1,-2}.

And, the command expand can't play that rule on 1/{(p^2+1)^2} as its original rule is

to expand the mere numerator. And, anyway, 1/{(p^2+1)^2} is interpleted by maple as (p^2+1)^(-2),

which is not 1 devided by (p^2+1)^2, the latter of which is seen to be expanded to be p^4+2*p^2+1, but

the interpletation by maple of it is not so, and if applyop(`denom`,expand,m) works, even it is good.

But, it doesn't follow the syntax of maple. Then, can't use applyop in this case?

Best wishes.



It might be a silly question but here it goes. I have a sin function in terms of sin(omega*(T0-T)+Phi) and i need to expand it by keeping omega*T0+phi as a single term. One way is by subs omega*T0+phi as a constant 'c' and then after expanding we can back substitute. But is there any option in expand function itself?




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.



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



like this 


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.



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)



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


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.)




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)



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


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


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


X = [zetabar, zeta, v, u]

X = [zetabar, zeta, v, u]


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



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



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}))




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}]


gamma_[4, 1, 1] = 0

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


gamma_[4, 2, 2] = 0

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


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


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


gamma_[3, 4, 4] = 0

0 = 0


gamma_[4, 4, 4] = 0

0 = 0


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


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


SlashD(f(X), 1)

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


SlashD(f(X), 2)

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


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))


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)



  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



0 = 0

0 = 0



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



When I write in maple the following:



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




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

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