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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

there is a solution of equation,so the equation can be divided by the solution,but because the equation is complex,it can't be simplify by the soution,can anyone give me some help?thanks a lot.


I am trying to do a substitution as shown in the attached document. I know variants of this question have been asked before but dont quiet get what to do. It is problem with algsubs and how it handles denominators I think. Can get substiturion to work for simple fractions but more complicated ones fail. Would appreciate any guidance here.

restart 

``

``

CR := proc (a, b, c, d) options operator, arrow; (a-c)*(b-d)/((a-d)*(b-c)) end proc

proc (a, b, c, d) options operator, arrow; (a-c)*(b-d)/((a-d)*(b-c)) end proc

(1)

eqns := CR(a, b, c, d)

(a-c)*(b-d)/((a-d)*(b-c))

(2)

e1 := CR(b, a, c, d)

(b-c)*(a-d)/((b-d)*(a-c))

(3)

simplify(e1, {(a-c)*(b-d)/((a-d)*(b-c)) = lambda})

(a*b-a*c-b*d+c*d)/(a*b-a*d-b*c+c*d)

(4)

e1

(b-c)*(a-d)/((b-d)*(a-c))

(5)

``

lambda

lambda

(6)

applyrule((a-c)*(b-d)/((a-d)*(b-c)) = lambda, e1)

(b-c)*(a-d)/((b-d)*(a-c))

(7)

alias(lambda = (a-c)*(b-d)/((a-d)*(b-c)))

lambda

(8)

e1

(b-c)*(a-d)/((b-d)*(a-c))

(9)

``

NULL

``

f := a/b

a/b

(10)

``

f := algsubs(a/b = alpha, f)

alpha

(11)

f

alpha

(12)

algsubs((a-c)*(b-d)/((a-d)*(b-c)) = lambda, e1)

Error, (in algsubs) cannot compute degree of pattern in a

 

``

 

Download UHG5_substitution.mw

Why this simplifes:

z1:=n*(Int(cos(x)^(n-2), x))-(Int(cos(x)^(n-2), x));

simplify(z1);

But when adding an extra term to z1, it no longer simplfies the above any more:

z2 := cos(x)^(n-1)*sin(x)+n*(Int(cos(x)^(n-2), x))-(Int(cos(x)^(n-2), x));

simplify(z2);

You can see the second term, which is z1, was not simplfied any more.

Why? And how would one go about simplifying z2 such that the second term gets simplfies as with z1, but while using z2 expression. It seems simplify stopped at first term and did not look ahead any more?

Maple 18.02, windows.

Hi,

I use the VectorCalculus package to calcutate derivative formula for geometric functions, and met difficulity simplifying the result expression.

For example, I define some vectors P, S, V like below:

P:=<Px, Py, Pz>, S:=<Sx, Sy, Sz>, V:=<Vx, Vy, Vz>

then define an intermediate variable Q:=P - S,

then define a function d:= sqrt(DotProduct(Q, Q)-(DotProuct(Q,V))^2)

by calculating the function's derivative w.r.t Px I got a very complex result expression:

dpx:=1/2 * (2Px - 2Sx - 2 ( (Px - Sx) Vx + (Py - Sy) Vy + (Pz - Sz)Vz )Vx ) / (sqrt( (Px-Sx)^2 + (Py-Sy)^2 + (Pz-Sz)^2 - .....)

 

Apparently this expression can be simplified by substituting its sub-expression with pre-defined variables like Q and d.

I know I can use subs, eval, and subsalg to do it manually:

subs(1/(sqrt( (Px-Sx)^2 + (Py-Sy)^2 + (Pz-Sz)^2 - .....) = 1/dv, dfdpx)

subs((Px - Sx) Vx + (Py - Sy) Vy + (Pz - Sz)Vz = dotproduct_q_v, dfdpx)

and I can get a simplified expression like this:

(qx-dotproduct_q_v*vx)/d

 

But it's like my brain does the simplification first, and Maple only does the text substitution for me.

Is there any way to do it automatically?

 

Thanks,

-Kai

 

Hello,

 

How can one simplify following expression:

After applying 'simplify' command I am getting this:

Powers are not distributed between bases.

How to force Maple simplify it further to

 

Thank you.

 

restart:
tmp:=Vector(
[
1+(-s[2]-s[4]+2*w[1]/(1+1/exp(mu[p]))^2+(2*(-w[1]+1))/(1+1/(exp(mu[p])*exp(eta[p2])))^2)*s[1]^3+(-s[2]+s[3])*s[1]^2-s[2]*s[1],

(s[2]+s[4]-2*w[1]/(1+1/exp(mu[p]))^2-(2*(-w[1]+1))/(1+1/(exp(mu[p])*exp(eta[p2])))^2)*s[1]^3
]
);

tmp := Vector(2, {(1) = 1+(-s[2]-s[4]+2*w[1]/(1+1/exp(mu[p]))^2+(-2*w[1]+2)/(1+1/(exp(mu[p])*exp(eta[p2])))^2)*s[1]^3+(-s[2]+s[3])*s[1]^2-s[2]*s[1], (2) = (s[2]+s[4]-2*w[1]/(1+1/exp(mu[p]))^2-(-2*w[1]+2)/(1+1/(exp(mu[p])*exp(eta[p2])))^2)*s[1]^3})

(1)

rule3:=w[1]/(1+1/exp(mu[p]))^2+(-w[1]+1)/(1+1/(exp(mu[p])*exp(eta[p2])))^2 = s[3];

w[1]/(1+1/exp(mu[p]))^2+(-w[1]+1)/(1+1/(exp(mu[p])*exp(eta[p2])))^2 = s[3]

(2)

applyrule(rule3,tmp[1]);

1+(-s[2]-s[4]+2*w[1]/(1+1/exp(mu[p]))^2+2*(-w[1]+1)/(1+1/(exp(mu[p])*exp(eta[p2])))^2)*s[1]^3+(-s[2]+s[3])*s[1]^2-s[2]*s[1]

(3)

 

``

 

Download problem.mw

 

This is part of a large simplifcation where lots of terms are being substituted. In two of those terms, it did not simplify as we would expect.

I think the main thing is trying to find a way to factor out the "2".

 

I could do this

> rule3:=w[1]/(1+1/exp(mu[p]))^2+(-w[1]+1)/(1+1/(exp(mu[p])*exp(eta[p2])))^2 = s[3];
>rule3:=2*rule3;

> rule3ne:=-(w[1]/(1+1/exp(mu[p]))^2+(-w[1]+1)/(1+1/(exp(mu[p])*exp(eta[p2])))^2) = -s[3];
> rule3ne:=2*rule3ne;

> applyrule(rule3,tmp[1]);
> applyrule(rule3ne,tmp[2]);

For this example, this works.

But I hope for a more generic approach.

 

Thanks,

 

casper

 

 

 

@ecterrab 

I figured I'd start a new thread for odd things I come across whilst using the new physics package. 

I have found this, and am not sure if it is expected. 

 


restart

with(Physics):

Setup(mathematicalnotation = true):

``

Setup(Commutator(Psigma[i], Psigma[j]) = Physics:-`*`(Physics:-`*`(I, ep_[i, j, k]), Psigma[k]), AntiCommutator(Psigma[i], Psigma[j]) = Physics:-`*`(2, kd_[i, j]));

[algebrarules = {%AntiCommutator(Physics:-Psigma[i], Physics:-Psigma[j]) = 2*Physics:-KroneckerDelta[i, j], %Commutator(Physics:-Psigma[i], Physics:-Psigma[j]) = I*Physics:-LeviCivita[i, j, k]*Physics:-Psigma[k]}]

(1)

NULL

Psigma[1].Psigma[1]

Physics:-Psigma[1]^2

(2)

Simplify(%)

Physics:-Psigma[1]^2

(3)

Simplify(Physics:-Psigma[1]^2)

1

(4)

``


Download Simplify2.mw

Hello,
Maple does not cancel out a variable.

Why is that?

Is there a way to solve this? 

(I pasted my code on the bottom of this message)

 

Thanks for your help/advice,

Stephan

restart:
M(x):=piecewise(x<=l,1/2*(q*x^2)/(EI)-3/8*(q*l*x)/(EI),l<x,1/2*(q*x^2)/(EI)-13/8*(q*l*x)/(EI)+5/4*(q*l^2)/(EI)):
M(x):=M(x)*(-EI);
# simplify() does not work.....?
M(x):=simplify(%) assuming EI>0;
# Wiht EI cancelled out by hand it schould look like:
M(x):=piecewise(x<=l,1/2*(q*x^2)-3/8*(q*l*x),l<x,1/2*(q*x^2)-13/8*(q*l*x)+5/4*(q*l^2));

 

Hi all

kx,ky is the wavenumber, how can I get the 4 cases of piecewise function according to kx=0,kx≠0 and ky=0,ky≠0. Thanks

J := `assuming`([4*(int(int(JJ*exp(-I*(kx*x+ky*y))*sin(2*l*pi*x/a)*sin(2*k*pi*y/b), x = 0 .. a, AllSolutions), y = 0 .. b, AllSolutions))/(a*b)], [k::posint, l::posint, a > 0, b > 0, JJ > 0])

The following MWE shows what I mean:

with(Physics):Setup(mathematical=true):

Setup(noncommutativeprefix={MX,MY,MZ});

test:=proc()

    local eq;

    eq:=-Commutator(MX,MY)-Commutator(MZ,MY);

    eq:=simplify(subs(MX=-MZ,eq));

    return eq;

end proc:

 

test();  # yields -[-MZ,MY] - [MZ,MY]

 

%  # yields 0

 

 

Any ideas how I can solve this? I would like to return the simplified version.

kappa := Vector(7, [1,w[1]*(1-phi+phi*(1-1/(1+exp(-mu[p]-tau[p3]))))+(1-w[1])*
(1-phi+phi*(1-1/(1+exp(-mu[p]-tau[p3]-eta[p2])))),w[1]*phi/(1+exp(-mu[p]-tau[
p3]))+(1-w[1])*phi/(1+exp(-mu[p]-tau[p3]-eta[p2])),w[1]*(1-phi+phi*(1-1/(1+exp
(-mu[p])))*(1-phi)+phi^2*(1-1/(1+exp(-mu[p])))*(1-1/(1+exp(-mu[p]-tau[p3]))))+
(1-w[1])*(1-phi+phi*(1-1/(1+exp(-mu[p]-eta[p2])))*(1-phi)+phi^2*(1-1/(1+exp(-
mu[p]-eta[p2])))*(1-1/(1+exp(-mu[p]-tau[p3]-eta[p2])))),w[1]*phi^2*(1-1/(1+exp
(-mu[p])))/(1+exp(-mu[p]-tau[p3]))+(1-w[1])*phi^2*(1-1/(1+exp(-mu[p]-eta[p2]))
)/(1+exp(-mu[p]-tau[p3]-eta[p2])),w[1]*(phi/(1+exp(-mu[p]))*(1-phi)+phi^2/(1+
exp(-mu[p]))*(1-1/(1+exp(-mu[p]-tau[p3]))))+(1-w[1])*(phi/(1+exp(-mu[p]-eta[p2
]))*(1-phi)+phi^2/(1+exp(-mu[p]-eta[p2]))*(1-1/(1+exp(-mu[p]-tau[p3]-eta[p2]))
)),w[1]*phi^2/(1+exp(-mu[p]))/(1+exp(-mu[p]-tau[p3]))+(1-w[1])*phi^2/(1+exp(-
mu[p]-eta[p2]))/(1+exp(-mu[p]-tau[p3]-eta[p2]))]);

Download kappa.txt

Here is the expression, I am trying to simplify, given a set of rules. NEW_Cole.mw

I have tried different substitutions, using simplify with side rules, applyrule, eval, subs, algsubs.

But none seem to be working as the way I want them to be.

 

Is there a better way?

 

Thanks!

Hi Maple friends.

Maple tends to spit out results(which comprise of variables) in very complicated forms, and I have to use the context menu to select 'simplify' to reduce them.

Is there a setting which will automatically simplify Maple's output?

Thanks in advance.

I'm working on a complex problem in Composite Materials. I've gotten to a near-result 6x6 matrix, with several cells containing polynomial denominators. I have an equation for simplifying these, which boils the polynomials down to a single variable, but I can't seem to get it to substitute in. Can anyone help me solve this? The problem is also time-sensitive.

 

t := exp(2*(I*Pi*(1/11)))

u := t^10*a[10]+t^9*a[9]+t^8*a[8]+t^7*a[7]+t^6*a[6]+t^5*a[5]+t^4*a[4]+t^3*a[3]+t^2*a[2]+t*a[1]+a[0]

 

How can get maple to simplify expressions like u^3+u^2-1 so that the exponents are between 2*(I*Pi*(1/11)) and 1.

Essentially it keeps outputting things like exp(2*(I*Pi*(1/11)))^12 and not simplifying it as it is a root of unity

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