Items tagged with simplify

It is suggested  

hypergeom([1/3, 2/3], [3/2], (27/4)*z^2*(1-z)) = 1/z

if z > 1. Here is my try to prove that with Maple:


 

a := `assuming`([convert(hypergeom([1/3, 2/3], [3/2], (27/4)*z^2*(1-z)), elementary)], [z > 1])

-(1/((1/2)*(27*z^3-27*z^2+4)^(1/2)+(3/2)*z*(3*z-3)^(1/2))^(1/3)-1/((1/2)*(27*z^3-27*z^2+4)^(1/2)-(3/2)*z*(3*z-3)^(1/2))^(1/3))/(z*(3*z-3)^(1/2))

(1)

b := `assuming`([simplify(a, symbolic)], [z >= 1])

2*(-(12*(3*z+1)^(1/2)*z-12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)+(12*(3*z+1)^(1/2)*z+12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3))/((3*z-3)^(1/2)*(12*(3*z+1)^(1/2)*z+12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)*(12*(3*z+1)^(1/2)*z-12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)*z)

(2)

plot(1/b, z = 1 .. 10)

 

simplify(diff(1/b, z), symbolic)

-48*(((3*z-2)*(3*z+1)^(1/2)+z*(3*z-3)^(1/2))*((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(1/3)+((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(1/3)*((-3*z+2)*(3*z+1)^(1/2)+z*(3*z-3)^(1/2)))/((3*z+1)^(1/2)*(3*z-3)^(1/2)*((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(2/3)*((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(2/3)*(((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(1/3)-((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(1/3))^2)

(3)

``


 

Download simplification.mw

How do I convince MAPLE to simplify this Euclidean norm? > (D[1](P))(rho, theta, phi); Vector[column](%id = 230612588) > Norm(%, 2); / 2 2 2\ \|cos(phi) sin(theta)| + |sin(phi) sin(theta)| + |cos(theta)| /^ (1/2) > simplify(%, trig); / 2 2 2\ \|cos(phi) sin(theta)| + |sin(phi) sin(theta)| + |cos(theta)| /^ (1/2)

Dear all

I am facing to run the following expression for an arbitrary values of M, k and alpha.

u := simplify(sum(sum(c[p, q]*2^((K-1)*(1/2))*(sum(sum(sum(sum(2^((K-1)*(p-i-j+q-k-l))*GAMMA(p-i-j+1)*x^(p-i-j-alpha)*(1-p)^j*(1-q)^l*g[i]*binomial(p-i, j)*binomial(p, i)*binomial(p-k, l)*binomial(q, k)/GAMMA(p-i-alpha-j+1), l = 0 .. q-k), k = 0 .. q), j = 0 .. p-i-ceil(alpha)), i = ceil(alpha) .. p))/sqrt(2*(-1)^q*factorial(q)^2*g[2*q]/factorial(2*q)), q = 1 .. Delta), p = ceil(alpha) .. Delta));
FD := simplify(convert(%, StandardFunctions)); expand(radnormal(convert(FD, elementary)))

Please correct it and run it for M=10, k=1, alpha=0.5.

I'm looking to leanr the sign and to simplify a very long expression , how can i do this ? can anyone help me thank you in a

advance.

Hello dear! Hope you will be fine. I want to simplify the equation (4) like equation (3) in the attached file please correct it. I shall be thankful to you.

Help.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Dear Friends, I work with physics paсkage. And I don't know how to simplify the next expression: Dgamma[mu]*a[mu]*Dgamma[nu]*a[nu]

(I want to obtain  the well-known result a2 )

The command "Simplify" doesn't work in this case.

Hello people in mapleprimes,
I have a question.
I appended two pictures where from the same code, two different orders of
expression appear.
How can I do for this so as not to get error messages?
The cause of this is simplify(%,symbolic) brings different order of term a__0^(-k)*F__D ahead of a parenthesis in a jpg.file and F__D*a__0^(-k) after
that parenthesis in another jpg.fine both in the line above that of  "dairihensu1."

In this case, What I can do?
Please help me.
Best wishes.

taro

my_code.mw

Original code is

e7_4:=F__D*(Omega+1)*beta/(beta-1) = F__I*a__D^(-k)*a__0^k+T^((sigma-k-1)/(-1+sigma))*F__D*phi^(k/(-1+sigma))+F__D;

a1:=beta=k/(sigma-1);
subs_free:=
  proc(a,b,c)
    local b1;
    b1:=isolate(b,c);
    subs(b1,a);
  end proc;
isolate(e7_4,a__D^(-k));simplify(%,symbolic);dairihensu1:=subs_free(%,a1,sigma);e7_5:=applyop(simplify,[2,4,1,3,2],dairihensu1);

A case without error.

A case with a error.

 

Hello people in mapleprimes,

I want to simplify the next expression which has 1/k as its exponent,

especially, I want to collect for T. I hope you will teach me how to do it.

(F__X*(Omega+1)/(F__I*(beta-1)*T))^(1/k)*(T/phi)^(beta/k)

If I do as

simplify(%)assuming(symbolic);

the output is

F__X^(1/k)*(Omega+1)^(1/k)*F__I^(-1/k)*T^((beta-1)/k)*(1/(beta-1))^(1/k)*phi^(-beta/k)

But, as all variables has 1/k as its exponent, I want to collect it to (...)^(1/k).

Is this possible?

taro

The following product

 

(product(mu^x[i]/factorial(x[i]), i = 1 .. n))

 

does not simplify to the most obvious form whatever I try

 

mu^(sum(x[i], i = 1 .. n))/(product(factorial(x[i]), i = 1 .. n))

 

What can it be?

 

 

hi every one...

how i can simplify this result (R_arm_F2 $  Twflex) via tringular relations.

where Ixflex & tetadot and other... are constants

thanks

matrix_f.mw


NULL

NULL

R := (Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(teta), (2, 3) = -sin(teta), (3, 1) = 0, (3, 2) = sin(teta), (3, 3) = cos(teta)})).(Matrix(3, 3, {(1, 1) = cos(phi), (1, 2) = 0, (1, 3) = sin(phi), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(phi), (3, 2) = 0, (3, 3) = cos(phi)})).(Matrix(3, 3, {(1, 1) = cos(si), (1, 2) = -sin(si), (1, 3) = 0, (2, 1) = sin(si), (2, 2) = cos(si), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}))

R := Matrix(3, 3, {(1, 1) = cos(phi)*cos(si), (1, 2) = -cos(phi)*sin(si), (1, 3) = sin(phi), (2, 1) = sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si), (2, 2) = -sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si), (2, 3) = -sin(teta)*cos(phi), (3, 1) = -cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si), (3, 2) = cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si), (3, 3) = cos(teta)*cos(phi)})

(1)

NULL

RT := simplify(1/R)

RT := Matrix(3, 3, {(1, 1) = cos(phi)*cos(si), (1, 2) = sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si), (1, 3) = -cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si), (2, 1) = -cos(phi)*sin(si), (2, 2) = -sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si), (2, 3) = cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si), (3, 1) = sin(phi), (3, 2) = -sin(teta)*cos(phi), (3, 3) = cos(teta)*cos(phi)})

(2)

R_I_F2 := Matrix(3, 3, {(1, 1) = sin(phi)^2.(1-cos(si))+cos(si), (1, 2) = -(sin(phi).cos(phi).sin(teta))*(1-cos(si))-cos(phi).cos(teta).sin(si), (1, 3) = (sin(phi).cos(phi).cos(teta))*(1-cos(si))-sin(teta)*cos(phi).sin(si), (2, 1) = -(2*sin(phi).cos(phi).sin(teta).cos(teta))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2), (2, 2) = (2*cos(phi)^2.(sin(teta)^2).cos(teta))*(1-cos(si))+cos(teta).cos(si)-sin(teta).sin(phi).sin(si), (2, 3) = -(2*cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-sin(phi).cos(teta).sin(si)-sin(teta).cos(si), (3, 1) = (sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*cos(phi).cos(teta).sin(teta).sin(si), (3, 2) = (cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+sin(phi).cos(teta).sin(si), (3, 3) = (cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-sin(phi).sin(teta).sin(si)+cos(teta).cos(si)})

R_I_F2 := Matrix(3, 3, {(1, 1) = sin(phi)^2.(1-cos(si))+cos(si), (1, 2) = -(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)), (1, 3) = (`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si), (2, 1) = -2*(sin(phi).cos(phi).sin(teta).cos(teta))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2), (2, 2) = 2*(cos(phi)^2.(sin(teta)^2).cos(teta))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)), (2, 3) = -2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si), (3, 1) = (sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(cos(phi).cos(teta).sin(teta).sin(si)), (3, 2) = (cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si)), (3, 3) = (cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si)})

(3)

NULL

R_arm_F2 := RT.R_I_F2

R_arm_F2 := Matrix(3, 3, {(1, 1) = cos(phi)*cos(si)*(sin(phi)^2.(1-cos(si))+cos(si))+(sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si))*(-2*(`.`(sin(phi), cos(phi), sin(teta), cos(teta)))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2))+(-cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si))*((sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(`.`(cos(phi), cos(teta), sin(teta), sin(si)))), (1, 2) = cos(phi)*cos(si)*(-(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)))+(sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si))*(2*(`.`(cos(phi)^2, sin(teta)^2, cos(teta)))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)))+(-cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si))*((cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si))), (1, 3) = cos(phi)*cos(si)*((`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si))+(sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si))*(-2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si))+(-cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si))*((cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si)), (2, 1) = -cos(phi)*sin(si)*(sin(phi)^2.(1-cos(si))+cos(si))+(-sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si))*(-2*(`.`(sin(phi), cos(phi), sin(teta), cos(teta)))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2))+(cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si))*((sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(`.`(cos(phi), cos(teta), sin(teta), sin(si)))), (2, 2) = -cos(phi)*sin(si)*(-(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)))+(-sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si))*(2*(`.`(cos(phi)^2, sin(teta)^2, cos(teta)))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)))+(cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si))*((cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si))), (2, 3) = -cos(phi)*sin(si)*((`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si))+(-sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si))*(-2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si))+(cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si))*((cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si)), (3, 1) = sin(phi)*(sin(phi)^2.(1-cos(si))+cos(si))-sin(teta)*cos(phi)*(-2*(`.`(sin(phi), cos(phi), sin(teta), cos(teta)))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2))+cos(teta)*cos(phi)*((sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(`.`(cos(phi), cos(teta), sin(teta), sin(si)))), (3, 2) = sin(phi)*(-(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)))-sin(teta)*cos(phi)*(2*(`.`(cos(phi)^2, sin(teta)^2, cos(teta)))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)))+cos(teta)*cos(phi)*((cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si))), (3, 3) = sin(phi)*((`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si))-sin(teta)*cos(phi)*(-2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si))+cos(teta)*cos(phi)*((cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si))})

(4)

Twflex := Typesetting:-delayDotProduct(Ixflex, (Typesetting:-delayDotProduct(tetadot, Typesetting:-delayDotProduct(sin(phi)^2, 1-cos(si))+cos(si))+Typesetting:-delayDotProduct(sidot, sin(phi)^3+Typesetting:-delayDotProduct(cos(phi)^2, Typesetting:-delayDotProduct(sin(phi), cos(si)+Typesetting:-delayDotProduct(cos(teta), 1-cos(si)))+Typesetting:-delayDotProduct(sin(teta), sin(si)))))^2)

Ixflex.((tetadot.(sin(phi)^2.(1-cos(si))+cos(si))+sidot.(sin(phi)^3+cos(phi)^2.(sin(phi).(cos(si)+cos(teta).(1-cos(si)))+sin(teta).sin(si))))^2)

(5)

simplify(Twflex)

Ixflex.((tetadot.(sin(phi)^2.(1-cos(si))+cos(si))+sidot.(-sin(phi)*cos(phi)^2+sin(phi)+cos(phi)^2.(sin(phi).(cos(si)+cos(teta).(1-cos(si)))+sin(teta).sin(si))))^2)

(6)

expand(Twflex)

Ixflex.((tetadot.(sin(phi)^2.(1-cos(si))+cos(si))+sidot.(sin(phi)^3+cos(phi)^2.(sin(phi).(cos(si)+cos(teta).(1-cos(si)))+sin(teta).sin(si))))^2)

(7)

``

NULL


Download matrix_f.mw

Hello people in Mapleprimes,

 

I have an expression which I want to modify with another equation.

They are simple, and looks easy to simplify.

nb:=(k-sigma+1)*lambda*L*(gamma*upsilon-delta__1122^k*tau)*upsilon*tau*v/(f__F*sigma*(-tau^2+upsilon^2)*k);

hh := (L*lambda*(k-sigma+1)*upsilon*tau*v)/(f__F*sigma*(-tau^2+upsilon^2)*k)=rho;

 

I want to express nb with hh as

(gamma*upsilon-delta__1122^k*tau)*rho;

With the next code, that modification can be done.

isolate(hh,f__F);subs(%,nb);simplify(%);

But, this isolates hh for f__F, which does not look intuitive.

On the other hand, the outcome of the substitution looks so simple, which you find with executing  the codes of

nb, and hh.

But, algsubs, and subs, and simplify/siderel won't work properly.

 

What I want to ask is this. Isn't there any nice way to substitute hh into nb other than isolating f__F, so that the result is expressed with rho?

 

I will be very glad if you will give me answers.

 

Best wishes.

taro

 

 

 

 

I am trying to solve an equation using surd and I get a strange result.

solve(surd(x^4,8)=-2)
    4, -4, 4 I, -4 I

These solutions are clearly wrong.

The equation (x^4)^(1/8) = -2 has no solution.

This problem is equivalent to asking the computer to solve sqrt(x) = -2

which has no solution in R or C.

 

However if I type

solve((x^4)^(1/8) = -2) , then I get no answer, which is what I expected.

Why does surd behave in this unexpected way.

 

Also another thing I am wondering, why doesn't Maple simplify (x^4)^(1/8) to x^(1/2).

I tried the simplify command it didn't work.

 

What is the Maple command to simplify  -x^(a)+x^n  to zero under the assumption that a=n?

I have attempted the following command

simplify(-x^(a)+x^n) assuming a=n;

However, it did not produce zero. The following command however produces zero

subs(a=n,-x^(a)+x^n);

 How to do this operation using assumptions. How to inform Maple to assume that a=n.

 

Hi,

Here is my question.


restart

convert(diff(lambda(t-t1), t), diff)

eval(diff(lambda(t2), t2), {t2 = t-t1})

(1)

subs(lamda(t-t1) = sin(t-t1), %)

eval(diff(lambda(t2), t2), {t2 = t-t1})

(2)

``

I am trying to substitute value of lambda(t-t1) further but it is not taking the value.

Thanks in advance.

Regards

Sunit

Download question2.mw

Hello people in the mapleprimes,

I have a question, so I hope someone give me answers to it.

I calculated for the solution of the follwing differential equation.

restart
b:=diff(y(x),x)+a*y(x)=f(x);#where a and f(x) is not specified.
dsolve(b,y(x));

subs({f(x)=exp(x),a=2},%);where f(x) and a are specified.

c:=value(%);

The solution of the above was

y(x) = (1/3)*exp(x)+_C1/(exp(x))^2,  (A)

where please note that the second term takes

the form of fraction _C/(exp(x))^2.

 

On the other hand, next I calculated the following differential equation where f(x) and a are specified from the start.

restart
d:=diff(y(x),x)+2*y(x)=exp(x);

dsolve(b,y(x));

Then,

y(x) = (1/3)*exp(x)+exp(-2*x)*_C1  (B)

was the obtained solution.

 

Each (A) and (B) are the same substantially mathematically. But, for Maple, the variable powered to minus brabra

is not the same as one over variable powered to brabra, so that (A) and (B) takes different forms, and maple will see them 

different with each other.

 

  Surely, with algsubs, algsubs(_C1/(exp(x))^2=exp(-2*x)*_C1,c) transforms (A) to (B).

But, I want to know whether there are some other ways than that  to modify (A) to (B).

If there are any good ways for it, I will be happy if you teach them to me.

Thanks in advance.

 

taro

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