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guys,i computed a tensorial expression by maple but i think i made mistake.

 

 

tensorial.mw

sqrt(5) gives sqrt(5)

sqrt(1+sqrt(5)) gives "You have entered an invalid Maple expression"

sqrt(u) gives sqrt(u)

sqrt(1+u); gives "You have entered an invalid Maple expression"

 

when using the Maple Math icon. How can I get the correct input for the two expressions?

I have the following function

where A,B,Ψ, K1,K2,K3,α,β are all constants.

How to find the value of m for which the above expression is 0 or approximate to 0 for different values fo the constants.

e.g., Fixing all the parameters except A, I want to find the values of m for different values of A. How to do that in maple?

 

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 

Dear Friends

In differential expressions(See Maple file) how to find coefficiets of dependent variable "u(x,t)" and "v(x,t)" and of their differentials ? There is command "dcoeffs(function)", but that work for single dependent variable only but in our case there are two dependent variables in consideration. There are other options like "indets", "specindex" but those do not work.

 


with(PDEtools):

DepVars; -1; [u(x, t), v(x, t), r[1](t), r[2](t), s[1](t), s[2](t), p[1](t), p[2](t), alpha[1](x, t), beta[1](x, t), beta[2](x, t), delta[1](x, t), delta[2](x, t)]

[u(x, t), v(x, t), r[1](t), r[2](t), s[1](t), s[2](t), p[1](t), p[2](t), alpha[1](x, t), beta[1](x, t), beta[2](x, t), delta[1](x, t), delta[2](x, t)]

(1)

alias(u = u(x, t), v = v(x, t), r[1] = r[1](t), r[2] = r[2](t), s[1] = s[1](t), s[2] = s[2](t), p[1] = p[1](t), p[2] = p[2](t), alpha[1] = alpha[1](x, t), beta[1] = beta[1](x, t), beta[2] = beta[2](x, t), delta[1] = delta[1](x, t), delta[2] = delta[2](x, t))

u, v, r[1], r[2], s[1], s[2], p[1], p[2], alpha[1], beta[1], beta[2], delta[1], delta[2]

(2)

(diff(r[1], t))*(-s[1]*u*(diff(u, x))-p[1]*((diff(u, x))*v+u*(diff(v, x)))-alpha[1]*(diff(u, x))-beta[1]*u-delta[1])/r[1]+r[1]*(diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x, x))+(diff(s[1], t))*u*(diff(u, x))+s[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(u, x))+s[1]*u*(diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x))+(diff(p[1], t))*((diff(u, x))*v+u*(diff(v, x)))+p[1]*((diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x))*v+(diff(u, x))*(alpha[1]*(diff(v, x))+beta[2]*v+delta[2])+(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(v, x))+u*(diff(alpha[1]*(diff(v, x))+beta[2]*v+delta[2], x)))+(diff(alpha[1], t))*(diff(u, x))+alpha[1]*(diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x))+(diff(beta[1], t))*u+beta[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])+diff(delta[1], t)

(diff(r[1], t))*(-s[1]*u*(diff(u, x))-p[1]*((diff(u, x))*v+u*(diff(v, x)))-alpha[1]*(diff(u, x))-beta[1]*u-delta[1])/r[1]+r[1]*((diff(diff(alpha[1], x), x))*(diff(u, x))+2*(diff(alpha[1], x))*(diff(diff(u, x), x))+alpha[1]*(diff(diff(diff(u, x), x), x))+(diff(diff(beta[1], x), x))*u+2*(diff(beta[1], x))*(diff(u, x))+beta[1]*(diff(diff(u, x), x))+diff(diff(delta[1], x), x))+(diff(s[1], t))*u*(diff(u, x))+s[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(u, x))+s[1]*u*((diff(alpha[1], x))*(diff(u, x))+alpha[1]*(diff(diff(u, x), x))+(diff(beta[1], x))*u+beta[1]*(diff(u, x))+diff(delta[1], x))+(diff(p[1], t))*((diff(u, x))*v+u*(diff(v, x)))+p[1]*(((diff(alpha[1], x))*(diff(u, x))+alpha[1]*(diff(diff(u, x), x))+(diff(beta[1], x))*u+beta[1]*(diff(u, x))+diff(delta[1], x))*v+(diff(u, x))*(alpha[1]*(diff(v, x))+beta[2]*v+delta[2])+(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(v, x))+u*((diff(alpha[1], x))*(diff(v, x))+alpha[1]*(diff(diff(v, x), x))+(diff(beta[2], x))*v+beta[2]*(diff(v, x))+diff(delta[2], x)))+(diff(alpha[1], t))*(diff(u, x))+alpha[1]*((diff(alpha[1], x))*(diff(u, x))+alpha[1]*(diff(diff(u, x), x))+(diff(beta[1], x))*u+beta[1]*(diff(u, x))+diff(delta[1], x))+(diff(beta[1], t))*u+beta[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])+diff(delta[1], t)

(3)

In above differential expressions how to find coefficiets of dependent variable "u(x,t)" and "v(x,t)" and of their differentials ? There is command "dcoeffs(expr,u(x,t))", but that work for single dependent variable only but in our case there are two dependent variables in consideration. There are other options like "indets", "specindex" but those do not work.

``


Download Coefficients_in_differential_expression.mw

I'd like to differentiate  3*(r/sqrt(a))+ (r/sqrt(a))^2  w.r.t  r/sqrt(a) and obtain

    3 + 2* (r/sqrt(a))

in otherwords, treat (r/sqrt(a)) as a single variable. This is what I tried:

restart;
v:=r/sqrt(a);    #the single expression to differentiate w.r.t
p:=x->x^2+3*x;
expr:=Diff(p(v),v);
algsubs(v=x,expr);
algsubs(x=v,value(%));

The problem is that when doing x^2 and x is r/sqrt(a), then it become r^2/a and it does not remain (r/sqrt(a))^2, so now the algsubs does not "see" it. I get as final answer

ofcourse, one can now try to simplify the above to the required form, maybe using assumptions or by dividing by sqrt(a) the numerator and denominator of the first term above to get  3+2*(r/sqrt(a)) but this is all requires extra work and can be hard depending on the result.

is there a better way to do the above so it works in general? The problem is in the function p, I need a way to tell Maple now to simplify it somehow. In Mathematica, I can do this like this:

Clear[p, x, r, a]
p[x_] := x^2 + 3*x;
v = r/Sqrt[a];
With[{v = x}, Inactive[D][p[v], v]];
Activate[%];
% /. x -> v

 

 

Dear all
Please guide me how to convert system of expressions into system of equations, so as solve them using "solve command".

The following expressions are just coefficients extracted from certain equation.

16*a[2]^4*delta[1]^2-48*a[2]^3*a[3]*delta[1]*delta[2]-2*a[2]*b[2]*delta[1]^2, 48*a[2]^2*a[3]^2*delta[1]*delta[2]-80*a[3]^4*delta[1]*delta[2]-4*a[3]*b[3]*delta[1]*delta[2], 64*a[2]^3*a[3]*delta[1]*delta[2]-64*a[2]*a[3]^3*delta[1]*delta[2]-2*a[2]*b[3]*delta[1]*delta[2]-2*a[3]*b[2]*delta[1]*delta[2]

16*a[2]^4*delta[1]^2-48*a[2]^3*a[3]*delta[1]*delta[2]-2*a[2]*b[2]*delta[1]^2, 48*a[2]^2*a[3]^2*delta[1]*delta[2]-80*a[3]^4*delta[1]*delta[2]-4*a[3]*b[3]*delta[1]*delta[2], 64*a[2]^3*a[3]*delta[1]*delta[2]-64*a[2]*a[3]^3*delta[1]*delta[2]-2*a[2]*b[3]*delta[1]*delta[2]-2*a[3]*b[2]*delta[1]*delta[2]

(1)

It possible for me to write (1) in the following form

for EQ in 16*a[2]^4*delta[1]^2-48*a[2]^3*a[3]*delta[1]*delta[2]-2*a[2]*b[2]*delta[1]^2, 48*a[2]^2*a[3]^2*delta[1]*delta[2]-80*a[3]^4*delta[1]*delta[2]-4*a[3]*b[3]*delta[1]*delta[2], 64*a[2]^3*a[3]*delta[1]*delta[2]-64*a[2]*a[3]^3*delta[1]*delta[2]-2*a[2]*b[3]*delta[1]*delta[2]-2*a[3]*b[2]*delta[1]*delta[2] do EQ = 0 end do

16*a[2]^4*delta[1]^2-48*a[2]^3*a[3]*delta[1]*delta[2]-2*a[2]*b[2]*delta[1]^2 = 0

 

48*a[2]^2*a[3]^2*delta[1]*delta[2]-80*a[3]^4*delta[1]*delta[2]-4*a[3]*b[3]*delta[1]*delta[2] = 0

 

64*a[2]^3*a[3]*delta[1]*delta[2]-64*a[2]*a[3]^3*delta[1]*delta[2]-2*a[2]*b[3]*delta[1]*delta[2]-2*a[3]*b[2]*delta[1]*delta[2] = 0

(2)

But I want to write (1) in the following form

16*a[2]^4*delta[1]^2-48*a[2]^3*a[3]*delta[1]*delta[2]-2*a[2]*b[2]*delta[1]^2 = 0, 48*a[2]^2*a[3]^2*delta[1]*delta[2]-80*a[3]^4*delta[1]*delta[2]-4*a[3]*b[3]*delta[1]*delta[2] = 0, 64*a[2]^3*a[3]*delta[1]*delta[2]-64*a[2]*a[3]^3*delta[1]*delta[2]-2*a[2]*b[3]*delta[1]*delta[2]-2*a[3]*b[2]*delta[1]*delta[2] = 0

16*a[2]^4*delta[1]^2-48*a[2]^3*a[3]*delta[1]*delta[2]-2*a[2]*b[2]*delta[1]^2 = 0, 48*a[2]^2*a[3]^2*delta[1]*delta[2]-80*a[3]^4*delta[1]*delta[2]-4*a[3]*b[3]*delta[1]*delta[2] = 0, 64*a[2]^3*a[3]*delta[1]*delta[2]-64*a[2]*a[3]^3*delta[1]*delta[2]-2*a[2]*b[3]*delta[1]*delta[2]-2*a[3]*b[2]*delta[1]*delta[2] = 0

(3)

``

 

Download Maple_Query.mw

I am currently trying to solve a geometric problem where I have to calculate angles in two connected four bar linkages parallel to a serial chain of rotatory joints (closed-loop kinematic chain).

The angle is calculated with

 > alpha:=arctan(exp_y, exp_x):

The expressions exp_y and exp_x contain long products of sines and cosines of 6 other time-dependant angles, square roots of these products, constant geometric lengths (not time-dependant) and constant geometric angles (not time-dependant).

The lenghts are already assumed positive

 > assume (l1>0): # similar for all lengths l2, l3, ...

The time dependant angles are defined as

> qJ_t := Matrix(6, 1, [qJ1(t), qJ2(t), qJ3(t), qJ4(t), qJ5(t), qJ6(t)]): # generalized coordinates of the system in the sense of technical mechanics

Other assumptions are not set, since the angles can be positive as well as negative.

Calculating this expression takes up to two days on a fast computer. In my opinion this takes much too long compared to other calculations with similar amount of variables (more complex robotic structures).Also, the arctan function does not "calculate" a result, it just writes down "arctan(...)".

Is there a way to speed up this calculation e.g. by using more assumptions?

On the arctan help page, the examples suggest that Maple is trying to already simplify the solution e.g. by drawing Pi out of the solution.

 

 

 





 



hi .how i can clarify expression in maple that in running dont asked me again..

for example attached file

2)how i can deleted one parameter of 
Memory in maple or
Restart it??

Hello.

When I input an expression such as 3*(2*x-1)(x+1) > 0 into a Maple worksheet, Maple outputs this:

0 < 6*x(x+1)-3

(sorry, the formatter doesn't work for some reason).

I was wondering by which rules Maple determines to output that instead of, for example,

0 < 3(2*x^2+x-1)

or

0 < 6*x^2+3x-3

 

Also, Maple can't seem to be able to solve the inequality. It gives the following error to the command:

solve( { 3*(2*x-1)(1+x) > 0 } );

Error, (in solve) cannot solve for an unknown function with other operations in its arguments

 

So, I was wondering, is there a way to force Maple to output either in the most factorized form (which should be what I gave it as input) or in the least factorized form (that is, multiply it all)?

And, of course, why can't I solve the inequality with Maple?

I want to compute some matrix multiplications and i need this expression to be 1 always, i.e,

x^2+y^2+z^2+w^2=1

for every calculation I do.

I have tried x^2+y^2+z^2+w^2:=1 and assign(x^2+y^2+z^2+w^2,1) but it doesn't work.

What I should type to make it work?

 

Thank you

 

 

Hi all,

I have this system

> system1D := H = alpha*gamma[2, 2]*d[2, 1]-beta*d[1, 2]*gamma[1, 2]^2-gamma*d[1, 2]*gamma[2, 1]^2+alpha*gamma[2, 2]^2*d[2, 2]-beta*d[2, 2]*gamma[2, 2]^2-gamma*d[2, 2]*gamma[2, 2]^2, E = alpha*gamma[2, 1]*d[1, 1]-beta*d[1, 2]*gamma[1, 1]-gamma*d[1, 1]*gamma[2, 1]+alpha*gamma[2, 1]^2*d[1, 2]-beta*d[2, 2]*gamma[2, 1]-gamma*d[2, 1]*gamma[2, 2], B = alpha*gamma[1, 1]*d[2, 1]-beta*d[1, 1]*gamma[1, 1]^2-gamma*d[1, 1]*gamma[1, 1]^2+alpha*gamma[1, 1]^2*d[2, 2]-beta*d[2, 1]*gamma[2, 1]^2-gamma*d[2, 1]*gamma[1, 2]^2, D = alpha*gamma[1, 2]*d[2, 1]-beta*d[1, 1]*gamma[1, 2]^2-gamma*d[1, 2]*gamma[1, 1]^2+alpha*gamma[1, 2]^2*d[2, 2]-beta*d[2, 1]*gamma[2, 2]^2-gamma*d[2, 2]*gamma[1, 2]^2, A = alpha*gamma[1, 1]*d[1, 1]-beta*d[1, 1]*gamma[1, 1]-gamma*d[1, 1]*gamma[1, 1]+alpha*gamma[1, 1]^2*d[1, 2]-beta*d[2, 1]*gamma[2, 1]-gamma*d[2, 1]*gamma[1, 2], C = alpha*gamma[1, 2]*d[1, 1]-beta*d[1, 1]*gamma[1, 2]-gamma*d[1, 2]*gamma[1, 1]+alpha*gamma[1, 2]^2*d[1, 2]-beta*d[2, 1]*gamma[2, 2]-gamma*d[2, 2]*gamma[1, 2], F = alpha*gamma[2, 1]*d[2, 1]-beta*d[1, 2]*gamma[1, 1]^2-gamma*d[1, 1]*gamma[2, 1]^2+alpha*gamma[2, 1]^2*d[2, 2]-beta*d[2, 2]*gamma[2, 1]^2-gamma*d[2, 1]*gamma[2, 2]^2, G = alpha*gamma[2, 2]*d[1, 1]-beta*d[1, 2]*gamma[1, 2]-gamma*d[1, 2]*gamma[2, 1]+alpha*gamma[2, 2]^2*d[1, 2]-beta*d[2, 2]*gamma[2, 2]-gamma*d[2, 2]*gamma[2, 2], H = alpha*delta[2, 2]*d[2, 1]-beta*d[1, 2]*delta[1, 2]^2-gamma*d[1, 2]*delta[2, 1]^2+alpha*delta[2, 2]^2*d[2, 2]-beta*d[2, 2]*delta[2, 2]^2-gamma*d[2, 2]*delta[2, 2]^2, E = alpha*delta[2, 1]*d[1, 1]-beta*d[1, 2]*delta[1, 1]-gamma*d[1, 1]*delta[2, 1]+alpha*delta[2, 1]^2*d[1, 2]-beta*d[2, 2]*delta[2, 1]-gamma*d[2, 1]*delta[2, 2], B = alpha*delta[1, 1]*d[2, 1]-beta*d[1, 1]*delta[1, 1]^2-gamma*d[1, 1]*delta[1, 1]^2+alpha*delta[1, 1]^2*d[2, 2]-beta*d[2, 1]*delta[2, 1]^2-gamma*d[2, 1]*delta[1, 2]^2, D = alpha*delta[1, 2]*d[2, 1]-beta*d[1, 1]*delta[1, 2]^2-gamma*d[1, 2]*delta[1, 1]^2+alpha*delta[1, 2]^2*d[2, 2]-beta*d[2, 1]*delta[2, 2]^2-gamma*d[2, 2]*delta[1, 2]^2, A = alpha*delta[1, 1]*d[1, 1]-beta*d[1, 1]*delta[1, 1]-gamma*d[1, 1]*delta[1, 1]+alpha*delta[1, 1]^2*d[1, 2]-beta*d[2, 1]*delta[2, 1]-gamma*d[2, 1]*delta[1, 2], C = alpha*delta[1, 2]*d[1, 1]-beta*d[1, 1]*delta[1, 2]-gamma*d[1, 2]*delta[1, 1]+alpha*delta[1, 2]^2*d[1, 2]-beta*d[2, 1]*delta[2, 2]-gamma*d[2, 2]*delta[1, 2], F = alpha*delta[2, 1]*d[2, 1]-beta*d[1, 2]*delta[1, 1]^2-gamma*d[1, 1]*delta[2, 1]^2+alpha*delta[2, 1]^2*d[2, 2]-beta*d[2, 2]*delta[2, 1]^2-gamma*d[2, 1]*delta[2, 2]^2, G = alpha*delta[2, 2]*d[1, 1]-beta*d[1, 2]*delta[1, 2]-gamma*d[1, 2]*delta[2, 1]+alpha*delta[2, 2]^2*d[1, 2]-beta*d[2, 2]*delta[2, 2]-gamma*d[2, 2]*delta[2, 2];


> subs({A = 0, B = 0, C = 0, D = 0, E = 0, F = 0, G = 0, H = 0, delta[1, 1] = 1, delta[1, 2] = 0, delta[2, 1] = 0, delta[2, 2] = 0, gamma[1, 1] = 1, gamma[1, 2] = 0, gamma[2, 1] = 0, gamma[2, 2] = 0, delta[1, 1]^2 = 0, delta[1, 2]^2 = 0, delta[2, 1]^2 = 1, delta[2, 2]^2 = 0, gamma[1, 1]^2 = 0, gamma[1, 2]^2 = 1, gamma[2, 1]^2 = 0, gamma[2, 2]^2 = 0}, {system1D});

The problem is: there is any simple way to use command "subs" when some expression such that delta[1,1]=1, gamma[1,1]=1, gamma[1,2]^2=1 have value and others are zero.

Can someone please advice and help me on this?

thanks

witribm

guys, i have a tensorial expression which i want to compute it, but i have some problem tensor.mw

 

 

thanks in advance

hi,

how can I convert the decimal representation of the symbolic expressions: I dont want the result in terms of symbols like e^5 or ln(3) 

 

thanks

 

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