Items tagged with expressions

I have a question that I hope someone can help with. We perform extreme value analysis on expressions. My this I mean that we evaluate expressions for each combination of min or max values of each variable in the expression. For example, the expression a*b+c*d has 4 variables and we would evaluate the expression for all of the 16 combinations of a,b,c, and d to determine the worst-case result. I understand that the worst case results may not occur at the extreme values of the variables, but that is a different question.

 What I would like to know is if there is a way to reduce the number of calculations by splitting the expression into independent parts. In the example above, the expression consists of 2 parts a*b and c*d. These parts could be evaluated separately. Each has 2 variables, and each would therefore requires  4 combinations of variables to determine the extreme values of the results. So in this case, the number of calculations is 4+4=8, which is half of the initial 16  runs as would be done with a full-factorial analysis. Also, because each calculation is done on only part of the original expression, each calculation takes less time.

Is there a way to find the independent parts of an arbitrary expression so that each independent part could be evaluated separately to speed processing?

Thanks


Suppose I type certain math expression like as follow:

F^5*alpha[5]+F^4*G*gamma[1]+F*G^4*gamma[3]+G^5*beta[5]+F^4*alpha[4]+G^4*beta[4]+F^3*alpha[3]+F^2*G*gamma[2]+F*G^2*gamma[4]+G^3*beta[3]+F^2*alpha[2]+F*G*gamma[5]+G^2*beta[2]+F*alpha[1]+G*beta[1]+delta[0]

F^5*alpha[5]+F^4*G*gamma[1]+F*G^4*gamma[3]+G^5*beta[5]+F^4*alpha[4]+G^4*beta[4]+F^3*alpha[3]+F^2*G*gamma[2]+F*G^2*gamma[4]+G^3*beta[3]+F^2*alpha[2]+F*G*gamma[5]+G^2*beta[2]+F*alpha[1]+G*beta[1]+delta[0]

(1)

But when I enter this expression, Maple gives totally different look to this expression, can I force Maple to print similar looking expression as I typed in command line ? I mean without change of  position of intermediates and coefficients.


Download Forcing_Maple_Output.mw

Regards

Dear All


As a result of certain computation, Maple produce following result:

exp(epsilon[10])*a[2]*epsilon[6]*epsilon[9]^2/exp(epsilon[3]):

How can I force Maple to produce result like:

exp(epsilon[10]-epsilon[3])*a[2]*epsilon[6]*epsilon[9]^2:

Similar to this; Maple produce result:

(exp(epsilon[10]))^2*a[1]:

How I can force Maple to produce it like:

exp(2*epsilon[10])*a[1]:

As an example; I need to simplify following expression in manner as described above

-exp(epsilon[10])*a[2]*epsilon[6]*epsilon[9]*epsilon[2]/exp(epsilon[3])-2*a[10]*epsilon[7]*epsilon[9]-a[10]*epsilon[7]*epsilon[2]-a[3]*epsilon[9]^2*epsilon[11]-a[3]*epsilon[11]*epsilon[5]+exp(epsilon[10])*a[7]*epsilon[2]+a[10]*epsilon[6]*epsilon[4]-2*a[3]*epsilon[6]*epsilon[4]+(exp(epsilon[10]))^2*a[1]/exp(epsilon[3])+exp(epsilon[3])*a[11]*epsilon[9]^2+exp(epsilon[3])*a[11]*epsilon[5]+2*exp(epsilon[10])*a[7]*epsilon[9]-(exp(epsilon[10]))^2*a[5]*epsilon[11]/(exp(epsilon[3]))^2-exp(epsilon[10])*a[2]*epsilon[7]/exp(epsilon[3])-2*exp(epsilon[10])*a[9]*epsilon[7]/exp(epsilon[3])+a[10]*epsilon[6]*epsilon[8]*epsilon[2]-a[3]*epsilon[11]*epsilon[9]*epsilon[2]-2*a[3]*epsilon[6]*epsilon[8]*epsilon[2]+2*a[10]*epsilon[6]*epsilon[8]*epsilon[9]-4*a[3]*epsilon[6]*epsilon[8]*epsilon[9]-(exp(epsilon[10]))^3*a[4]*epsilon[6]/(exp(epsilon[3]))^3+(exp(epsilon[3]))^2*a[6]*epsilon[4]/exp(epsilon[10])+exp(epsilon[3])*a[11]*epsilon[9]*epsilon[2]-2*a[10]*epsilon[1]+a[3]*epsilon[1]-2*exp(epsilon[10])*a[9]*epsilon[11]*epsilon[9]/exp(epsilon[3])-(exp(epsilon[10]))^2*a[8]*epsilon[6]*epsilon[2]/(exp(epsilon[3]))^2-exp(epsilon[10])*a[9]*epsilon[11]*epsilon[2]/exp(epsilon[3])-exp(epsilon[10])*a[2]*epsilon[6]*epsilon[9]^2/exp(epsilon[3])+2*(exp(epsilon[3]))^2*a[6]*epsilon[8]*epsilon[9]/exp(epsilon[10])-exp(epsilon[10])*a[2]*epsilon[6]*epsilon[5]/exp(epsilon[3])+(exp(epsilon[3]))^2*a[6]*epsilon[8]*epsilon[2]/exp(epsilon[10])-2*(exp(epsilon[10]))^2*a[8]*epsilon[6]*epsilon[9]/(exp(epsilon[3]))^2


Download Expression.mwExpression.mw

Regards

Hello,

I have a maple code, which some expressions have more that 80000 terms and I need to double integrate them. The terms have sine, cossine trigonometric functions.

I tried to used de MAP command, it works for the first expressions but, after a while, Maple displays an error message related to too large expression.

Do you know how to handle large expressions ?

Thank you.

I am writing here because of a problem with writing mathematical expressions in Maple T.A.. I have been using it since two years, and I have a lot if questions created in version 9.0 and 9.5. A few months ago my university installed T.A. 10. At the beginning there were problems with the connections between T.A. and the Maple server. After the administrators got over these, there were another problems.

There are a lot of questions where I use greek letters, for example Sigma. Earlier it was easy, I wrote

in the 'Algorithm' section, and I could write

in the Text of the question. The letter had a perfect italic and bold style, like as it would be created with Equation Editor.

Now I have to write

sig2=maple("MathML:-ExportPresentation($sig1)");

Hi, I am completely new to Maple, and I need to use it to optimize my equations in order to make my PLC codes more compressed. I am calculating forward kinematics with the Denavit-Hartenberg method and as such I get long expressions. After a lot of google'ing and frustration, I thought I'd ask here in the hope that one of you might be able to assist me.

I have the following equations;

X := L10*cos(q5) - L16*(sin(q10)*(sin(q5)*sin(q8) - cos(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) - cos(q10)*(sin(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + cos(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6)))) - d2*(cos(q10)*(sin(q5)*sin(q8) - cos(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + sin(q10)*(sin(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + cos(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6)))) + L15*(sin(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + cos(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6))) - L11*cos(q5)*sin(q6) + d1*cos(q5)*cos(q6) - L13*sin(q5)*sin(q8) + L14*cos(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + L13*cos(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7)) - L14*sin(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6)) + L12*cos(q5)*cos(q6)*cos(q7) - L12*cos(q5)*sin(q6)*sin(q7);

Y := L10*sin(q5) - L9 + L16*(sin(q10)*(cos(q5)*sin(q8) - cos(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q10)*(sin(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6)))) + d2*(cos(q10)*(cos(q5)*sin(q8) - cos(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) + sin(q10)*(sin(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6)))) - L15*(sin(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6))) + L13*cos(q5)*sin(q8) - L11*sin(q5)*sin(q6) + d1*cos(q6)*sin(q5) - L14*cos(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - L13*cos(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5)) - L14*sin(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6)) + L12*cos(q6)*cos(q7)*sin(q5) - L12*sin(q5)*sin(q6)*sin(q7);

Z := L15*(cos(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - sin(q8)*sin(q9)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - L11*cos(q6) - L8 - d1*sin(q6) + L16*(cos(q10)*(cos(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - sin(q8)*sin(q9)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - cos(q8)*sin(q10)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - d2*(sin(q10)*(cos(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - sin(q8)*sin(q9)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) + cos(q8)*cos(q10)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - L13*cos(q8)*(cos(q6)*sin(q7) + cos(q7)*sin(q6)) - L14*sin(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - L12*cos(q6)*sin(q7) - L12*cos(q7)*sin(q6) - L14*cos(q9)*sin(q8)*(cos(q6)*sin(q7) + cos(q7)*sin(q6));

 

I need to optimize these equations, but still keep them separate. I would like to use mutual expressions for the calculations within, but still as I said keep the outputs of X, Y and Z separate.

This is MATLAB code.

 

Thanks in advance for any help.

Hi all,

which alternative options fo I have to prove the equality of two algebraic expressions if testeq fails?

The case im reffering to can be seen in the following document:

https://dl.dropboxusercontent.com/u/29147149/Exam%202006%20Question%20A.mw

Equation 14-18

I am pretty sure that the expressions are equal. evalb just returns false because it does not simplify expressions.

I am using Maple 12 in Win 64. I have some difficulties in evaluating expressions in Maple. For example simply writing cos(x) then differentiating it w.r.t x. After writing cos(x) in 2D Math mode, I do right click for selecting diff but it does not work. The pointer turns in to busy mode and nothing comes to select. Also, I tried this operation in the tutorial file teaching differentiation, however problem persists.

For context, I'm designing a work sheet based around quantum tunneling. Currently I'm looking at the boundary conditions.

What I want to be able to do is to set the expression psi[1] equal to psi[2], but only for the value x = 0. Is this possible? I've tried using if statements, and I've considered converting these expressions into functions for this purpose, but I'm not having much luck. 

Thanks

Blanky

Hi, 

I have an expression F that has an addend which is a definite integral,-(int(del_u0(x)*(diff(N_xx(x), x)), x = 0 .. L)), and addends that are not, all the rest of them.

How can I create an expression that is the integrated addend only without the other ones?

In other words, how do i separate the integral term from the rest of them?

F := -(int(del_u0(x)*(diff(N_xx(x), x)), x = 0 .. L))+del_u0(L)*N_xx(L)-del_u0(0)*N_xx(0)+ibp2+ibp3

Thanks!

Shai

 

Say I have the following loops:

for C from 1 to 10 do
    r:=[]:
    for K from 2 to 10 do
    r:=[op(r),2*K+2*C-3];
    end do:
    print(r);
end do:

for C from 1 to 10 do
    r:=[]:
    for K from 2 to 10 do
    r:=[op(r),K*C+K+C-2];
    end do:
    print(r);
end do:

I wonder how could I write a procedure, say use expressions "2*K+2*C-3" and "K*C+K+C-2" as input arguments?

so I can call up like :

 

myfun(K*C+K+C-2) or myfun("K*C+K+C-2")

myfun(2*K+2*C-3)

 

I dont care whether the output(s) are lists, tables, or matrices.

My main difficulty is to get the expression to be procedure inputs.

Though if the output can be a  10 by 9 matrix, it's better.

Thanks,

 

casper

 

Dear guys!

I have two expressions in terms of one variable. For example A(t) and B(t). Now, I want to plot A in terms of B. What should I do?

I cannot obtain this relation analytically because both expressions in terms of "t" are very complicated. But I can plot both of them. Now, I need to plot A in terms of B.

Thanks a lot.



`ρ__rta` := proc (lambda) options operator, arrow; product(rho[l](lambda), l = 1 .. 4) end proc

Hello, I am a student of physics, actually I study Celestial Mechanics.

I am working on a Maple program that the output are very huge expressions of up to three thousand lines.

My objective is to select certain terms, the difficult to do that it's because when I save such expression into a archive.txt the terms are separated between two lines, what difficults a lot to create a AWK algoritm to do such a task.

What I want to do is to write these terms...

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