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hi,

i want to compute the determining PDE system satisfied by the infinitesimals, such as the KdV equation.

but i have a problem, if i use the command

DeterminingPDE(PDE1, integrabilityconditions = false, split = false)

i can get the coefficients of independent objects, but u[t] exists. 

i want to replace u[t] by (-u[x]u-u[x,x,x]), then extract the coefficients.

but i can't collect the coefficients. 

 

my code:

with(PDEtools, DeterminingPDE, declare, diff_table, casesplit, InfinitesimalGenerator, Infinitesimals, SymmetryTest, ReducedForm, FromJet, ToJet);

declare(u(x, t));

U := diff_table(u(x, t));

PDE1 := U[]*U[x]+U[t]+U[x, x, x] = 0;

DetSys := DeterminingPDE(PDE1, integrabilityconditions = false, split = false);
detsys := FromJet(DetSys, u(x, t), differentiationnotation = diff);
pd1 := subs(U[t] = -U[]*U[x]-U[x, x, x], detsys); #u[t]->(-u[x]u-u[x,x,x])
pd2 := ToJet(pd1, [u(x, t)]);

how do i collect the coefficients?

help!

Dear All

Please see following query:

 

 

 For following Algeraic expression

 

(3*a[1]+5*a[2])*U[1]+(-6*a[1]+2*a[2])*U[2]

 

How one can construct a matrix of the following form:

 

Matrix([[3, 5], [-6, 2]])

Matrix(2, 2, {(1, 1) = 3, (1, 2) = 5, (2, 1) = -6, (2, 2) = 2})

(1)

 

Where first row corresponds to U[1]and second row corresponds to U[2] and the entries of matrix are coefficients of a[1]and a[2]

 

 

Download Constructing_matrix_from_algebraic_expression.mw

Regards

Dear maple users,

I have a lengthy formulation of function f(x) which contains some constant coefficients (A1, A2, A3 ...). I would like to simplify f(x) for functions of same above mentioned coefficients as following:

f(x) = f1(x) A1 + f2(x) A2 + ... + fn(x) An

I tried the following command:

collect(simplify(f(x)), [A1, A2, A3 ...])

Maple returns the expected form of functions but the problem is that Maple did not simplify f1(x), f2(x)... Obviously, I do not want to simplify manually : simplify(f1(x)) ... again

How can I solve this problem?

Thankyou.

I am trying to extract the coefficients of z from its series expansion. In two cases I succeed in finding the coefficients, but in the last one I fail to get the correct coefficients. Some garbage value is obtained. What is the reason behind this? I have attached my maple program.

 

 

test.mw

I need to complete the definition of bcount so that bcount(n) returns the total number
of odd coefficients 
n
k , 0 ≤ k ≤ n. For instance, the values of 
n
k for n = 6, with odd values highlighted, are:
1, 6, 15, 20, 15, 6, 1,

bcount:=
proc(n::TYPE)
description "Count odd binomial coefficients.";
---MORE STUFF HERE---
end proc; # bcount

Any help appreciated

I have an ODE with L(x,y), which includes partial derivatives of L(x,y) and coefficients y,_y1 and _y1^2. I want to split this equation into seperate equations of these coefficients. So I can solve for the unknown variable L(x,y).

 

ODE:=diff(L(x,y),x,x)+2*_y1(x)*diff(L(x,y),x,y)+_y1(x)^2*diff(L(x,y),y,y)+y(x)/x*diff(L(x,y),x)+(y(x)*_y1(x)/x+_y1(x))*diff(L(x,y),y)-y(x)/x^2*L(x,y)=0;

Could someone help me? 

 

I am currently trying to use the coeffs command but not really getting anywhere.

 

Thank you.

Note added: Issue resolved, see my comment below.

I have a sum of several thousands addends each of which is the product of a c-number times a product of 6 Grassmann-odd degrees of freedom, the latter of which does each belong to a set of 24 Grassmannians. The specific numbers are not that important, though.

This sum should equal zero. So I would like to add all c-numbers multiplying the same product of six Grassmannians, taking proper care of anticommutativity, of course. The sum would then be zero if all these sums of c-numbers are zero. Unfortunately, using Physics:-Coefficients is far too slow; actually, it has never succeeded in even completing the calculation.

Therefore, I have tried to loop through all the addends, splitting each one of them using selectremove(), and then adding the c-numbers in an Array (properly indexed), or in a table (associatively indexed, of course). Consistently, by converting the Array and table to two sets, the two methods result in the same set of equations. But solving these equations yields a result that is not stable: it varies from session to session.

I am baffled. Can anyone give me a hint to a safe and reasonably quick method for extracting these c-number-valued equations?, for there has to be something wrong with what I do.

I have double indexed functiions f[j,k] of one variable and double indexed coefficients a[j,k].

I want my print do look like a[1,1]f11+a[1,2]f12 that is, the values of a[j,k] should appear beside the functions' names, like

7f11+2f12-3f21 etc.

Thank yopu for any help

Hello,

 

I'm writing to ask how to equalize the coefficients of two multivariate polynomials. In particluar, I have two polynomials whose arguments are ln(E),ln(K),ln(L) (their levels, squared levels and interaction terms). The first one is:

(1/2*(p*a*b+(g-p)*b-g))*b*v*a*ln(E)^2-(-1+b)*v*(g-p+a*p)*b*a*ln(E)*ln(K)-b*p*(a-1)*v*a*ln(E)*ln(L)+v*a*b*ln(E)+(1/2*(p*(-1+b)*a+(g-p)*b+p))*(-1+b)*v*a*ln(K)^2+(-1+b)*v*p*(a-1)*a*ln(K)*ln(L)-v*a*(-1+b)*ln(K)+(1/2)*a*p*v*(a-1)*ln(L)^2-v*(a-1)*ln(L)

the second one is:

x_1*ln(E)+x_11*ln(E)^2+x_12*ln(E)*ln(K)+x_13*ln(E)*ln(L)+x_2*ln(K)+x_22*ln(K)^2+x_23*ln(K)*ln(L)+x_3*ln(L)`+x_33*ln(L)^2

I would like to know if it is possible to equalize the coefficients of the two polynomials and find the following system:

v*a*b = x_1, -v*(a-1) x_3, -v*a*(-1+b) = x_2, a*b*v*(b*rho*a-b*rho+g*(-1+b)) = x_11, v*rho*a*(a-1) = x_33, v*a*(rho*(-1+b)*a-rho*(-1+b)+b*g)*(-1+b) = x_22, -a*v*rho*(a-1)*b = x_13, -a*v*(a*rho-rho*u+g)*b*(-1+b) = x_12, a*v*u*rho*(a-1)*(-1+b) = x_23

I tried using "coeffs" and creating a sequence of values for x but then I don't know how to equalize them.

Thank you very much in advance for your time,

Elena

I am using Maple-9 to simplify the expression and the expression is not having numerical coefficients. Example expression is given below.

a2:=(18*d^2*R^2*r-4*d1^3*r+5*R^6-z1*r^3*p-14*r1^3*r*rc+k1*d^2*R^2*r);

 

The question here is: I want to collect all "positive terms" and "negative terms" and assign to new variable.

 

Please suggest steps for the above problem

 

Thank you in advance.

 

consider quadratic equation ax^2+bx+c =0 :
the coefficients vary between -1 and +1 . just like this :
-1<a<+1 , -1<b<+1 , -1<c<+1 ;
how can some one proove that this equation should have real answers ?! can anybody help ? thanks in advance.

Given a polynomial in several variables is it possible to split it so that all the coefficients of the monomials are +1 or -1.

Example:

p:=-z+2*x+4*y-3*x*y.

I would lie to obtain

f:=-z +x+x +y+y+y+y -x*y-x*y-x*y.

Hello dear forum,

I'm trying to create a function in maple, but I'm stuck at this problem:

I need to extract the values from an expression, for example I've got the expression:

544X-228412+1836Y-1296Z=0

I want to get/extract all the values from the expression, but ONLY the numerical values like "544", "228412", "1836", "1296" and "0". How would this be done?

My goal is to then insert these values in a igcd command and get a common divider for the function, so I'll be able to end up with something like 4(136X-57103+459Y-324Z)=0

 

Thank you in advance, and have a lovely day!
Best regards, Martin.

Hi,

Recently a a simple problem which i can not handle by myself, made me confused.

I have simple code of maple which is not stable at all. Everytime I run the code, the final result which is the determinant of a matrix, changes and I can not see the problem with the code. In fact i noticed that problem occures when the matrix is being build by culculating the coefficients of some constant values.  I have attached the code. Could you see what is wrong here?

Thanks by the way.

Download Code.mw

 

Dear Maple users

I have a question which is maybe easily solved, but I cannot seem to find the solution myself. A vector X of coefficients has been computed earlier in the Maple document and I want these coefficients placed in front of some written symbols in order to make Maple display the final result in a nice way. I made an attempt with the Vector command as shown in the image, but I cannot make the indices start at -2. In addition I want some written math placed in front of the expression. In fact I want it displayed like shown on the image marked with a red rectangle. I did write this manually, but want Maple to do it automatically when given the coefficients vector calculated earlier. I hope someone can help me here!

(It is about finite difference methods, by the way)

 

Regards,

Erik 

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