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I’m trying to figure out how to find a basis for a subspace, V, of Rdefined by V = {(x, y, z)l(2x-3y+6z=0)}

 

I’m using the student linear algebra module for maple 17

 

I’ve tried defining the subspace and asking for the basis of V but I always get an error code.

 

I’ve tried consulting the maple website and looking through their help menu, but can’t find anything that answers how to find a basis... At least a basis from the subspace defined in my problem.

I know how to find a basis for the subspace by hand but not with maple.

Any help will be greatly appreciated. 

computer a Gröbner basis for <f_[1] = x^2*y - 2*y*z + 1, f_[2] = x*y^2-z^2+ 2*x,  f_[3] = y^2*z - x^2+ 5 > belong to Q[x,y,z], using ≺= <_grlex with x≺y≺z. compare your output to the Gröbner basis the Maple computers with a different order.

Two questions:

The algortihms that Groebner[Basis] uses at each step computes some "tentative" or "pseudo-basis". The "tentative" basis is not a Groebner basis but it is in the ideal generated by the original system of polynomial eq.

1) Is this correct ? Provided this is correct, then

2) How can one retrive the last "tentative" basis?
 If I just use timelimit I can abort the computations but how can one retrive the last computation?

 

I have been struggling (reading Ore/Weyl Algebra documentation) to understand how to input a PDE system with polynomial coeff. in Weyl algebra notation so I can compute a Groebner basis for it. I would be very grateful if someone could  show, using the simple example below, which differential operators in Ore_algebra[diff_algebra] should one declare to express the system in Weyl algebra notation. The systems I'm working are more complicated but all have many dependent variables, f and g functions in this example:

pdesys:= [ x*diff( f(x,y,z),x)- z*diff( g(x,y,z),y) = 0, (x^2-y)*diff( f(x,y,z),z)- y*diff( g(x,y,z),z) = 0 ]

I am using the ColumnSpace command (from the LinearAlgebra package) to generate a basis for the column space of a matrix. Is there any way to "force" the command to express the basis in terms of columns of A and not in the canonical form with leading 1's?

For example, for

A:=Matrix([[-3,6,-1,1-7],[1,-2,2,3,-1],[2,-4,5,8,-4]]):

I would like to obtain the following basis for the column space:

{[-3,1,2],[-1,2,5]}

 

I've been playing around with the Basis command in the LinearAlgebra package. It's very easy to get a Basis for any subspace of R^n. However, if you're dealing with finite-dimensional polynomial or matrix spaces, the Basis command doesn't work. Due to some basic isomorphism theorems, we can always associate these vectors with those in R^n. I was wondering if there is a way to get Maple, via the Basis command, to handle "other types" of vectors. For example, how might one get Maple to return a basis of {x^2+x+4,x+3,2x^2-x-5,5x^2+x-7} in P_2, the space of polynomials of degree less than or equal to 2, or, a basis for {[[2,3],[5,6]],[[3,2],[0,1]],[[1,1],[0,5]]} in M_{2,2}, the space of 2 x 2 matrices, without converting to R^n?

hard code in this way is quite complex, how to do without hard code

after i get G which is an array for below, 

Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4],a*G[5],a*G[6],a*G[7],a*G[8],a*G[9],a*G[10],a*G[11],a*G[12],a*G[13],a*G[14], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,r,u,v,w));

the goal is to check kernel belong to image in Maple

restart;
with(Groebner):
K := {r-x^4,u-(x^3)*y,v-x*y^3,w-y^4};
G := Basis(K, 'tord', degrevlex(r,u,v,w));
R1 := eliminate(G, {r,u,v,w}); # eliminate is the reverse of Basis
Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4],a*G[5],a*G[6],a*G[7],a*G[8],a*G[9],a*G[10],a*G[11],a*G[12],a*G[13],a*G[14], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,r,u,v,w));
Ga := remove(has, Ga, [x,y,a]);

below code is calculate basis of kernel and kernel

i guess basis of image is 

remove(has, Ga, [r,u,v,w]); if this correct, i eliminate this, i can get the image
however it include variable 'a'
is it correct? if not, how to calculate? 
my final goal is to make unexact sequence into exact sequence

Hello. I am trying to do a project. Howerver the following code is causing Windows 7(x64) to error.

First, I get a message from mserver.exe saying: mserver has stopped working.

I click "Close the program" and I get "Kernel connection has been lost."

This is happening when I calculate the Groebner Basis by the following code. It is all right when I calculate the Groebner Basis when the problem to be solved is simpler. The memory of my computer is...

I would like some help in order to build the following algorithm (Gianni-Kalkbrener) on Maple.

I have a cyclic-5 problem of the following polynomials

L := [a*b*c*d+b*c*d*e+c*d*e*a+d*e*a*b+e*a*b*c, a*b+b*c+c*d+d*e+e*a, a+b+c+d+e, a*b*c*d*e-1, a*b*c+b*c*d+c*d*e+d*e*a+e*a*b]

 

I found the Grobner basis of that using:

GrobnerBasisOfL := Basis(L, tdeg(a, b, c, d, e))

 

Then, I have found the FGLM of the Basis using:

I need to write a procedure to check whether a group of input vectors is an orthonormal basis. If anyone can help me with this I would really appreciate it. Thanks.

I am trying to find the coordinate vector of v and w with respect to the basis T.

v= <1,5>  

w= <5,4>

T= [<1,1>|<2,3>]

 

I found this help page:

 

http://www.maplesoft.com/support/help/Maple/view.aspx?path=Task/VectorCoordinateVector

 

"Enter a vector in the vector space spanned by this basis"  -how do you know what to put in?

 

> V:=...

If S= { <0,1>,<1,2>} and T={<1,1>,<2,3>} are ordered bases for R2 and v=<1,5> and w=<5,4>, then can someone help me:

-find the coordinate vector of v and w with respect to the basis T by creating a procedure?

-I can make a procedure to find the transition matrix PS<-T from T to S-basis, but can you help find the coordinate vector of v and w with respect to the basis S. Using PS<-T?

Hi guys, I would like some help writing a procedure that checks whether the group of input vectors is an orthogonal basis. Any help would be great!

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