## how to find possible system of polynomials which h...

is it possible to find the input ideal from given hilbert series ?

i ask this because maple out of memory when computing all combination of ideals

which book teach how to design hilbert series

i want to research hilbert series and construct similar invariants to classify ideals

i do not know how many memory in order to do this. hope maple can display how much memory need before computation of all combination and display how long will wait for it finish computation.

my home computer can not afford this computation

## How to find Gröbner basis the order in maple ?...

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.

## how to basis this...

with(Groebner):
with(LinearAlgebra):
T := lexdeg([x1,x2,x3],[e1,e2,e3]);
GB := Basis([e1+.999987406876435, e2-.999919848203811],T):

Error, (in LinearAlgebra:-Basis) invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, {set(Vector), list(Vector)}} but received [e1+HFloat(0.9999874068764352), e2-HFloat(0.9999198482038109)]

with(Groebner):
with(LinearAlgebra):
T := lexdeg([x1,x2,x3,x4,x5,x6,x7,x8],[e1,e2]);
GB := Basis([e1-x4*x2^3*x5/(x3*x1^4*x6), e2-x1*x8/(x3*x7)],T):

Error, (in LinearAlgebra:-Basis) invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, {set(Vector), list(Vector)}} but received [e1-x4*x2^3*x5/(x3*x1^4*x6), e2-x1*x8/(x3*x7)]

## how to make a matrix in terms of other matrix...

with(Groebner):
with(LinearAlgebra):
T := lexdeg([x1,x2,x3],[e1,e2,e3]);
hello1 := proc(xx,yy)
return MatrixMatrixMultiply(xx,yy);
end proc:
hello2 := proc(xx,yy)
return xx+yy- MatrixMatrixMultiply(xx,yy);
end proc:
m1 := Matrix(3, 3, {(1, 1) = -.737663975994461+0.*I, (1, 2) = -.588973463383001+0.*I, (1, 3) = .330094104689369+0.*I, (2, 1) = -.588012653178741+0.*I, (2, 2) = .320157823261769+0.*I, (2, 3) = -.742792089286083+0.*I, (3, 1) = -.331802619371428+0.*I, (3, 2) = .742030476217061+0.*I, (3, 3) = .582492741708719+0.*I});
m2 := Matrix(3, 3, {(1, 1) = -.742269137704830+0.*I, (1, 2) = -.590598631673326+0.*I, (1, 3) = .316590877121441+0.*I, (2, 1) = -.593533033362923+0.*I, (2, 2) = .360143915024171+0.*I, (2, 3) = -.719732518911068+0.*I, (3, 1) = -.311054762892221+0.*I, (3, 2) = .722142379823161+0.*I, (3, 3) = .617863510611693+0.*I});
m3 := Matrix(3, 3, {(1, 1) = -.751491355856820+0.*I, (1, 2) = -.574908634018322+0.*I, (1, 3) = .323636840615627+0.*I, (2, 1) = -.575794245520782+0.*I, (2, 2) = .332066412772496+0.*I, (2, 3) = -.747123071744916+0.*I, (3, 1) = -.322058579916187+0.*I, (3, 2) = .747804760642505+0.*I, (3, 3) = .580574121936877+0.*I});
AA := hello1(m1, m2);
BB := hello2(m1, m2);
GB := Basis([e1- AA,e2- BB],T):
NormalForm(m3, GB, T);

## How to write a PDE system in a Weyl Algebra?...

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 ]

## which version of Maple has Groebner basis of Modul...

http://www.maplesoft.com/support/help/view.aspx?sid=2953

g1 := Vector([1, 1]);g2 := Vector([x+y, 0]);g3 := Vector([y^2+1, 0]);g4 := Vector([0, y^3+y]);g5 := Vector([0, x-y]);

i pass and tdeg(x, y, h251, h252, h253, h254, h255) to Basis

failed in Maple 15

## how to calculate the kernel from groebner basis of...

http://www.mapleprimes.com/questions/144384-Polynomials-Not-In-The-Correct-Indeterminates

above link's comment said eliminate will NOT generate a polynomial in all cases

make me think that eliminate in above link can not return correct one.

what is the correct way to convert groebner basis of kernel into kernel?

## How to calculate the image of ideal in maple?...

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`

## Why do match and solve not work in this case?...

`restart;with(Groebner):g1 := x^2-w*y;g2 := x*y-w*z;g3 := y^2-x*z;S13 := -y^3*w+x^3*z;eq1:= S13 = h131*g1 + h132*g2 + h133*g3;`
`hsol := solve(identity(eq1, x), [h131, h132, h133]);match(eq1,{x,y,z,w},'s');s;`
` `
`h131 should be x*z`
`h312 should be 0`
`h133 should be -y*w`
` `

## how to find solution minimize the cost function wi...

3*rho1 - 2*rho2 + rho3 - rho4 = -1

4*rho1 +   rho2 - rho3        = 5

original without cost function:

with(Groebner):
K := {y1-(x1^3)*(x2^4),y2-(x2^(1+2))*(w^2),y3-(x1^(1+1))*(w^1),y4-(x2^1)*w,(y1^1000)*(y2^1)*(y3^1)*(y4^100)- x1*x2*w + 1};
G := Basis(K, plex(x1, x2, w, y1, y2, y3, y4));
Reduce((x2^(5+1))*(w^1), G, plex(x1, x2, w, y1, y2, y3, y4));

after have cost function 1000*rho1 + rho2...

## Kernel connection has been lost when calculating G...

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...

## Solving system of linear and nonlinear equations w...

Hi,

I'm trying to solve system of linear and nonlinear equations with inequalities and it looks like this:

SX := solve(
[
seq(diff(EX,WX[k+1])=0, k = 0..m), # these are linear
...

## Dividing a multivatiate polynomial...

I have a rather large multivatiate polynomial "Dtest"  I need to divie it by a cubic poly "DGm" using rem and quo. Both are determinants multiplied out,  both given below. Have spent the past 2 nights trying to sort, collect, expand, equate coefficients plex groebner etc. Am trying to collect up all the powers of c3 but cant anything to work. even expand doesn't fully expand "Dtest". If I set c1 and c2 to 1 things are...