Items tagged with polynomialideals

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When one uses the PolynomialIdeals package, then how should he ask the elemnts in an ideal or the number of generators?

An idea can be writing a proc getting a polynomialideal and returning a list with the generators as its elements in this way. Converting the polynomialideal to a list, then deleting its three last entries. But I'm wondering if there is any other way to do this? It's reasonable to be able to ask generators of an ideal of result of some computations in polynomialideal package.

 

Hello all, 

I am trying to compute the Groebner basis for a set of 3 coupled nonlinear equations. The variables I wish to solve for are A0,B0, and B1; however, my equations also have the variables DC, a, nu, q, and t. I wish to solve the 3 equations in terms of these other 5 variables such that I can substitute in any values I desire and obtain a result. When attempting to put the three equations into the PolynomialIdeal command from the PolynomialIdeals package, Maple gives me an error stating that the inputs must be polynomials with respect to all 8 variables. How would I go about declaring the other 5 variables such that they are considered arbitrary constants? 

I was able to get around the errors by assigning values to these 5 variables, though this is not what I am trying to accomplish. I need these 5 values to remain arbitrary.

I am very new to the concept of Groebner Bases and these commands so any help would be appreciated. I have attached my worksheet for reference. I am also happy to supply any additional information that may be needed to assist with this issue.

Thanks!
 

restart

NULL

``

SED2 := proc (A0, B0, B1) options operator, arrow; (32/3)*(nu+7)*A0^2*Pi*DC/(a^2*(1+nu))+3*DC*Pi*((1+nu)^4*(B0^2+(13/42)*B1^2+(4/5)*B0*B1)*a^2+(328/315)*A0^2*(1+nu)^2*((B0+(142/451)*B1)*nu^3+((323/41)*B0+(1490/451)*B1)*nu^2+(11*B0+(3874/451)*B1)*nu-(1847/41)*B0-(8034/451)*B1)*a+(128/105)*A0^4*(nu^4+18*nu^3+132*nu^2+494*nu+939))/(t^2*a^2*(1+nu)^4)-(1/6)*q*a^2*A0-(-(1/4)/a^2-(1/4)*(5+nu)/(a^2*(1+nu)))*A0*q*a^4-(1/2)*(5+nu)*A0*q*a^2/(1+nu) end proc;

proc (A0, B0, B1) options operator, arrow; (32/3)*(nu+7)*A0^2*Pi*DC/(a^2*(1+nu))+3*DC*Pi*((1+nu)^4*(B0^2+(13/42)*B1^2+(4/5)*B0*B1)*a^2+(328/315)*A0^2*(1+nu)^2*((B0+(142/451)*B1)*nu^3+((323/41)*B0+(1490/451)*B1)*nu^2+(11*B0+(3874/451)*B1)*nu-(1847/41)*B0-(8034/451)*B1)*a+(128/105)*A0^4*(nu^4+18*nu^3+132*nu^2+494*nu+939))/(t^2*a^2*(1+nu)^4)-(1/6)*q*a^2*A0-(-(1/4)/a^2-(1/4)*(5+nu)/(a^2*(1+nu)))*A0*q*a^4-(1/2)*(5+nu)*A0*q*a^2/(1+nu) end proc

(1)

NULL

``

eqA0 := proc (A0, B0, B1) options operator, arrow; diff(SED2(A0, B0, B1), A0) end proc:

eqB0 := proc (A0, B0, B1) options operator, arrow; diff(SED2(A0, B0, B1), B0) end proc:

eqB1 := proc (A0, B0, B1) options operator, arrow; diff(SED2(A0, B0, B1), B1) end proc:

NULL

``

type(SED2, polynom);

true

(2)

type(eqA0, polynom);

true

(3)

type(eqB0, polynom);

true

(4)

type(eqB1, polynom);

true

(5)

NULL

``

with(Groebner):

with(PolynomialIdeals):

NULL

NULL

WL := PolynomialIdeal({eqA0(A0, B0, B1), eqB0(A0, B0, B1), eqB1(A0, B0, B1)})

Error, (in PolynomialIdeals:-PolynomialIdeal) generators must be polynomials with respect to, {A0, B0, B1, DC, a, nu, q, t}

 

NULL

type(WL, PolynomialIdeals:-PolynomialIdeal);

false

(6)

``

NULL

GB := Basis(WL, lexdeg([B0, B1], [A0]))

Error, (in Groebner:-Basis) the first argument must be a list or set of polynomials or a PolynomialIdeal

 

NULL

``

GB[1];

GB[1]

(7)

GB[2];

GB[2]

(8)

GB[3];

GB[3]

(9)

``

``

A00 := solve(GB[1], A0):

A00 := simplify(remove(has, [A00], I)):

A0 := A00[1]

Error, invalid subscript selector

 

B10 := solve(GB[2], B1):

B10 := simplify(remove(has, [B10], I)):

B1 := B10[1]

Error, invalid subscript selector

 

B00 := solve(GB[3], B0):

B00 := simplify(remove(has, [B00], I)):

B0 := B00[1]

Error, invalid subscript selector

 

NULL

``


 

Download Groebner_Basis_Work.mw

 

Hi, I have a big system with 27 polynomial equations in 16 unknowns: f_1=...=f_27=0.  I can store these equations but I cannot calculate a Grobner basis of the ideal  J generated by my polynomials (allocation problem) - I use the library "with(FGb)"-  What interests me is whether my system is minimal in the following sense.

If, for example,  I remove f_1, is the ideal generated by (f_2,...f_27)  J again ? That is to say, is f_1 in the ideal generated by f_2,...,f_27 ? I would like to get an answer "yes" or "no" for each removed  f_i.

My question: can we solve the problem above  without calculating a Grobner basis of J?

Thanks in advance.

 

 

 

 

 

After using the Groebner and PolynomialIdeals packages, Maple goes into a long calculation when I make an entry of the form

name:=polynomial expression. This can take 10's of minutes for an expression of two lines. The only solution I have found is to save the sheet and restart it and enter the line name:= etc. before loading Groebner and PolynomialIdeals. This is most inconvenient. Is there a better workaround?

How to create polynomial ideals over algebraic extensions of the field of  rationals Q with Maple?
The Maple help to PolynomialIdeals
"All package commands support computations over the rational numbers, algebraic number fields, rational function fields, and algebraic function fields, as well as finite fields. Coefficients from algebraic extension fields can be specified using radicals or RootOfs"
is too poor. I also don't find any example on this topic in examples,PolynomialIdeals.

I think that I found a bug in Maple! Please run the following command:

I need the Generators of above Ideal. What is your idea?!

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