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Groebner

  

Support

  

compute the support of a polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Support(f, T)

Parameters

f

-

polynomial or a list or set of polynomials

T

-

(optional) list or set of variables, MonomialOrder, or ShortMonomialOrder

Description

• 

The Support command returns the list of the monomials present in a polynomial f. It automatically maps onto lists and sets, and can be used to quickly reveal the structure of a large Groebner basis.

• 

An optional second argument T may be a list or set of variables or a MonomialOrder or ShortMonomialOrder.  If a monomial order is supplied then the resulting list of monomials is sorted in the monomial order.  If T is a list then the monomials are sorted in lexicographical order, or if T is a set then the monomials are not sorted.

Examples

withGroebner:

f87xy56xyz262x2z3+97xy3z73yz4

f:=62x2z3+97xy3z73yz456xyz2+87xy

(1)

Here, Support returns an unsorted list of monomials.

Supportf

x2z3,xy3z,yz4,xyz2,xy

(2)

The monomials are sorted in lexicographic order with x>y>z .

Supportf,x,y,z

x2z3,xy3z,xyz2,xy,yz4

(3)

The monomials are sorted in graded lexicographic order with x>y>z .

Supportf,grlexx,y,z

x2z3,xy3z,yz4,xyz2,xy

(4)

Fx2+5y4,x88y4,z8+64y2x8+100

F:=5y4+x2,x88y4,x8+z8+64y2+100

(5)

Sometimes it is hard to see the structure of a Groebner basis. Support can quickly reveal the structure.

GGroebner[Basis]F,plexx,y,z

G:=390625z64+312500000z56+109375000000z48+21874994880000z40+2734360643520000z32+218740742876160000z24+10935189454281097216z16+312260738651419443200z8+3897556646490972160000,264000003515625z56+141792004560937500z48+36975233639881250000z40+5116635466117234680000z32+535841466606972146400000z244111661799133622084480000z16+27769709934963826285883486208z8+2305845823963169687985887117312y2+3096625863672405027833148620800,1320000017578125z56708960022804687500z48184876168199406250000z4025583177330586173400000z322679207333034860732000000z24+20558308995668110422400000z16+41295655322303500444480000000z8+288230727995396210998235889664x2+2531291181350238048224000000000

(6)

SupportG,plexx,y,z

z64,z56,z48,z40,z32,z24,z16,z8,1,y2,z56,z48,z40,z32,z24,z16,z8,1,x2,z56,z48,z40,z32,z24,z16,z8,1

(7)

See Also

Groebner basis

InitialForm

LeadingTerm

Monomial Orders

MonomialOrder

 


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