# multiReesIdeal(...,VariableBaseName=>...) -- Choose a base name for variables in the created ring

## Synopsis

• Usage:
multiReesIdeal(..., VariableBaseName => X)
homIdealPolytope(..., VariableBaseName => X)
mixedVolume(..., VariableBaseName => X)

## Description

Each of these functions creates a new ring of the form $R[X_0,\ldots, X_r]$ or $k[X_0,\ldots, X_r]$, where $R$ is the ring of the input ideal and $k$ is the coefficient ring of the output ideal. This option allows the user to change the base names of the new variables in this ring. The default variable is X.

 i1 : S = QQ[x_0..x_3] o1 = S o1 : PolynomialRing i2 : C = trim monomialCurveIdeal(S,{2,3,5}) 3 2 3 2 o2 = ideal (x x - x x , x - x x , x - x x ) 1 2 0 3 2 1 3 1 0 2 o2 : Ideal of S i3 : multiReesIdeal ({C}, VariableBaseName => "T") 2 2 3 2 3 o3 = ideal (x T - x T - x T , x T - x T - x T , (x - x x )T + (- x + 2 1 1 2 3 3 1 1 0 2 2 3 1 0 2 2 2 ------------------------------------------------------------------------ 2 x x )T ) 1 3 3 o3 : Ideal of S[T ..T ] 1 3
 i4 : homIdealPolytope ({(0,1),(1,0),(2,1),(1,2)}, VariableBaseName => "T") 2 2 2 2 o4 = ideal (T T , T T , T T , T T ) 1 2 1 2 1 3 2 3 o4 : Ideal of QQ[T ..T ] 1 3

## Further information

• Default value: X
• Function: multiReesIdeal -- Compute the defining ideal of multi-Rees algebra of ideals
• Option key: VariableBaseName -- make or retrieve a monoid

## Functions with optional argument named VariableBaseName :

• "graphIdeal(...,VariableBaseName=>...)" -- see graphIdeal(RingMap) -- the ideal of the graph of the regular map corresponding to a ring map
• "graphRing(...,VariableBaseName=>...)" -- see graphRing(RingMap) -- the coordinate ring of the graph of the regular map corresponding to a ring map
• "monoid(...,VariableBaseName=>...)" -- see monoid -- make or retrieve a monoid
• "homIdealPolytope(...,VariableBaseName=>...)"
• "mixedVolume(...,VariableBaseName=>...)"
• multiReesIdeal(...,VariableBaseName=>...) -- Choose a base name for variables in the created ring
• "newRing(...,VariableBaseName=>...)" -- see newRing -- make a copy of a ring, with some features changed
• "polarize(...,VariableBaseName=>...)" -- see polarize -- given a monomial ideal, computes the squarefree monomial ideal obtained via polarization
• "symmetricAlgebra(...,VariableBaseName=>...)" -- see symmetricAlgebra -- the symmetric algebra of a module
• "symmetricAlgebraIdeal(...,VariableBaseName=>...)" -- see symmetricAlgebraIdeal -- Ideal of the symmetric algebra of an ideal or module
• "tensor(...,VariableBaseName=>...)" -- see tensor(Ring,Ring) -- tensor product