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

Synopsis

Usage:

multiReesIdeal(..., VariableBaseName => X)

homIdealPolytope(..., 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];

i2 : C = trim monomialCurveIdeal(S,{2,3,5});

o2 : Ideal of S

i3 : multiReesIdeal (C, VariableBaseName => "w")

             2                   2
o3 = ideal (x w  - x w  - x w , x w  - x w  - x w )
             2 0    1 1    3 2   1 0    0 1    2 2

o3 : Ideal of S[w ..w ]
                 0   2

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 -- an optional argument

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(...,Variables=>...) -- specify the names of the indeterminates
homIdealPolytope(...,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(Monoid,Monoid,VariableBaseName=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids
tensor(Ring,Ring,VariableBaseName=>...) -- see tensor(Monoid,Monoid) -- tensor product of monoids