next | previous | forward | backward | up | top | index | toc | Macaulay2 website
MixedMultiplicity :: multiReesIdeal(...,VariableBaseName=>...)

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

Synopsis

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

Functions with optional argument named VariableBaseName :