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A.1.1 Basic programming

We show in the example below the following:

  • define the ring R of characteristic 32003, variables x,y,z, monomial ordering dp (implementing F_32003[x,y,z])
  • list the information about R by typing its name
  • check the order of the variables
  • define the integers a,b,c,t
  • define a polynomial f (depending on a,b,c,t) and display it
  • define the jacobian ideal i of f
  • compute a Groebner basis of i
  • compute the dimension of the algebraic set defined by i (requires the computation of a Groebner basis)
  • create and display a string in order to comment the result (text between quotes " "; is a 'string')
  • load a library (see primdec_lib)
  • compute a primary decomposition for i and assign the result to a list L (which is a list of lists of ideals)
  • display the number of primary components and the first primary and prime components (entries of the list L[1])
  • implement the localization of F_32003[x,y,z] at the homogeneous maximal ideal (generated by x,y,z) by defining a ring with local monomial ordering (ds in place of dp)
  • map i to this ring (see imap) - we may use the same name i, since ideals are ring dependent data
  • compute the local dimension of the algebraic set defined by i at the origin (= dimension of the ideal generated by i in the localization)
  • compute the local dimension of the algebraic set defined by i at the point (-2000,-6961,-7944) (by applying a linear coordinate transformation)
For a more basic introduction to programming in SINGULAR, we refer to Getting started.

 


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