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A.1.1 Basic programming
We show in the example below the following:
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define the ring
R of characteristic 32003, variables x,y,z , monomial
ordering dp (implementing F_32003[x,y,z])
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list the information about
R by typing its name
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check the order of the variables
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define the integers
a,b,c,t
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define a polynomial
f (depending on a,b,c,t ) and display it
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define the jacobian ideal
i of f
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compute a Groebner basis of
i
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compute the dimension of the algebraic set defined by
i (requires
the computation of a Groebner basis)
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create and display a string in order to comment the result (text between
quotes " "; is a 'string')
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load a library (see primdec_lib)
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compute a primary decomposition for
i and assign the result to a
list L (which is a list of lists of ideals)
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display the number of primary components and the first primary and prime
components (entries of the list L[1])
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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 )
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map i to this ring (see imap) - we may use the same name
i ,
since ideals are ring dependent data
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compute the local dimension of the algebraic set defined by
i at
the origin (= dimension of the ideal generated by i in the localization)
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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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