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DiffAlg :: substitute(DiffAlgElement,Ring)

substitute(DiffAlgElement,Ring) -- gets the RingElement of a differential form or vector field in a ring

Synopsis

Description

By its nature, the package DiffAlg is constantly changing the rings where its differential forms and vector fields are defined. This function is useful to get information of DiffAlg out to some common polynomial rings and work with the rest of Macaulay2 packages.


In this example we get the singular locus of a logarithmic form and compute its Hilbert polynomial.

i1 : w = random logarithmicForm(2,{1,1},"a",Projective => true)

o1 = (35x  + 21x )dx  + (- 35x  + 7x )dx  + (- 21x  - 7x )dx
         1      2   0         0     2   1         0     1   2

o1 : DiffAlgForm
i2 : I = singularIdeal w

o2 = ideal (35x  + 21x , - 35x  + 7x , - 21x  - 7x )
               1      2       0     2       0     1

               QQ[i]
o2 : Ideal of ------[][x ..x ]
               2        0   2
              i  + 1
i3 : S = QQ[gens ring I]

o3 = S

o3 : PolynomialRing
i4 : hilbertPolynomial (sub(I,S))

o4 = P
      0

o4 : ProjectiveHilbertPolynomial