Given a differential form or vector field, this routine returns the ideal generated by the polynomial coefficients of such element.
In this example we compute the singular locus of a differential form w.
i1 : w = random newForm(2,1,2,"a")
2 2 2 2
o1 = (2x - 2x x + 6x - 3x x + 6x x )dx + (- 7x + 5x x - x - 2x x -
0 0 1 1 0 2 1 2 0 0 0 1 1 0 2
------------------------------------------------------------------------
2 2 2 2
x x + x )dx + (- 3x - 4x x + 7x + 2x x - 7x x - 3x )dx
1 2 2 1 0 0 1 1 0 2 1 2 2 2
o1 : DiffAlgForm
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i2 : singularIdeal(w)
2 2 2 2
o2 = ideal (2x - 2x x + 6x - 3x x + 6x x , - 7x + 5x x - x - 2x x -
0 0 1 1 0 2 1 2 0 0 1 1 0 2
------------------------------------------------------------------------
2 2 2 2
x x + x , - 3x - 4x x + 7x + 2x x - 7x x - 3x )
1 2 2 0 0 1 1 0 2 1 2 2
QQ[i]
o2 : Ideal of ------[][x , x , x ]
2 0 1 2
i + 1
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This routine is usefull to obtain the RingElement representing a 0-form
i3 : w = random newForm(2,1,2,"a"); |
i4 : r = radial 2; |
i5 : F = r_w
3 2 2 3 2 2 2 2 3
o5 = x + 6x x + 3x x - 4x + 5x x - 10x x x + 6x x + 3x x - x x + x
0 0 1 0 1 1 0 2 0 1 2 1 2 0 2 1 2 2
o5 : DiffAlgForm
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i6 : degree F
o6 = {2, 0, 3}
o6 : List
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i7 : (gens singularIdeal F)_0_0
3 2 2 3 2 2 2 2 3
o7 = x + 6x x + 3x x - 4x + 5x x - 10x x x + 6x x + 3x x - x x + x
0 0 1 0 1 1 0 2 0 1 2 1 2 0 2 1 2 2
QQ[i]
o7 : ------[][x , x , x ]
2 0 1 2
i + 1
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