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projectiveFatPoints(...,VerifyPoints=>...) -- Option to projectiveFatPoints.

Description

Default is true, in which case the function removes zero columns and duplicate columns giving rise to the same projective point. For duplicate points, a single instance is retained with the largest multiplicity.

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing
 
i2 : Mbad = matrix {{1,2,0,1}, {0,0,0,1}, {0,0,0,1}}

o2 = | 1 2 0 1 |
     | 0 0 0 1 |
     | 0 0 0 1 |

              3       4
o2 : Matrix ZZ  <-- ZZ
 
i3 : Mclean = matrix {{1,1}, {0,1}, {0,1}}

o3 = | 1 1 |
     | 0 1 |
     | 0 1 |

              3       2
o3 : Matrix ZZ  <-- ZZ
 
i4 : mults = {1,3,5,2}

o4 = {1, 3, 5, 2}

o4 : List
 
i5 : multsClean = {3,2}

o5 = {3, 2}

o5 : List
 
i6 : (inF1,GF1) = projectiveFatPoints(Mbad,mults,R)

              2    3       2   2 3     2        2    3   3       2     3 
o6 = (ideal (y z, y , x*y*z , x z ), {y z - 2y*z  + z , y  - 3y*z  + 2z ,
     ------------------------------------------------------------------------
          2      3      3    4   2 3       4    5
     x*y*z  - x*z  - y*z  + z , x z  - 2x*z  + z })

o6 : Sequence
 
i7 : (inF2,GF2) = projectiveFatPoints(Mclean,multsClean,R)

              2    3       2   2 3     2        2    3   3       2     3 
o7 = (ideal (y z, y , x*y*z , x z ), {y z - 2y*z  + z , y  - 3y*z  + 2z ,
     ------------------------------------------------------------------------
          2      3      3    4   2 3       4    5
     x*y*z  - x*z  - y*z  + z , x z  - 2x*z  + z })

o7 : Sequence
 
i8 : (inF1 == inF2, GF1 == GF2)

o8 = (true, true)

o8 : Sequence

See also

Functions with optional argument named VerifyPoints:

Further information

  • Default value: true
  • Function: projectiveFatPoints -- produces the ideal and initial ideal from the coordinates of a finite set of fat points
  • Option key: VerifyPoints -- Option to projectivePoints.

The source of this document is in Points.m2:1222:0.