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

Description

Default is true, in which case the function removes zero columns and duplicate columns giving rise to the same projective point.

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 : (inG1,G1) = projectivePoints(Mbad,R)

                                     2
o4 = (ideal (y, x*z), {y - z, x*z - z })

o4 : Sequence
 
i5 : (inG2,G2) = projectivePoints(Mclean,R)

                                     2
o5 = (ideal (y, x*z), {y - z, x*z - z })

o5 : Sequence
 
i6 : (inG1 == inG2, G1 == G2)

o6 = (true, true)

o6 : Sequence

See also

Functions with optional argument named VerifyPoints:

Further information

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

The source of this document is in Points.m2:1200:0.