next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
RandomPlaneCurves (missing documentation) :: completeLinearSystemOnNodalPlaneCurve

completeLinearSystemOnNodalPlaneCurve -- Compute the complete linear system of a divisor on a nodal plane curve

Synopsis

Description

Compute the complete linear series of D0-D1 on the normalization of C via adjoint curves and double linkage.
i1 : R=ZZ/101[x_0..x_2];
i2 : J=(random nodalPlaneCurve)(6,3,R);

o2 : Ideal of R
i3 : D={J+ideal random(R^1,R^{1:-3}),J+ideal 1_R};
i4 : l=completeLinearSystemOnNodalPlaneCurve(J,D)

                                                
o4 = (| x_1^2x_2^3+12x_0x_2^4+20x_1x_2^4+38x_2^5
                                                
     ------------------------------------------------------------------------
                                                           
     x_1^3x_2^2+12x_0x_1x_2^3-38x_0x_2^4+42x_1x_2^4+48x_2^5
                                                           
     ------------------------------------------------------------------------
                                                        
     x_0x_1^2x_2^2+12x_0^2x_2^3+20x_0x_1x_2^3+38x_0x_2^4
                                                        
     ------------------------------------------------------------------------
                                                                      
     x_1^4x_2-43x_0^2x_2^3+25x_0x_1x_2^3+50x_0x_2^4+16x_1x_2^4+20x_2^5
                                                                      
     ------------------------------------------------------------------------
                                                                      
     x_0x_1^3x_2+12x_0^2x_1x_2^2-38x_0^2x_2^3+42x_0x_1x_2^3+48x_0x_2^4
                                                                      
     ------------------------------------------------------------------------
                                                            
     x_0^2x_1^2x_2+12x_0^3x_2^2+20x_0^2x_1x_2^2+38x_0^2x_2^3
                                                            
     ------------------------------------------------------------------------
                                                                             
     x_1^5-43x_0^2x_1x_2^2+3x_0^2x_2^3-46x_0x_1x_2^3-31x_0x_2^4+3x_1x_2^4-2x_
                                                                             
     ------------------------------------------------------------------------
                                                                             
     2^5 x_0x_1^4-43x_0^3x_2^2+25x_0^2x_1x_2^2+50x_0^2x_2^3+16x_0x_1x_2^3+20x
                                                                             
     ------------------------------------------------------------------------
                                                                             
     _0x_2^4 x_0^2x_1^3+12x_0^3x_1x_2-38x_0^3x_2^2+42x_0^2x_1x_2^2+48x_0^2x_2
                                                                             
     ------------------------------------------------------------------------
                                                        
     ^3 x_0^3x_1^2+12x_0^4x_2+20x_0^3x_1x_2+38x_0^3x_2^2
                                                        
     ------------------------------------------------------------------------
                                                                             
     x_0^4x_1-8x_0^4x_2-46x_0^3x_1x_2+6x_0^3x_2^2-47x_0^2x_1x_2^2-30x_0^2x_2^
                                                                             
     ------------------------------------------------------------------------
                                                  
     3-19x_0x_1x_2^3-23x_0x_2^4-17x_1x_2^4-38x_2^5
                                                  
     ------------------------------------------------------------------------
                                                                             
     x_0^5-41x_0^4x_2+47x_0^3x_1x_2+29x_0^3x_2^2+17x_0^2x_1x_2^2+20x_0^2x_2^3
                                                                             
     ------------------------------------------------------------------------
                                                      3 2      2 3        4  
     +23x_0x_1x_2^3+27x_0x_2^4-36x_1x_2^4+18x_2^5 |, x x  - 27x x  - 44x x  -
                                                      0 1      0 1      0 1  
     ------------------------------------------------------------------------
        5      4      3          2 2          3        4       3 2      2   2
     19x  + 12x x  - x x x  - 44x x x  - 39x x x  - 35x x  + 4x x  - 38x x x 
        1      0 2    0 1 2      0 1 2      0 1 2      1 2     0 2      0 1 2
     ------------------------------------------------------------------------
           2 2      3 2      2 3          3      2 3        4       4      5
     + 4x x x  + 47x x  + 32x x  + 18x x x  - 38x x  - 44x x  - 9x x  + 49x )
         0 1 2      1 2      0 2      0 1 2      1 2      0 2     1 2      2

o4 : Sequence
i5 : C=imageUnderRationalMap(J,l_0);

               ZZ
o5 : Ideal of ---[x , x , x , x , x , x , x , x , x , x , x  , x  ]
              101  0   1   2   3   4   5   6   7   8   9   10   11
i6 : (dim C, degree C, genus C)

o6 = (2, 18, 7)

o6 : Sequence

See also

Ways to use completeLinearSystemOnNodalPlaneCurve :