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

i1 : setRandomSeed("alpha");

i2 : R=ZZ/32003[x_0..x_2];

i3 : J=(random nodalPlaneCurve)(6,3,R);

o3 : Ideal of R

i4 : D={J+ideal random(R^1,R^{1:-3}),J+ideal 1_R};

i5 : l=completeLinearSystemOnNodalPlaneCurve(J,D)

                                                        
o5 = (| x_1^2x_2^3-15905x_0x_2^4-3127x_1x_2^4-14505x_2^5
                                                        
     ------------------------------------------------------------------------
                                                                   
     x_1^3x_2^2-15905x_0x_1x_2^3-2273x_0x_2^4+284x_1x_2^4-8884x_2^5
                                                                   
     ------------------------------------------------------------------------
                                                                
     x_0x_1^2x_2^2-15905x_0^2x_2^3-3127x_0x_1x_2^3-14505x_0x_2^4
                                                                
     ------------------------------------------------------------------------
                                                                          
     x_1^4x_2+14690x_0^2x_2^3-4546x_0x_1x_2^3+12199x_0x_2^4+15103x_1x_2^4-
                                                                          
     ------------------------------------------------------------------------
                                                                            
     8967x_2^5 x_0x_1^3x_2-15905x_0^2x_1x_2^2-2273x_0^2x_2^3+284x_0x_1x_2^3-
                                                                            
     ------------------------------------------------------------------------
                                                                             
     8884x_0x_2^4 x_0^2x_1^2x_2-15905x_0^3x_2^2-3127x_0^2x_1x_2^2-14505x_0^2x
                                                                             
     ------------------------------------------------------------------------
                                                                             
     _2^3 x_1^5+14690x_0^2x_1x_2^2-9353x_0^2x_2^3+6189x_0x_1x_2^3-14853x_0x_2
                                                                             
     ------------------------------------------------------------------------
                               
     ^4+13689x_1x_2^4+8480x_2^5
                               
     ------------------------------------------------------------------------
                                                                             
     x_0x_1^4+14690x_0^3x_2^2-4546x_0^2x_1x_2^2+12199x_0^2x_2^3+15103x_0x_1x_
                                                                             
     ------------------------------------------------------------------------
                                                                             
     2^3-8967x_0x_2^4 x_0^2x_1^3-15905x_0^3x_1x_2-2273x_0^3x_2^2+284x_0^2x_1x
                                                                             
     ------------------------------------------------------------------------
                                                                             
     _2^2-8884x_0^2x_2^3 x_0^3x_1^2-15905x_0^4x_2-3127x_0^3x_1x_2-14505x_0^3x
                                                                             
     ------------------------------------------------------------------------
                                                                             
     _2^2 x_0^4x_1-11073x_0^4x_2-14059x_0^3x_1x_2-14725x_0^3x_2^2+15715x_0^2x
                                                                             
     ------------------------------------------------------------------------
                                                                             
     _1x_2^2+5589x_0^2x_2^3-5681x_0x_1x_2^3+9449x_0x_2^4-752x_1x_2^4-4257x_2^
                                                                             
     ------------------------------------------------------------------------
                                                                             
     5 x_0^5-11952x_0^4x_2+4264x_0^3x_1x_2-13256x_0^3x_2^2-8472x_0^2x_1x_2^2-
                                                                             
     ------------------------------------------------------------------------
                                                                          3 2
     1481x_0^2x_2^3+1434x_0x_1x_2^3-x_0x_2^4-13158x_1x_2^4-15984x_2^5 |, x x 
                                                                          0 1
     ------------------------------------------------------------------------
            2 3           4         5         4          3            2 2    
     + 7632x x  - 14167x x  + 15007x  - 15905x x  - 2708x x x  + 2874x x x  +
            0 1         0 1         1         0 2        0 1 2        0 1 2  
     ------------------------------------------------------------------------
             3          4          3 2     2   2           2 2         3 2  
     10670x x x  + 8250x x  + 7181x x  - 3x x x  + 15061x x x  - 15223x x  -
           0 1 2        1 2        0 2     0 1 2         0 1 2         1 2  
     ------------------------------------------------------------------------
           2 3            3        2 3          4           4        5
     10388x x  + 6271x x x  - 2509x x  + 7640x x  - 14385x x  - 1297x )
           0 2        0 1 2        1 2        0 2         1 2        2

o5 : Sequence

i6 : C=imageUnderRationalMap(J,l_0);

                ZZ
o6 : Ideal of -----[x ..x  ]
              32003  0   11

i7 : (dim C, degree C, genus C)

o7 = (2, 18, 7)

o7 : Sequence