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D.4.13.3 resolve

Procedure from library resolve.lib (see resolve_lib).

Usage:
resolve (J); or resolve (J,i[,k]);
J ideal
i,k int

Compute:
a resolution of J,
if i > 0 debugging is turned on according to the following switches:
j1: value 0 or 1; turn off or on correctness checks in all steps
j2: value 0 or 2; turn off or on debugCenter
j3: value 0 or 4; turn off or on debugBlowUp
j4: value 0 or 8; turn off or on debugCoeff
j5: value 0 or 16:turn off or on debugging of Intersection with E^-
j6: value 0 or 32:turn off or on stop after pass throught the loop
i=j1+j2+j3+j4+j5+j6

Return:
a list l of 2 lists of rings
l[1][i] is a ring containing a basic object BO, the result of the resolution.
l[2] contains all rings which occured during the resolution process

Example:
 
LIB "resolve.lib";
ring R=0,(x,y,z),dp;
ideal J=x3+y5+yz2+xy4;
list L=resolve(J,1);
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 1
==> 1
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=xy4+y5+x3+yz2
==>       
==> ==== E: 
==> empty list
==>    
==> ==== Intersection
==> 0
==>      
==> -------  Center ------------
==> _[1]=z
==> _[2]=y
==> _[3]=x
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 0
==> 3
==> 2
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)^2*y(1)^5+x(3)^2*y(1)^4*y(2)+y(2)^3+y(1)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0
==>      
==> -------  Center ------------
==> _[1]=x(3)^2*y(1)^5+x(3)^2*y(1)^4*y(2)+y(2)^3+y(1)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 1
==> 3
==> 3
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^2*y(2)+y(2)^3+x(2)^2+y(0)^2
==>       
==> ==== E: 
==> [1]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=y(0)
==> _[3]=x(2)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 1
==> 5
==> 4
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)*y(2)^2+y(1)^2+y(2)^2+x(3)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(2)
==> [2]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=y(1)
==> _[3]=x(3)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 1
==> 7
==> 5
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)*y(0)^3+x(1)*y(0)+y(1)^2+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,
==> 0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)*y(0)^3+x(1)*y(0)+y(1)^2+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 2
==> 7
==> 6
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)*y(1)^2+x(3)^2*y(2)+x(3)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(2)
==> [3]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=x(3)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 2
==> 9
==> 7
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^2*y(0)^2*y(2)+x(2)*y(0)^2+x(2)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(0)
==> [2]:
==>    _[1]=y(2)
==> [3]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0,1,1,
==> 0,0,1,
==> 0,0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=y(0)
==> _[3]=x(2)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 2
==> 12
==> 8
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)^2*y(1)^2+x(2)^2*y(1)+y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=y(1)
==> [4]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,0,
==> 0,0,1,1,
==> 0,0,0,1,
==> 0,0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(3)^2*y(1)^2+x(2)^2*y(1)+y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 3
==> 12
==> 9
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^2*y(0)+x(2)^2+y(0)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(0)
==> [3]:
==>    _[1]=1
==> [4]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,0,
==> 0,0,1,1,
==> 0,0,0,1,
==> 0,0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^2*y(0)+x(2)^2+y(0)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 4
==> 12
==> 10
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(3)^4*y(1)^2*y(2)^2+x(3)^2*y(1)^2*y(2)+y(2)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(1)
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=y(2)
==> [4]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,1,
==> 0,0,1,1,
==> 0,0,0,1,
==> 0,0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(3)^4*y(1)^2*y(2)^2+x(3)^2*y(1)^2*y(2)+y(2)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 5
==> 12
==> 11
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(2)^4*y(0)*y(2)^2+x(2)^2*y(2)+y(0)+y(2)
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(0)
==> [3]:
==>    _[1]=y(2)
==> [4]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0,1,1,1,
==> 0,0,1,1,
==> 0,0,0,1,
==> 0,0,0,0 
==>      
==> -------  Center ------------
==> _[1]=y(2)
==> _[2]=y(0)
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 5
==> 14
==> 12
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*y(0)*y(1)^2+x(1)^2*y(1)^2+y(0)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=y(1)
==> [2]:
==>    _[1]=y(0)
==> [3]:
==>    _[1]=1
==> [4]:
==>    _[1]=x(1)
==>    
==> ==== Intersection
==> 0,1,1,1,
==> 0,0,1,1,
==> 0,0,0,1,
==> 0,0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*y(0)*y(1)^2+x(1)^2*y(1)^2+y(0)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 6
==> 14
==> 13
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(3)^2*y(1)+x(1)^2+y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=1
==> [4]:
==>    _[1]=x(1)
==> [5]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,1,0,
==> 0,0,1,1,1,
==> 0,0,0,1,1,
==> 0,0,0,0,1,
==> 0,0,0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(3)^2*y(1)+x(1)^2+y(1)+1
==> ----------------------------
==> ++++++++++++++    BO    +++++++++++++++++++++++
==> 7
==> 14
==> 14
==> +++++++++++++++++++++++++++++++++++++++++++++++
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(2)^2*y(0)^2+x(1)^2*y(0)+y(0)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=1
==> [3]:
==>    _[1]=y(0)
==> [4]:
==>    _[1]=x(1)
==> [5]:
==>    _[1]=x(2)
==>    
==> ==== Intersection
==> 0,1,1,1,0,
==> 0,0,1,1,1,
==> 0,0,0,1,1,
==> 0,0,0,0,1,
==> 0,0,0,0,0 
==>      
==> -------  Center ------------
==> _[1]=x(1)^4*x(2)^2*y(0)^2+x(1)^2*y(0)+y(0)+1
==> ----------------------------
==> ============= result will be tested ==========
==>                                               
==> the number of charts obtained: 8
==> =============     result is o.k.    ==========
def Q=L[1][7];
setring Q;
showBO(BO);
==>                        
==> ==== W: 
==> _[1]=0
==>       
==> ==== J: 
==> _[1]=x(1)^4*x(3)^2*y(1)+x(1)^2+y(1)+1
==>       
==> ==== E: 
==> [1]:
==>    _[1]=1
==> [2]:
==>    _[1]=y(1)
==> [3]:
==>    _[1]=1
==> [4]:
==>    _[1]=x(1)
==> [5]:
==>    _[1]=x(3)
==>    
==> ==== Intersection
==> 0,1,1,1,0,
==> 0,0,1,1,1,
==> 0,0,0,1,1,
==> 0,0,0,0,1,
==> 0,0,0,0,0 
==>      


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