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D.2.4.8 extend

Procedure from library grobcov.lib (see grobcov_lib).

Return:
When calling extend(grobcov(S,"rep",2)) the result is of the form ( (lpp_1,basis_1,segment_1,lpph_1), ... (lpp_s,basis_s,segment_s,lpph_s) ) where each function of the basis can be given by an ideal of representants.

Note:
The basering R, must be of the form Q[a][x], (a=parameters, x=variables), and should be defined previously. The ideal must be defined on R.

parametric ideal, full representation.

Example:
 
LIB "grobcov.lib";
ring R=(0,a0,b0,c0,a1,b1,c1),(x), dp;
short=0;
ideal S=a0*x^2+b0*x+c0,
a1*x^2+b1*x+c1;
def GCS=grobcov(S,"rep",2);
GCS;
==> [1]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=0
==>          [2]:
==>             [1]:
==>                _[1]=(a0^2*c1^2-a0*b0*b1*c1-2*a0*c0*a1*c1+a0*c0*b1^2+b0^2*\
   a1*c1-b0*c0*a1*b1+c0^2*a1^2)
==>    [4]:
==>       [1]:
==>          _[1]=0
==>       [2]:
==>          _[1]=(a0^2*c1^2-a0*b0*b1*c1-2*a0*c0*a1*c1+a0*c0*b1^2+b0^2*a1*c1-\
   b0*c0*a1*b1+c0^2*a1^2)
==>    [5]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       _[1]=(b0*a1*c1-c0*a1*b1)*x+(-a0*c1^2+b0*b1*c1+c0*a1*c1-c0*b1^2)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a0^2*c1^2-a0*b0*b1*c1-2*a0*c0*a1*c1+a0*c0*b1^2+b0^2*a1*\
   c1-b0*c0*a1*b1+c0^2*a1^2)
==>          [2]:
==>             [1]:
==>                _[1]=(b0*c1-c0*b1)
==>                _[2]=(a0*c1-c0*a1)
==>                _[3]=(a0*b1-b0*a1)
==>             [2]:
==>                _[1]=(a1)
==>                _[2]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(a0^2*c1^2-a0*b0*b1*c1-2*a0*c0*a1*c1+a0*c0*b1^2+b0^2*a1*c1-\
   b0*c0*a1*b1+c0^2*a1^2)
==>       [2]:
==>          _[1]=(-a0*c1+c0*a1)
==>          _[2]=(-a0*b1+b0*a1)
==>          _[3]=(-a0*b0*c1+a0*c0*b1)
==>    [5]:
==>       x
==> [3]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       _[1]=(b1)*x+(c1)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a1)
==>             _[2]=(b0*c1-c0*b1)
==>             _[3]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(b1)
==>                _[2]=(a1)
==>                _[3]=(b0)
==>                _[4]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(a1)
==>          _[2]=(a0)
==>          _[3]=(-b0*c1+c0*b1)
==>       [2]:
==>          _[1]=(b1)
==>          _[2]=(a1)
==>          _[3]=(b0)
==>          _[4]=(a0)
==>    [5]:
==>       x*@t
==> [4]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b1)
==>             _[2]=(a1)
==>             _[3]=(b0)
==>             _[4]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(c1)
==>                _[2]=(b1)
==>                _[3]=(a1)
==>                _[4]=(c0)
==>                _[5]=(b0)
==>                _[6]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(b1)
==>          _[2]=(a1)
==>          _[3]=(b0)
==>          _[4]=(a0)
==>       [2]:
==>          _[1]=(c1)
==>          _[2]=(b1)
==>          _[3]=(a1)
==>          _[4]=(c0)
==>          _[5]=(b0)
==>          _[6]=(a0)
==>    [5]:
==>       @t^2
==> [5]:
==>    [1]:
==>       _[1]=0
==>    [2]:
==>       _[1]=0
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(c1)
==>             _[2]=(b1)
==>             _[3]=(a1)
==>             _[4]=(c0)
==>             _[5]=(b0)
==>             _[6]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       [1]:
==>          _[1]=(c1)
==>          _[2]=(b1)
==>          _[3]=(a1)
==>          _[4]=(c0)
==>          _[5]=(b0)
==>          _[6]=(a0)
==>       [2]:
==>          _[1]=1
==>    [5]:
==>       0
==> [6]:
==>    [1]:
==>       _[1]=x^2
==>    [2]:
==>       _[1]=(a1)*x^2+(b1)*x+(c1)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b0*c1-c0*b1)
==>             _[2]=(a0*c1-c0*a1)
==>             _[3]=(a0*b1-b0*a1)
==>          [2]:
==>             [1]:
==>                _[1]=(a1)
==>                _[2]=(b0*c1-c0*b1)
==>                _[3]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(-b0*c1+c0*b1)
==>          _[2]=(-a0*c1+c0*a1)
==>          _[3]=(-a0*b1+b0*a1)
==>       [2]:
==>          _[1]=(a1)
==>          _[2]=(a0)
==>          _[3]=(-b0*c1+c0*b1)
==>    [5]:
==>       x^2
==> [7]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a1)
==>             _[2]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(a1)
==>                _[2]=(b0*c1-c0*b1)
==>                _[3]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(a1)
==>          _[2]=(a0)
==>       [2]:
==>          _[1]=(a1)
==>          _[2]=(a0)
==>          _[3]=(-b0*c1+c0*b1)
==>    [5]:
==>       @t
def FGC=extend(GCS,"rep",0);
// Full representation=
FGC;
==> [1]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=0
==>          [2]:
==>             [1]:
==>                _[1]=(a0^2*c1^2-a0*b0*b1*c1-2*a0*c0*a1*c1+a0*c0*b1^2+b0^2*\
   a1*c1-b0*c0*a1*b1+c0^2*a1^2)
==>    [4]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       _[1]=(a0*b1-b0*a1)*x+(a0*c1-c0*a1)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a0^2*c1^2-a0*b0*b1*c1-2*a0*c0*a1*c1+a0*c0*b1^2+b0^2*a1*\
   c1-b0*c0*a1*b1+c0^2*a1^2)
==>          [2]:
==>             [1]:
==>                _[1]=(b0*c1-c0*b1)
==>                _[2]=(a0*c1-c0*a1)
==>                _[3]=(a0*b1-b0*a1)
==>             [2]:
==>                _[1]=(a1)
==>                _[2]=(a0)
==>    [4]:
==>       x
==> [3]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       [1]:
==>          _[1]=(b1)*x+(c1)
==>          _[2]=(b0)*x+(c0)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a1)
==>             _[2]=(b0*c1-c0*b1)
==>             _[3]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(b1)
==>                _[2]=(a1)
==>                _[3]=(b0)
==>                _[4]=(a0)
==>    [4]:
==>       x*@t
==> [4]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b1)
==>             _[2]=(a1)
==>             _[3]=(b0)
==>             _[4]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(c1)
==>                _[2]=(b1)
==>                _[3]=(a1)
==>                _[4]=(c0)
==>                _[5]=(b0)
==>                _[6]=(a0)
==>    [4]:
==>       @t^2
==> [5]:
==>    [1]:
==>       _[1]=0
==>    [2]:
==>       _[1]=0
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(c1)
==>             _[2]=(b1)
==>             _[3]=(a1)
==>             _[4]=(c0)
==>             _[5]=(b0)
==>             _[6]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       0
==> [6]:
==>    [1]:
==>       _[1]=x^2
==>    [2]:
==>       [1]:
==>          _[1]=(a1)*x^2+(b1)*x+(c1)
==>          _[2]=(a0)*x^2+(b0)*x+(c0)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b0*c1-c0*b1)
==>             _[2]=(a0*c1-c0*a1)
==>             _[3]=(a0*b1-b0*a1)
==>          [2]:
==>             [1]:
==>                _[1]=(a1)
==>                _[2]=(b0*c1-c0*b1)
==>                _[3]=(a0)
==>    [4]:
==>       x^2
==> [7]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a1)
==>             _[2]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(a1)
==>                _[2]=(b0*c1-c0*b1)
==>                _[3]=(a0)
==>    [4]:
==>       @t


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