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D.2.4.7 extend

Procedure from library grobcov.lib (see grobcov_lib).

Return:
The list ( (lpp_1,basis_1,segment_1,lpph_1), ... (lpp_s,basis_s,segment_s,lpph_s) )

The lpp are constant over a segment and correspond to the set of lpp of the reduced Groebner basis for each point of the segment.
The lpph corresponds to the lpp of the homogenized ideal and is different for each segment. It is given as a string.

Basis: to each element of lpp corresponds an I-regular function given in full representation. The
I-regular function is the corresponding element of the reduced Groebner basis for each point of the segment with the given lpp. For each point in the segment, the polynomial or the set of polynomials representing it, if they do not specialize to 0, then after normalization, specializes to the corresponding element of the reduced Groebner basis. In the full representation at least one of the polynomials representing the I-regular function specializes to non-zero.

With the default option ("rep",0) the segments are given in P-representation.
With option ("rep",1) the segments are given
in C-representation.
With option ("rep",2) both representations of the segments are given.

The P-representation of a segment is of the form
((p_1,(p_11,..,p_1k1)),..,(p_r,(p_r1,..,p_rkr))
representing the segment U_i (V(p_i) \ U_j (V(p_ij))), where the p's are prime ideals.

The C-representation of a segment is of the form
(E,N) representing V(E)\V(N), and the ideals E and N are radical and N contains E.

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,a2,b2,c2),(x), dp;
short=0;
ideal S=a0*x^2+b0*x+c0,
a1*x^2+b1*x+c1,
a2*x^2+b2*x+c2;
"System S="; S;
==> System S=
==> S[1]=(a0)*x^2+(b0)*x+(c0)
==> S[2]=(a1)*x^2+(b1)*x+(c1)
==> S[3]=(a2)*x^2+(b2)*x+(c2)
def GCS=grobcov(S,"rep",2,"comment",1);
==> Begin grobcov with options: can,1,comment,1,out,0,null,0,nonnull,1,ext,0,\
   rep,2
==> Begin cgsdr with options: can,1,comment,1,out,0,null,0,nonnull,1
==> Homogenizing the whole ideal: option can=1
==> Homogenized system = 
==> BH[1]=(a1^2*c2^2-a1*b1*b2*c2-2*a1*c1*a2*c2+a1*c1*b2^2+b1^2*a2*c2-b1*c1*a2\
   *b2+c1^2*a2^2)
==> BH[2]=(a0*b1*c2-a0*c1*b2-b0*a1*c2+b0*c1*a2+c0*a1*b2-c0*b1*a2)
==> BH[3]=(a0*a1*c2^2-a0*c1*a2*c2-b0*a1*b2*c2+b0*b1*a2*c2-c0*a1*a2*c2+c0*a1*b\
   2^2-c0*b1*a2*b2+c0*c1*a2^2)
==> BH[4]=(a0*a1*c1*c2-a0*c1^2*a2-b0*a1*c1*b2+b0*b1*c1*a2-c0*a1^2*c2+c0*a1*b1\
   *b2+c0*a1*c1*a2-c0*b1^2*a2)
==> BH[5]=(a0*a1*c1^2*b2-a0*b1*c1^2*a2+b0*a1^2*c1*c2-b0*a1*b1*c1*b2-b0*a1*c1^\
   2*a2+b0*b1^2*c1*a2-c0*a1^2*b1*c2-c0*a1^2*c1*b2+c0*a1*b1^2*b2+2*c0*a1*b1*c\
   1*a2-c0*b1^3*a2)
==> BH[6]=(a0^2*c2^2-a0*b0*b2*c2-2*a0*c0*a2*c2+a0*c0*b2^2+b0^2*a2*c2-b0*c0*a2\
   *b2+c0^2*a2^2)
==> BH[7]=(a0^2*c1*c2-a0*b0*c1*b2-a0*c0*a1*c2+a0*c0*b1*b2-a0*c0*c1*a2+b0^2*c1\
   *a2-b0*c0*b1*a2+c0^2*a1*a2)
==> BH[8]=(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)
==> BH[9]=(b1*a2*c2-c1*a2*b2)*x+(-a1*c2^2+b1*b2*c2+c1*a2*c2-c1*b2^2)*@t
==> BH[10]=(a1*c2-c1*a2)*x+(b1*c2-c1*b2)*@t
==> BH[11]=(a1*b2-b1*a2)*x+(a1*c2-c1*a2)*@t
==> BH[12]=(b0*a2*c2-c0*a2*b2)*x+(-a0*c2^2+b0*b2*c2+c0*a2*c2-c0*b2^2)*@t
==> BH[13]=(b0*c1*a2-c0*b1*a2)*x+(-a0*c1*c2+b0*c1*b2+c0*a1*c2-c0*b1*b2)*@t
==> BH[14]=(b0*a1*c1-c0*a1*b1)*x+(-a0*c1^2+b0*b1*c1+c0*a1*c1-c0*b1^2)*@t
==> BH[15]=(a0*c2-c0*a2)*x+(b0*c2-c0*b2)*@t
==> BH[16]=(a0*b2-b0*a2)*x+(a0*c2-c0*a2)*@t
==> BH[17]=(a0*c1-c0*a1)*x+(b0*c1-c0*b1)*@t
==> BH[18]=(a0*b1-b0*a1)*x+(a0*c1-c0*a1)*@t
==> BH[19]=(a2)*x^2+(b2)*x*@t+(c2)*@t^2
==> BH[20]=(a1)*x^2+(b1)*x*@t+(c1)*@t^2
==> BH[21]=(a0)*x^2+(b0)*x*@t+(c0)*@t^2
==> Begin KSW with null = 0 nonnull = 1
==> Number of segments in KSW (total) = 49
==> Time in KSW = 2
==> Number of lpp segments = 7
==> Time in KSW + group + Prep = 5
==> Time in LCUnion + combine = 1
==> Time in grobcov = 6
==> Number of segments of grobcov = 7
"grobcov(S,'rep',2,'comment',1)="; GCS;
==> grobcov(S,'rep',2,'comment',1)=
==> [1]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=0
==>          [2]:
==>             [1]:
==>                _[1]=(a1^2*c2^2-a1*b1*b2*c2-2*a1*c1*a2*c2+a1*c1*b2^2+b1^2*\
   a2*c2-b1*c1*a2*b2+c1^2*a2^2)
==>                _[2]=(a0*b1*c2-a0*c1*b2-b0*a1*c2+b0*c1*a2+c0*a1*b2-c0*b1*a\
   2)
==>                _[3]=(a0*a1*c2^2-a0*c1*a2*c2-b0*a1*b2*c2+b0*b1*a2*c2-c0*a1\
   *a2*c2+c0*a1*b2^2-c0*b1*a2*b2+c0*c1*a2^2)
==>                _[4]=(a0*a1*c1*c2-a0*c1^2*a2-b0*a1*c1*b2+b0*b1*c1*a2-c0*a1\
   ^2*c2+c0*a1*b1*b2+c0*a1*c1*a2-c0*b1^2*a2)
==>                _[5]=(a0*a1*c1^2*b2-a0*b1*c1^2*a2+b0*a1^2*c1*c2-b0*a1*b1*c\
   1*b2-b0*a1*c1^2*a2+b0*b1^2*c1*a2-c0*a1^2*b1*c2-c0*a1^2*c1*b2+c0*a1*b1^2*b\
   2+2*c0*a1*b1*c1*a2-c0*b1^3*a2)
==>                _[6]=(a0^2*c2^2-a0*b0*b2*c2-2*a0*c0*a2*c2+a0*c0*b2^2+b0^2*\
   a2*c2-b0*c0*a2*b2+c0^2*a2^2)
==>                _[7]=(a0^2*c1*c2-a0*b0*c1*b2-a0*c0*a1*c2+a0*c0*b1*b2-a0*c0\
   *c1*a2+b0^2*c1*a2-b0*c0*b1*a2+c0^2*a1*a2)
==>                _[8]=(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*b1*c2+a0*c1*b2+b0*a1*c2-b0*c1*a2-c0*a1*b2+c0*b1*a2)
==>          _[2]=(a1^2*c2^2-a1*b1*b2*c2-2*a1*c1*a2*c2+a1*c1*b2^2+b1^2*a2*c2-\
   b1*c1*a2*b2+c1^2*a2^2)
==>          _[3]=(a0*a1*c2^2-a0*b1*b2*c2-a0*c1*a2*c2+a0*c1*b2^2+b0*b1*a2*c2-\
   b0*c1*a2*b2-c0*a1*a2*c2+c0*c1*a2^2)
==>          _[4]=(a0^2*c2^2-a0*b0*b2*c2-2*a0*c0*a2*c2+a0*c0*b2^2+b0^2*a2*c2-\
   b0*c0*a2*b2+c0^2*a2^2)
==>          _[5]=(a0*a1*c1*c2-a0*b1^2*c2+a0*b1*c1*b2-a0*c1^2*a2+b0*a1*b1*c2-\
   b0*a1*c1*b2-c0*a1^2*c2+c0*a1*c1*a2)
==>          _[6]=(a0^2*c1*c2-a0*b0*b1*c2-a0*c0*a1*c2+a0*c0*b1*b2-a0*c0*c1*a2\
   +b0^2*a1*c2-b0*c0*a1*b2+c0^2*a1*a2)
==>          _[7]=(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)
==>          _[8]=(2*a0*a1*b1*c1*c2-a0*a1*c1^2*b2-a0*b1^3*c2+a0*b1^2*c1*b2-a0\
   *b1*c1^2*a2-b0*a1^2*c1*c2+b0*a1*b1^2*c2-b0*a1*b1*c1*b2+b0*a1*c1^2*a2-c0*a\
   1^2*b1*c2+c0*a1^2*c1*b2)
==>    [5]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       _[1]=(b1*a2*c2-c1*a2*b2)*x+(-a1*c2^2+b1*b2*c2+c1*a2*c2-c1*b2^2)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a1^2*c2^2-a1*b1*b2*c2-2*a1*c1*a2*c2+a1*c1*b2^2+b1^2*a2*\
   c2-b1*c1*a2*b2+c1^2*a2^2)
==>             _[2]=(a0*b1*c2-a0*c1*b2-b0*a1*c2+b0*c1*a2+c0*a1*b2-c0*b1*a2)
==>             _[3]=(a0*a1*c2^2-a0*c1*a2*c2-b0*a1*b2*c2+b0*b1*a2*c2-c0*a1*a2\
   *c2+c0*a1*b2^2-c0*b1*a2*b2+c0*c1*a2^2)
==>             _[4]=(a0*a1*c1*c2-a0*c1^2*a2-b0*a1*c1*b2+b0*b1*c1*a2-c0*a1^2*\
   c2+c0*a1*b1*b2+c0*a1*c1*a2-c0*b1^2*a2)
==>             _[5]=(a0*a1*c1^2*b2-a0*b1*c1^2*a2+b0*a1^2*c1*c2-b0*a1*b1*c1*b\
   2-b0*a1*c1^2*a2+b0*b1^2*c1*a2-c0*a1^2*b1*c2-c0*a1^2*c1*b2+c0*a1*b1^2*b2+2\
   *c0*a1*b1*c1*a2-c0*b1^3*a2)
==>             _[6]=(a0^2*c2^2-a0*b0*b2*c2-2*a0*c0*a2*c2+a0*c0*b2^2+b0^2*a2*\
   c2-b0*c0*a2*b2+c0^2*a2^2)
==>             _[7]=(a0^2*c1*c2-a0*b0*c1*b2-a0*c0*a1*c2+a0*c0*b1*b2-a0*c0*c1\
   *a2+b0^2*c1*a2-b0*c0*b1*a2+c0^2*a1*a2)
==>             _[8]=(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]=(a2)
==>                _[2]=(a1)
==>                _[3]=(a0)
==>             [2]:
==>                _[1]=(b1*c2-c1*b2)
==>                _[2]=(a1*c2-c1*a2)
==>                _[3]=(a1*b2-b1*a2)
==>                _[4]=(b0*c2-c0*b2)
==>                _[5]=(b0*c1-c0*b1)
==>                _[6]=(a0*c2-c0*a2)
==>                _[7]=(a0*b2-b0*a2)
==>                _[8]=(a0*c1-c0*a1)
==>                _[9]=(a0*b1-b0*a1)
==>    [4]:
==>       [1]:
==>          _[1]=(-a0*b1*c2+a0*c1*b2+b0*a1*c2-b0*c1*a2-c0*a1*b2+c0*b1*a2)
==>          _[2]=(a1^2*c2^2-a1*b1*b2*c2-2*a1*c1*a2*c2+a1*c1*b2^2+b1^2*a2*c2-\
   b1*c1*a2*b2+c1^2*a2^2)
==>          _[3]=(a0*a1*c2^2-a0*b1*b2*c2-a0*c1*a2*c2+a0*c1*b2^2+b0*b1*a2*c2-\
   b0*c1*a2*b2-c0*a1*a2*c2+c0*c1*a2^2)
==>          _[4]=(a0^2*c2^2-a0*b0*b2*c2-2*a0*c0*a2*c2+a0*c0*b2^2+b0^2*a2*c2-\
   b0*c0*a2*b2+c0^2*a2^2)
==>          _[5]=(a0*a1*c1*c2-a0*b1^2*c2+a0*b1*c1*b2-a0*c1^2*a2+b0*a1*b1*c2-\
   b0*a1*c1*b2-c0*a1^2*c2+c0*a1*c1*a2)
==>          _[6]=(a0^2*c1*c2-a0*b0*b1*c2-a0*c0*a1*c2+a0*c0*b1*b2-a0*c0*c1*a2\
   +b0^2*a1*c2-b0*c0*a1*b2+c0^2*a1*a2)
==>          _[7]=(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)
==>          _[8]=(2*a0*a1*b1*c1*c2-a0*a1*c1^2*b2-a0*b1^3*c2+a0*b1^2*c1*b2-a0\
   *b1*c1^2*a2-b0*a1^2*c1*c2+b0*a1*b1^2*c2-b0*a1*b1*c1*b2+b0*a1*c1^2*a2-c0*a\
   1^2*b1*c2+c0*a1^2*c1*b2)
==>       [2]:
==>          _[1]=(-a1*c2+c1*a2)
==>          _[2]=(-a1*b2+b1*a2)
==>          _[3]=(-a0*c2+c0*a2)
==>          _[4]=(-a0*b2+b0*a2)
==>          _[5]=(-a0*c1+c0*a1)
==>          _[6]=(-a0*b1+b0*a1)
==>          _[7]=(-a1*b1*c2+a1*c1*b2)
==>          _[8]=(-a0*b1*c2+a0*c1*b2)
==>          _[9]=(-a0*b0*c2+a0*c0*b2)
==>          _[10]=(-a0*b0*c1+a0*c0*b1)
==>    [5]:
==>       x
==> [3]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a2)
==>             _[2]=(a1)
==>             _[3]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(a2)
==>                _[2]=(b1*c2-c1*b2)
==>                _[3]=(a1)
==>                _[4]=(b0*c2-c0*b2)
==>                _[5]=(b0*c1-c0*b1)
==>                _[6]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(a2)
==>          _[2]=(a1)
==>          _[3]=(a0)
==>       [2]:
==>          _[1]=(a2)
==>          _[2]=(a1)
==>          _[3]=(a0)
==>          _[4]=(-b1*c2+c1*b2)
==>          _[5]=(-b0*c2+c0*b2)
==>          _[6]=(-b0*c1+c0*b1)
==>    [5]:
==>       @t
==> [4]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       _[1]=(b2)*x+(c2)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a2)
==>             _[2]=(b1*c2-c1*b2)
==>             _[3]=(a1)
==>             _[4]=(b0*c2-c0*b2)
==>             _[5]=(b0*c1-c0*b1)
==>             _[6]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(b2)
==>                _[2]=(a2)
==>                _[3]=(b1)
==>                _[4]=(a1)
==>                _[5]=(b0)
==>                _[6]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(a2)
==>          _[2]=(a1)
==>          _[3]=(a0)
==>          _[4]=(-b1*c2+c1*b2)
==>          _[5]=(-b0*c2+c0*b2)
==>          _[6]=(-b0*c1+c0*b1)
==>       [2]:
==>          _[1]=(b2)
==>          _[2]=(a2)
==>          _[3]=(b1)
==>          _[4]=(a1)
==>          _[5]=(b0)
==>          _[6]=(a0)
==>    [5]:
==>       x*@t
==> [5]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b2)
==>             _[2]=(a2)
==>             _[3]=(b1)
==>             _[4]=(a1)
==>             _[5]=(b0)
==>             _[6]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(c2)
==>                _[2]=(b2)
==>                _[3]=(a2)
==>                _[4]=(c1)
==>                _[5]=(b1)
==>                _[6]=(a1)
==>                _[7]=(c0)
==>                _[8]=(b0)
==>                _[9]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(b2)
==>          _[2]=(a2)
==>          _[3]=(b1)
==>          _[4]=(a1)
==>          _[5]=(b0)
==>          _[6]=(a0)
==>       [2]:
==>          _[1]=(c2)
==>          _[2]=(b2)
==>          _[3]=(a2)
==>          _[4]=(c1)
==>          _[5]=(b1)
==>          _[6]=(a1)
==>          _[7]=(c0)
==>          _[8]=(b0)
==>          _[9]=(a0)
==>    [5]:
==>       @t^2
==> [6]:
==>    [1]:
==>       _[1]=0
==>    [2]:
==>       _[1]=0
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(c2)
==>             _[2]=(b2)
==>             _[3]=(a2)
==>             _[4]=(c1)
==>             _[5]=(b1)
==>             _[6]=(a1)
==>             _[7]=(c0)
==>             _[8]=(b0)
==>             _[9]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       [1]:
==>          _[1]=(c2)
==>          _[2]=(b2)
==>          _[3]=(a2)
==>          _[4]=(c1)
==>          _[5]=(b1)
==>          _[6]=(a1)
==>          _[7]=(c0)
==>          _[8]=(b0)
==>          _[9]=(a0)
==>       [2]:
==>          _[1]=1
==>    [5]:
==>       0
==> [7]:
==>    [1]:
==>       _[1]=x^2
==>    [2]:
==>       _[1]=(a2)*x^2+(b2)*x+(c2)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b1*c2-c1*b2)
==>             _[2]=(a1*c2-c1*a2)
==>             _[3]=(a1*b2-b1*a2)
==>             _[4]=(b0*c2-c0*b2)
==>             _[5]=(b0*c1-c0*b1)
==>             _[6]=(a0*c2-c0*a2)
==>             _[7]=(a0*b2-b0*a2)
==>             _[8]=(a0*c1-c0*a1)
==>             _[9]=(a0*b1-b0*a1)
==>          [2]:
==>             [1]:
==>                _[1]=(a2)
==>                _[2]=(b1*c2-c1*b2)
==>                _[3]=(a1)
==>                _[4]=(b0*c2-c0*b2)
==>                _[5]=(b0*c1-c0*b1)
==>                _[6]=(a0)
==>    [4]:
==>       [1]:
==>          _[1]=(-b1*c2+c1*b2)
==>          _[2]=(-b0*c2+c0*b2)
==>          _[3]=(-a1*c2+c1*a2)
==>          _[4]=(-a1*b2+b1*a2)
==>          _[5]=(-a0*c2+c0*a2)
==>          _[6]=(-a0*b2+b0*a2)
==>          _[7]=(-b0*c1+c0*b1)
==>          _[8]=(-a0*c1+c0*a1)
==>          _[9]=(-a0*b1+b0*a1)
==>       [2]:
==>          _[1]=(a2)
==>          _[2]=(a1)
==>          _[3]=(a0)
==>          _[4]=(-b1*c2+c1*b2)
==>          _[5]=(-b0*c2+c0*b2)
==>          _[6]=(-b0*c1+c0*b1)
==>    [5]:
==>       x^2
def FGC=extend(GCS,"rep",0,"comment",1);
==> Time in extend = 17
"Full representation="; FGC;
==> Full representation=
==> [1]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=0
==>          [2]:
==>             [1]:
==>                _[1]=(a1^2*c2^2-a1*b1*b2*c2-2*a1*c1*a2*c2+a1*c1*b2^2+b1^2*\
   a2*c2-b1*c1*a2*b2+c1^2*a2^2)
==>                _[2]=(a0*b1*c2-a0*c1*b2-b0*a1*c2+b0*c1*a2+c0*a1*b2-c0*b1*a\
   2)
==>                _[3]=(a0*a1*c2^2-a0*c1*a2*c2-b0*a1*b2*c2+b0*b1*a2*c2-c0*a1\
   *a2*c2+c0*a1*b2^2-c0*b1*a2*b2+c0*c1*a2^2)
==>                _[4]=(a0*a1*c1*c2-a0*c1^2*a2-b0*a1*c1*b2+b0*b1*c1*a2-c0*a1\
   ^2*c2+c0*a1*b1*b2+c0*a1*c1*a2-c0*b1^2*a2)
==>                _[5]=(a0*a1*c1^2*b2-a0*b1*c1^2*a2+b0*a1^2*c1*c2-b0*a1*b1*c\
   1*b2-b0*a1*c1^2*a2+b0*b1^2*c1*a2-c0*a1^2*b1*c2-c0*a1^2*c1*b2+c0*a1*b1^2*b\
   2+2*c0*a1*b1*c1*a2-c0*b1^3*a2)
==>                _[6]=(a0^2*c2^2-a0*b0*b2*c2-2*a0*c0*a2*c2+a0*c0*b2^2+b0^2*\
   a2*c2-b0*c0*a2*b2+c0^2*a2^2)
==>                _[7]=(a0^2*c1*c2-a0*b0*c1*b2-a0*c0*a1*c2+a0*c0*b1*b2-a0*c0\
   *c1*a2+b0^2*c1*a2-b0*c0*b1*a2+c0^2*a1*a2)
==>                _[8]=(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]:
==>          _[1]=(a1*b2-b1*a2)*x+(a1*c2-c1*a2)
==>          _[2]=(a0*b2-b0*a2)*x+(a0*c2-c0*a2)
==>          _[3]=(a0*b1-b0*a1)*x+(a0*c1-c0*a1)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a1^2*c2^2-a1*b1*b2*c2-2*a1*c1*a2*c2+a1*c1*b2^2+b1^2*a2*\
   c2-b1*c1*a2*b2+c1^2*a2^2)
==>             _[2]=(a0*b1*c2-a0*c1*b2-b0*a1*c2+b0*c1*a2+c0*a1*b2-c0*b1*a2)
==>             _[3]=(a0*a1*c2^2-a0*c1*a2*c2-b0*a1*b2*c2+b0*b1*a2*c2-c0*a1*a2\
   *c2+c0*a1*b2^2-c0*b1*a2*b2+c0*c1*a2^2)
==>             _[4]=(a0*a1*c1*c2-a0*c1^2*a2-b0*a1*c1*b2+b0*b1*c1*a2-c0*a1^2*\
   c2+c0*a1*b1*b2+c0*a1*c1*a2-c0*b1^2*a2)
==>             _[5]=(a0*a1*c1^2*b2-a0*b1*c1^2*a2+b0*a1^2*c1*c2-b0*a1*b1*c1*b\
   2-b0*a1*c1^2*a2+b0*b1^2*c1*a2-c0*a1^2*b1*c2-c0*a1^2*c1*b2+c0*a1*b1^2*b2+2\
   *c0*a1*b1*c1*a2-c0*b1^3*a2)
==>             _[6]=(a0^2*c2^2-a0*b0*b2*c2-2*a0*c0*a2*c2+a0*c0*b2^2+b0^2*a2*\
   c2-b0*c0*a2*b2+c0^2*a2^2)
==>             _[7]=(a0^2*c1*c2-a0*b0*c1*b2-a0*c0*a1*c2+a0*c0*b1*b2-a0*c0*c1\
   *a2+b0^2*c1*a2-b0*c0*b1*a2+c0^2*a1*a2)
==>             _[8]=(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]=(a2)
==>                _[2]=(a1)
==>                _[3]=(a0)
==>             [2]:
==>                _[1]=(b1*c2-c1*b2)
==>                _[2]=(a1*c2-c1*a2)
==>                _[3]=(a1*b2-b1*a2)
==>                _[4]=(b0*c2-c0*b2)
==>                _[5]=(b0*c1-c0*b1)
==>                _[6]=(a0*c2-c0*a2)
==>                _[7]=(a0*b2-b0*a2)
==>                _[8]=(a0*c1-c0*a1)
==>                _[9]=(a0*b1-b0*a1)
==>    [4]:
==>       x
==> [3]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a2)
==>             _[2]=(a1)
==>             _[3]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(a2)
==>                _[2]=(b1*c2-c1*b2)
==>                _[3]=(a1)
==>                _[4]=(b0*c2-c0*b2)
==>                _[5]=(b0*c1-c0*b1)
==>                _[6]=(a0)
==>    [4]:
==>       @t
==> [4]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       [1]:
==>          _[1]=(b2)*x+(c2)
==>          _[2]=(b1)*x+(c1)
==>          _[3]=(b0)*x+(c0)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a2)
==>             _[2]=(b1*c2-c1*b2)
==>             _[3]=(a1)
==>             _[4]=(b0*c2-c0*b2)
==>             _[5]=(b0*c1-c0*b1)
==>             _[6]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(b2)
==>                _[2]=(a2)
==>                _[3]=(b1)
==>                _[4]=(a1)
==>                _[5]=(b0)
==>                _[6]=(a0)
==>    [4]:
==>       x*@t
==> [5]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b2)
==>             _[2]=(a2)
==>             _[3]=(b1)
==>             _[4]=(a1)
==>             _[5]=(b0)
==>             _[6]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=(c2)
==>                _[2]=(b2)
==>                _[3]=(a2)
==>                _[4]=(c1)
==>                _[5]=(b1)
==>                _[6]=(a1)
==>                _[7]=(c0)
==>                _[8]=(b0)
==>                _[9]=(a0)
==>    [4]:
==>       @t^2
==> [6]:
==>    [1]:
==>       _[1]=0
==>    [2]:
==>       _[1]=0
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(c2)
==>             _[2]=(b2)
==>             _[3]=(a2)
==>             _[4]=(c1)
==>             _[5]=(b1)
==>             _[6]=(a1)
==>             _[7]=(c0)
==>             _[8]=(b0)
==>             _[9]=(a0)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       0
==> [7]:
==>    [1]:
==>       _[1]=x^2
==>    [2]:
==>       [1]:
==>          _[1]=(a2)*x^2+(b2)*x+(c2)
==>          _[2]=(a1)*x^2+(b1)*x+(c1)
==>          _[3]=(a0)*x^2+(b0)*x+(c0)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b1*c2-c1*b2)
==>             _[2]=(a1*c2-c1*a2)
==>             _[3]=(a1*b2-b1*a2)
==>             _[4]=(b0*c2-c0*b2)
==>             _[5]=(b0*c1-c0*b1)
==>             _[6]=(a0*c2-c0*a2)
==>             _[7]=(a0*b2-b0*a2)
==>             _[8]=(a0*c1-c0*a1)
==>             _[9]=(a0*b1-b0*a1)
==>          [2]:
==>             [1]:
==>                _[1]=(a2)
==>                _[2]=(b1*c2-c1*b2)
==>                _[3]=(a1)
==>                _[4]=(b0*c2-c0*b2)
==>                _[5]=(b0*c1-c0*b1)
==>                _[6]=(a0)
==>    [4]:
==>       x^2


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