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D.2.4.9 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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