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D.2.4.3 gencase1
Procedure from library grobcov.lib (see grobcov_lib).
- Return:
- The list of the generic case, when its basis is 1, or
the empty list if not.
The output is of the form
(lpp=1,basis=1,(null ideal=0,(p1,..ps)),N)
where (0,(p1,..,ps)) is the P-representation of the generic segment
(the pi's are the prime components) and N is its intersection
- 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.
Example:
| LIB "grobcov.lib";
"Generic segment for the extended Steiner-Lehmus theorem";
==> Generic segment for the extended Steiner-Lehmus theorem
ring R=(0,x,y),(a,b,m,n,p,r),lp;
ideal S=p^2-(x^2+y^2),
-a*(y)+b*(x+p),
-a*y+b*(x-1)+y,
(r-1)^2-((x-1)^2+y^2),
-m*(y)+n*(x+r-2) +y,
-m*y+n*x,
(a^2+b^2)-((m-1)^2+n^2);
short=0;
gencase1(S);
==> _[1]=1 _[1]=1 [1]:
==> _[1]=0
==> [2]:
==> [1]:
==> _[1]=(y)
==> [2]:
==> _[1]=(8*x^10-40*x^9+41*x^8*y^2+76*x^8-164*x^7*y^2-64*x^7+84*x^6*y^4\
+246*x^6*y^2+16*x^6-252*x^5*y^4-164*x^5*y^2+8*x^5+86*x^4*y^6+278*x^4*y^4+\
31*x^4*y^2-4*x^4-172*x^3*y^6-136*x^3*y^4+20*x^3*y^2+44*x^2*y^8+122*x^2*y^\
6+14*x^2*y^4-10*x^2*y^2-44*x*y^8-36*x*y^6+12*x*y^4+9*y^10+14*y^8-y^6-6*y^\
4+y^2)
==> [3]:
==> _[1]=(2*x-1)
==> _[1]=(16*x^11*y-88*x^10*y+82*x^9*y^3+192*x^9*y-369*x^8*y^3-204*x^8*y+168*\
x^7*y^5+656*x^7*y^3+96*x^7*y-588*x^6*y^5-574*x^6*y^3+172*x^5*y^7+808*x^5*\
y^5+226*x^5*y^3-16*x^5*y-430*x^4*y^7-550*x^4*y^5+9*x^4*y^3+4*x^4*y+88*x^3\
*y^9+416*x^3*y^7+164*x^3*y^5-40*x^3*y^3-132*x^2*y^9-194*x^2*y^7+10*x^2*y^\
5+10*x^2*y^3+18*x*y^11+72*x*y^9+34*x*y^7-24*x*y^5+2*x*y^3-9*y^11-14*y^9+y\
^7+6*y^5-y^3)
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