> %P
load BBb;
function Nterm(r,a)
return t^2*
 (t^(r-2)*(1+t^be)*InverseMod(Denom([be,be,r-be]) div (1-t)^3,((1-t^r) div 
(1-t)))
 mod ((1-t^r) div (1-t)))/Denom([1,1,1,r]) where be is InverseMod(a,r);
end function;
function P(A)
return (1-t^A[6])/Denom(A[1..5]);
end function;
function PI(A) // Initial term P_I, only for CY 3folds
n1 := #[i : i in A | i eq 1];
n2 := #[i : i in A | i eq 2];
return (1 + (n1-4)*t + (n2+Binomial(n1-3,2))*t^2 + (n1-4)*t^3 + t^4)/(1-t)^4;
end function;
function Bask(A);
 B := []; C := [];
 Relevant := [r : r in [2..A[5]] | r eq GCD([Integers()
 | A[i] : i in [1..5] | A[i] mod r eq 0])];
 for r in Relevant do
 Amod := [a mod r : a in A ];
 case [#[a : a in Amod[1..5] | a eq 0],#[a : a in Amod[6..6] | a eq 0]]:
 // when 0:; // no sing, do nothing when 4:; //error when 5:; //error
 when [1,0]:
 Append(~B, Insert(Sort(Exclude(Exclude(Amod[1..5],Amod[6]),0)),1,r));
 // end this case: If ai divides d then Pi not on X
 when [2,1]:
 // calculate the number S^0(d) in PP(ai,aj)
 Num := Floor(A[6]/LCM([a : a in A[1..5] | a mod r eq 0]));
 for i in [1..Num] do
 Append(~B, Insert(Sort(Exclude(Exclude(Amod[1..5],0),0)),1,r));
 end for;
 // end if; If r does not divides d then Lij is line of 1/r
 when [2,0]:
 Append(~C, Insert(Exclude(Exclude(Exclude(Amod[1..5],0),0),Amod[6]),1,r));
 when [3,1]:; // necessarily r divides d and curve of 1/r
 Append(~C, Insert(Exclude(Exclude(Exclude(Amod[1..5],0),0),0),1,r));
 end case;
end for;
return B, C;
end function;
function PointTerms(B)
return &+[K | Qorb(b[1],b[2..4],0) : b in B];
end function;
function X(A)
return P(A)-PI(A)-PointTerms(Bask(A));
end function;
function PC(A) // The curve terms P_C
B,C := Bask(A);
YY := PartialFractionDecomposition(X(A)/t^3*(1-t)^4);
return [t^3/(1-t)^4*&+[K|y[3]/y[1]^y[2] : y in YY
 | IsDivisibleBy(1-t^r,y[1])] where r is c[1] : c in C];
end function;
n:=20;
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
X := PC(A)[2];
X;
X - Qorb(3,[1,2],3)/(1-t^3) - Nterm(3,1);
X - Qorb(3,[1,2],3)/(1-t^3) - 0* Nterm(3,1);
X - Qorb(3,[1,2],3)/(1-t^3) - 2* Nterm(3,1);
b:=1; N:=2; X-Qorb(3,[1,2],3)/(1-t^3);
b:=1; N:=2; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm;;
b:=1; N:=2; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
X := PC(A)[1];
X-Qorb(4,[1,3],4)/(1-t^4);
PartialFractionDecomposition($1);
X-Qorb(4,[1,3],4)/(1-t^4);
PartialFractionDecomposition($1*(1-t)^4);
Denom([1,1,1,1,2]);
Nterm(4,1);
X-Qorb(4,[1,3],4)/(1-t^4)-2*Nterm(4,1);
A;
X-Qorb(4,[1,3],4)/(1-t^4)-2*Nterm(4,1);
n;
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
PC(A)[1];
X:=PC(A)[1];
b:=1; N:=2; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
b:=1; N:=3; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
PC(A)[2];
X:=PC(A)[2];
b:=0; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
X:=PC(A)[2];
b:=1; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
b:=1; N:=4; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
b:=1; N:=-3; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
b:=1; N:=-2; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
Nterm(3,1);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
X:=PC(A)[2];
b:=5; N:=-2; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
b:=5; N:=0; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
X:=PC(A)[1];
X-Qorb(4,[1,3],4)/(1-t^4)-2*Nterm(4,1);
X-Qorb(4,[1,3],4)/(1-t^4)-5*Nterm(4,1);
X-Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
SetLogFile("MagExperiments");
> n;
41
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 3, 3, 5, 15 ]
[
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 3, 3, 3, 5, 15 ]
[]
[
    [ 3, 1, 2 ]
]
[
    (5*t^5 + 5*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> b:=5; N:=0; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
5*t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
> b:=5; N:=5; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 4, 5, 15 ]
[
    [ 4, 1, 1, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 2, 5, 5, 15 ]
[
    [ 5, 1, 2, 2 ],
    [ 5, 1, 2, 2 ],
    [ 5, 1, 2, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 5, 5, 15 ]
[
    [ 5, 1, 1, 3 ],
    [ 5, 1, 1, 3 ],
    [ 5, 1, 1, 3 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 3, 6, 15 ]
[
    [ 6, 1, 2, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    0,
    (t^5 - t^4 + t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t + 
        1)
]
> b:=2; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
(4*t^5 + t^4 + 4*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t + 
    1)
> b:=3; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
(4*t^5 + 2*t^4 + 4*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t +
    1)
> b:=-1; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
(4*t^5 - 2*t^4 + 4*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t +
    1)
> b:=5; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
4*t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
> b:=5; N:=-3; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
8*t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
> b:=5; N:=5; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 4, 6, 15 ]
[
    [ 3, 1, 1, 1 ],
    [ 3, 1, 1, 1 ],
    [ 4, 1, 1, 2 ],
    [ 6, 1, 1, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 2, 3, 7, 15 ]
[
    [ 7, 2, 2, 3 ]
]
[
    [ 2, 1, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 3, 7, 15 ]
[
    [ 3, 1, 1, 1 ],
    [ 3, 1, 1, 1 ],
    [ 3, 1, 1, 1 ],
    [ 3, 1, 1, 1 ],
    [ 3, 1, 1, 1 ],
    [ 7, 1, 3, 3 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 2, 4, 7, 15 ]
[
    [ 4, 1, 1, 2 ],
    [ 7, 1, 2, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 1, 5, 7, 15 ]
[
    [ 7, 1, 1, 5 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 3, 3, 4, 4, 16 ]
[
    [ 4, 2, 3, 3 ],
    [ 4, 2, 3, 3 ],
    [ 4, 2, 3, 3 ],
    [ 4, 2, 3, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 2, 1 ]
]
[
    -4*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    (2*t^5 + t^4 + 2*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t
        + 1)
]
> X:=PC(A)[2];
> b:=1; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
> b:=1; N:=2; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 3, 4, 4, 4, 16 ]
[
    [ 3, 1, 1, 1 ]
]
[
    [ 4, 1, 3 ]
]
[
    (2*t^7 + 4*t^6 + 4*t^4 + 2*t^3)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 
        + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> X-4*Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
3*t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> X-4*Qorb(4,[1,3],4)/(1-t^4)+4*Nterm(4,1);
6*t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> X-4*Qorb(4,[1,3],4)/(1-t^4)-5*Nterm(4,1);
-3*t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> X-4*Qorb(4,[1,3],4)/(1-t^4)-3*Nterm(4,1);
-t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> X-4*Qorb(4,[1,3],4)/(1-t^4)-2*Nterm(4,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 3, 3, 4, 5, 16 ]
[
    [ 5, 3, 3, 4 ]
]
[
    [ 3, 1, 2 ]
]
[
    (3*t^5 + 2*t^4 + 3*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1)
]
> X:=PC(A)[1];
> b:=1; N:=2; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
> b:=1; N:=1; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
2*t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
> b:=1; N:=3; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 4, 4, 5, 16 ]
[
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 5, 2, 4, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 4, 5, 5, 16 ]
[]
[
    [ 5, 1, 4 ]
]
[
    (2*t^9 + 4*t^8 + 6*t^7 + 5*t^6 + 6*t^5 + 4*t^4 + 2*t^3)/(t^12 - 2*t^11 + 
        t^10 - 2*t^7 + 4*t^6 - 2*t^5 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> X-Qorb(5,[1,4],5)/(1-t^5)-0*Nterm(5,1);
(2*t^5 + 2*t^4 + 2*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> X-Qorb(5,[1,4],5)/(1-t^5)-1*Nterm(5,1);
(t^5 + t^4 + t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> X-Qorb(5,[1,4],5)/(1-t^5)-2*Nterm(5,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 4, 6, 16 ]
[
    [ 6, 1, 2, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 2, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 4, 4, 6, 16 ]
[
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 6, 1, 1, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    2*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 2, 3, 7, 16 ]
[
    [ 3, 2, 2, 2 ],
    [ 7, 2, 2, 3 ]
]
[
    [ 2, 1, 1 ]
]
[
    -8*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 3, 7, 16 ]
[
    [ 7, 1, 3, 3 ]
]
[
    [ 3, 2, 1 ]
]
[
    (2*t^5 + t^4 + 2*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t
        + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 2, 4, 7, 16 ]
[
    [ 7, 1, 2, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    -4*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 2, 5, 7, 16 ]
[
    [ 5, 1, 2, 2 ],
    [ 7, 1, 1, 5 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 2, 3, 8, 16 ]
[
    [ 3, 2, 2, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    -2*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 3, 8, 16 ]
[]
[
    [ 3, 1, 2 ]
]
[
    (4*t^5 + 3*t^4 + 4*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 2, 4, 8, 16 ]
[
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 1, 5, 8, 16 ]
[
    [ 5, 1, 1, 3 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 3, 3, 4, 5, 17 ]
[
    [ 4, 2, 3, 3 ],
    [ 5, 3, 3, 4 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    (-2*t^5 - 3*t^4 - 2*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 3, 5, 5, 17 ]
[
    [ 3, 2, 2, 2 ]
]
[
    [ 2, 1, 1 ],
    [ 5, 2, 3 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    (-5*t^9 - 2*t^8 - 6*t^7 - 8*t^6 - 6*t^5 - 2*t^4 - 5*t^3)/(t^12 - 2*t^11 + 
        t^10 - 2*t^7 + 4*t^6 - 2*t^5 + t^2 - 2*t + 1)
]
> X:=PC(A)[2];
> X-1*Qorb(5,[2,3],5)/(1-t^5);
(-5*t^5 + 3*t^4 - 5*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> Nterm(5,2);
(3*t^5 - 2*t^4 + 3*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> Nterm(5,1);
(t^5 + t^4 + t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> -2*Nterm(5,2)+Nterm(5,1);
(-5*t^5 + 5*t^4 - 5*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> -2*Nterm(5,2)-Nterm(5,1);
(-7*t^5 + 3*t^4 - 7*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> -3*Nterm(5,2)-Nterm(5,1);
(-10*t^5 + 5*t^4 - 10*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> -3*Nterm(5,2)-2*Nterm(5,1);
(-11*t^5 + 4*t^4 - 11*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> -3*Nterm(5,2)+2*Nterm(5,1);
(-7*t^5 + 8*t^4 - 7*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> -3*Nterm(5,2)+3*Nterm(5,1);
(-6*t^5 + 9*t^4 - 6*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> -8/5*Nterm(5,2)+1/5*Nterm(5,1);
(-23/5*t^5 + 17/5*t^4 - 23/5*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t
    + 1)
> -8/5*Nterm(5,2)-1/5*Nterm(5,1);
(-5*t^5 + 3*t^4 - 5*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 5, 6, 17 ]
[
    [ 5, 1, 1, 3 ],
    [ 6, 1, 2, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    0,
    -t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
]
> Nterm(3,1);
t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 3, 3, 7, 17 ]
[
    [ 7, 2, 2, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 2, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    (-3*t^5 - 4*t^4 - 3*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 4, 7, 17 ]
[
    [ 3, 1, 1, 1 ],
    [ 4, 2, 3, 3 ],
    [ 7, 1, 2, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 5, 7, 17 ]
[
    [ 3, 1, 1, 1 ],
    [ 5, 1, 1, 3 ],
    [ 7, 1, 1, 5 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 3, 8, 17 ]
[
    [ 8, 2, 3, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    2*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    (-t^5 - 2*t^4 - t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t 
        + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 4, 8, 17 ]
[
    [ 3, 1, 1, 1 ],
    [ 8, 1, 3, 4 ]
]
[
    [ 4, 1, 3 ]
]
[
    (2*t^7 + 3*t^6 + 3*t^5 + 3*t^4 + 2*t^3)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 
        - 2*t^4 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> X-Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
(3*t^5 + 5*t^4 + 3*t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> X-0*Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
(3*t^7 + 5*t^6 + 5*t^5 + 5*t^4 + 3*t^3)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 
    2*t^4 + t^2 - 2*t + 1)
> X-Qorb(4,[1,3],4)/(1-t^4)+2*Nterm(4,1);
(4*t^5 + 7*t^4 + 4*t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> Nterm(4,1);
t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> X-Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
(3*t^5 + 5*t^4 + 3*t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> Denom([1,1,2,2]);
t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1
> Denom([1,1,2,4]);
t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1
> 
> 
> 
> n:=n-5;
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 3, 3, 7, 17 ]
[
    [ 7, 2, 2, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 2, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    (-3*t^5 - 4*t^4 - 3*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 4, 7, 17 ]
[
    [ 3, 1, 1, 1 ],
    [ 4, 2, 3, 3 ],
    [ 7, 1, 2, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 5, 7, 17 ]
[
    [ 3, 1, 1, 1 ],
    [ 5, 1, 1, 3 ],
    [ 7, 1, 1, 5 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 3, 8, 17 ]
[
    [ 8, 2, 3, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    2*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    (-t^5 - 2*t^4 - t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t 
        + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 4, 8, 17 ]
[
    [ 3, 1, 1, 1 ],
    [ 8, 1, 3, 4 ]
]
[
    [ 4, 1, 3 ]
]
[
    (2*t^7 + 3*t^6 + 3*t^5 + 3*t^4 + 2*t^3)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 
        - 2*t^4 + t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 2, 5, 8, 17 ]
[
    [ 5, 1, 1, 3 ],
    [ 8, 1, 2, 5 ]
]
[
    [ 2, 1, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 3, 3, 5, 5, 18 ]
[
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ]
]
[
    [ 5, 2, 3 ]
]
[
    (4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3)/(t^12 - 2*t^11 + t^10 - 
        2*t^7 + 4*t^6 - 2*t^5 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> x := -t^3*((1-t^5) div (1-t))*(3-2*t+3*t^2);
> y := t^3*(1+t^2)*(1+t^2+t^4);
> X;
(4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3)/(t^12 - 2*t^11 + t^10 - 
    2*t^7 + 4*t^6 - 2*t^5 + t^2 - 2*t + 1)
> x+y;
-2*t^9 - t^8 - 2*t^7 - 4*t^6 - 2*t^5 - t^4 - 2*t^3
> x-2*y;
-5*t^9 - t^8 - 8*t^7 - 4*t^6 - 8*t^5 - t^4 - 5*t^3
> 2*x-y;
-7*t^9 - 2*t^8 - 10*t^7 - 8*t^6 - 10*t^5 - 2*t^4 - 7*t^3
> 
> x;
-3*t^9 - t^8 - 4*t^7 - 4*t^6 - 4*t^5 - t^4 - 3*t^3
> y;
t^9 + 2*t^7 + 2*t^5 + t^3
> x+6*y;
3*t^9 - t^8 + 8*t^7 - 4*t^6 + 8*t^5 - t^4 + 3*t^3
> x+7*y;
4*t^9 - t^8 + 10*t^7 - 4*t^6 + 10*t^5 - t^4 + 4*t^3
> X;
(4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3)/(t^12 - 2*t^11 + t^10 - 
    2*t^7 + 4*t^6 - 2*t^5 + t^2 - 2*t + 1)
> Denom([1,1,5,5]);
t^12 - 2*t^11 + t^10 - 2*t^7 + 4*t^6 - 2*t^5 + t^2 - 2*t + 1
> x+y;
-2*t^9 - t^8 - 2*t^7 - 4*t^6 - 2*t^5 - t^4 - 2*t^3
> -2*

> -2*x+y;
7*t^9 + 2*t^8 + 10*t^7 + 8*t^6 + 10*t^5 + 2*t^4 + 7*t^3
> -*x+y;

>> -*x+y;
    ^
User error: bad syntax
> -x+y;
4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3
> A;
[ 2, 3, 3, 5, 5, 18 ]
> Bask(A);
[
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ]
]
[
    [ 5, 2, 3 ]
]
> X:=PC(A)[1];
> X;
(4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3)/(t^12 - 2*t^11 + t^10 - 
    2*t^7 + 4*t^6 - 2*t^5 + t^2 - 2*t + 1)
> -2*x+y;
7*t^9 + 2*t^8 + 10*t^7 + 8*t^6 + 10*t^5 + 2*t^4 + 7*t^3
> -x+y;
4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 3, 3, 4, 6, 18 ]
[
    [ 4, 2, 3, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 2, 1 ]
]
[
    -2*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    -3*t^4/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t + 1)
]
> X:=PC(A)[2];
> b:=3; N:=0; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 3, 5, 6, 18 ]
[
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 5, 1, 2, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    -3*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 3, 3, 5, 6, 18 ]
[
    [ 5, 1, 1, 3 ]
]
[
    [ 3, 1, 2 ]
]
[
    (3*t^5 + 3*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> b:=3; N:=3; X-b*Qorb(3,[1,2],3)/(1-t^3)-N*Nterm(3,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 6, 6, 18 ]
[
    [ 6, 1, 2, 3 ],
    [ 6, 1, 2, 3 ],
    [ 6, 1, 2, 3 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    0,
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 4, 6, 6, 18 ]
[
    [ 4, 1, 1, 2 ],
    [ 6, 1, 1, 4 ],
    [ 6, 1, 1, 4 ],
    [ 6, 1, 1, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    2*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 3, 4, 7, 18 ]
[
    [ 4, 2, 3, 3 ],
    [ 7, 2, 2, 3 ]
]
[
    [ 2, 1, 1 ]
]
[
    -5*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 3, 3, 8, 18 ]
[
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ],
    [ 8, 2, 3, 3 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 2, 5, 8, 18 ]
[
    [ 5, 1, 2, 2 ],
    [ 8, 1, 2, 5 ]
]
[
    [ 2, 1, 1 ]
]
[
    -3*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 2, 6, 8, 18 ]
[
    [ 8, 1, 1, 6 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 2, 2, 3, 9, 18 ]
[
    [ 3, 2, 2, 2 ],
    [ 3, 2, 2, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    -9*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 3, 9, 18 ]
[]
[
    [ 3, 1, 2 ]
]
[
    (t^5 - t^4 + t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t + 
        1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 2, 4, 9, 18 ]
[
    [ 4, 1, 1, 2 ]
]
[
    [ 2, 1, 1 ]
]
[
    -4*t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 1, 6, 9, 18 ]
[
    [ 3, 1, 1, 1 ]
]
[]
[]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 3, 3, 4, 4, 5, 19 ]
[
    [ 5, 3, 3, 4 ]
]
[
    [ 3, 1, 2 ],
    [ 4, 3, 1 ]
]
[
    (3*t^5 + 2*t^4 + 3*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1),
    (-2*t^7 - 4*t^6 - 5*t^5 - 4*t^4 - 2*t^3)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5
        - 2*t^4 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> X-Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
(4*t^11 + 12*t^10 + 26*t^9 + 40*t^8 + 45*t^7 + 40*t^6 + 26*t^5 + 12*t^4 + 
    4*t^3)/(t^14 - 2*t^11 - 2*t^10 + t^8 + 4*t^7 + t^6 - 2*t^4 - 2*t^3 + 1)
> X:=PC(A)[2];
> X-Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
-t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> Nterm(4,1);
t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 3, 4, 5, 6, 19 ]
[
    [ 4, 1, 1, 2 ],
    [ 5, 1, 1, 3 ],
    [ 6, 3, 4, 5 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    0,
    (2*t^5 + t^4 + 2*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t
        + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 4, 5, 7, 19 ]
[
    [ 4, 1, 1, 2 ],
    [ 5, 1, 2, 2 ],
    [ 7, 1, 2, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 3, 3, 4, 8, 19 ]
[
    [ 8, 1, 3, 4 ]
]
[
    [ 3, 1, 2 ],
    [ 4, 1, 3 ]
]
[
    (4*t^5 + 3*t^4 + 4*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1),
    (-t^6 - t^5 - t^4)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t +
        1)
]
> X:=PC(A)[2];
> X-0*Qorb(4,[1,3],4)/(1-t^4)+1*Nterm(4,1);
(t^7 + t^6 + t^5 + t^4 + t^3)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 
    - 2*t + 1)
> X;
(-t^6 - t^5 - t^4)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
> Denom([1,1,4,4]);
t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1
> Qorb(4,[1,3],4)/(1-t^4);
-t^5/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
> X;
(-t^6 - t^5 - t^4)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
> X-Qorb(4,[1,3],4)/(1-t^4)+0*Nterm(4,1);
-t^4/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> Nterm(4,1);
t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> X-2*Qorb(4,[1,3],4)/(1-t^4)+0*Nterm(4,1);
(-t^6 + t^5 - t^4)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
> X-3*Qorb(4,[1,3],4)/(1-t^4)+0*Nterm(4,1);
-t^4/(t^8 - 2*t^4 + 1)
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 6, 8, 19 ]
[
    [ 6, 1, 2, 3 ],
    [ 8, 1, 1, 6 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1),
    2*t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 3, 4, 9, 19 ]
[
    [ 4, 1, 1, 2 ],
    [ 9, 2, 3, 4 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 2, 1 ]
]
[
    0,
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 2, 2, 5, 9, 19 ]
[
    [ 5, 1, 2, 2 ],
    [ 9, 2, 2, 5 ]
]
[
    [ 2, 1, 1 ]
]
[
    -t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 5, 9, 19 ]
[
    [ 5, 1, 1, 3 ],
    [ 9, 1, 3, 5 ]
]
[
    [ 3, 1, 2 ]
]
[
    2*t^3/(t^6 - 3*t^5 + 3*t^4 - 2*t^3 + 3*t^2 - 3*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 1, 1, 2, 6, 9, 19 ]
[
    [ 6, 1, 2, 3 ],
    [ 9, 1, 2, 6 ]
]
[
    [ 2, 1, 1 ],
    [ 3, 1, 2 ]
]
[
    0,
    t^4/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 3, 4, 4, 4, 5, 20 ]
[
    [ 3, 1, 1, 1 ]
]
[
    [ 4, 3, 1 ]
]
[
    -5*t^5/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> X-5*Qorb(4,[1,3],4)/(1-t^4)+0*Nterm(4,1);
0
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 3, 3, 4, 5, 5, 20 ]
[
    [ 5, 3, 3, 4 ],
    [ 5, 3, 3, 4 ],
    [ 5, 3, 3, 4 ],
    [ 5, 3, 3, 4 ]
]
[
    [ 3, 1, 2 ]
]
[
    (-2*t^5 - 3*t^4 - 2*t^3)/(t^8 - 2*t^7 + t^6 - 2*t^5 + 4*t^4 - 2*t^3 + t^2 - 
        2*t + 1)
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 4, 4, 5, 5, 20 ]
[
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 4, 1, 1, 2 ],
    [ 5, 2, 4, 4 ],
    [ 5, 2, 4, 4 ],
    [ 5, 2, 4, 4 ],
    [ 5, 2, 4, 4 ]
]
[
    [ 2, 1, 1 ]
]
[
    0
]
> n:=n+1; A:=BB[n]; A; Bask(A); PC(A);
[ 2, 3, 5, 5, 5, 20 ]
[
    [ 3, 2, 2, 2 ]
]
[
    [ 5, 2, 3 ]
]
[
    (-2*t^9 - 2*t^8 - 8*t^6 - 2*t^4 - 2*t^3)/(t^12 - 2*t^11 + t^10 - 2*t^7 + 
        4*t^6 - 2*t^5 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> X-4*Qorb(5,[2,3],5)/(1-t^5);
(-2*t^5 - 2*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> Nterm(5,2);
(3*t^5 - 2*t^4 + 3*t^3)/(t^8 - 3*t^7 + 3*t^6 - t^5 - t^3 + 3*t^2 - 3*t + 1)
> Qorb(8,[1,3,4]);

>> Qorb(8,[1,3,4]);
       ^
Runtime error in procedure call: Number of arguments (2) does not equal expected
number of arguments (3)
> Qorb(8,[1,3,4],0);
(t^8 - t^7 + t^6)/(t^14 - 2*t^13 + t^12 - t^10 + 2*t^9 - t^8 - t^6 + 2*t^5 - t^4
    + t^2 - 2*t + 1)
> PartialFractionDecomposition($1*(1-t)^4);
[
    <t + 1, 1, -9/8>,
    <t + 1, 2, 3/8>,
    <t^2 + 1, 1, 3/8*t - 1/2>,
    <t^2 + 1, 2, 1/4>,
    <t^4 + 1, 1, 3/4*t^3 - 3/4*t + 1>
]
> (3/4*t^3 - 3/4*t + 1)/(1+t^4);
(3/4*t^3 - 3/4*t + 1)/(t^4 + 1)
> S!$1;
1 - 3/4*s + 3/4*s^3 - s^4 + 3/4*s^5 - 3/4*s^7 + s^8 - 3/4*s^9 + 3/4*s^11 - s^12 
    + 3/4*s^13 - 3/4*s^15 + s^16 - 3/4*s^17 + 3/4*s^19 - s^20 + 3/4*s^21 - 
    3/4*s^23 + s^24 - 3/4*s^25 + 3/4*s^27 - s^28 + 3/4*s^29 - 3/4*s^31 + s^32 - 
    3/4*s^33 + 3/4*s^35 - s^36 + 3/4*s^37 - 3/4*s^39 + s^40 - 3/4*s^41 + 
    3/4*s^43 - s^44 + 3/4*s^45 - 3/4*s^47 + s^48 - 3/4*s^49 + O(s^50)
> (3/4*t^3 - 3/4*t + 1)/(1+t^4)-1/(1-t)^4;
(3/4*t^7 - 3*t^6 + 15/4*t^5 - 31/4*t^3 + 9*t^2 - 19/4*t)/(t^8 - 4*t^7 + 6*t^6 - 
    4*t^5 + 2*t^4 - 4*t^3 + 6*t^2 - 4*t + 1)
> (3/4*t^3 - 3/4*t + 1)/(1+t^4)+(19*t-1)/(1-t)^4;
(3/4*t^7 - 3*t^6 + 91/4*t^5 - 31/4*t^3 + 9*t^2 + 57/4*t)/(t^8 - 4*t^7 + 6*t^6 - 
    4*t^5 + 2*t^4 - 4*t^3 + 6*t^2 - 4*t + 1)
> (3/4*t^3 - 3/4*t + 1)/(1+t^4)+(19/4*t-1)/(1-t)^4;
(3/4*t^7 - 3*t^6 + 17/2*t^5 - 31/4*t^3 + 9*t^2)/(t^8 - 4*t^7 + 6*t^6 - 4*t^5 + 
    2*t^4 - 4*t^3 + 6*t^2 - 4*t + 1)
> (3/4*t^3 - 3/4*t + 1)/(1+t^4)+(-9*t^2+19/4*t-1)/(1-t)^4;
(3/4*t^7 - 12*t^6 + 17/2*t^5 - 31/4*t^3)/(t^8 - 4*t^7 + 6*t^6 - 4*t^5 + 2*t^4 - 
    4*t^3 + 6*t^2 - 4*t + 1)
> (3/4*t^3 - 3/4*t + 1)/(1+t^4)+(+31/4*t^3-9*t^2+19/4*t-1)/(1-t)^4;
(17/2*t^7 - 12*t^6 + 17/2*t^5)/(t^8 - 4*t^7 + 6*t^6 - 4*t^5 + 2*t^4 - 4*t^3 + 
    6*t^2 - 4*t + 1)
> (3/4*t^3 - 3/4*t + 1)/(1+t^4)+(-17/2*t^5+31/4*t^3-9*t^2+19/4*t-1)/(1-t)^4;
(-17/2*t^9 + 17/2*t^7 - 12*t^6)/(t^8 - 4*t^7 + 6*t^6 - 4*t^5 + 2*t^4 - 4*t^3 + 
    6*t^2 - 4*t + 1)
> Qorb(8,[1,3,4],0);
(t^8 - t^7 + t^6)/(t^14 - 2*t^13 + t^12 - t^10 + 2*t^9 - t^8 - t^6 + 2*t^5 - t^4
    + t^2 - 2*t + 1)
> PartialFractionDecomposition($1*(1-t)^4);
[
    <t + 1, 1, -9/8>,
    <t + 1, 2, 3/8>,
    <t^2 + 1, 1, 3/8*t - 1/2>,
    <t^2 + 1, 2, 1/4>,
    <t^4 + 1, 1, 3/4*t^3 - 3/4*t + 1>
]
> X := Qorb(8,[1,3,4],0);
> PartialFractionDecomposition(X*(1-t)^4);
[
    <t + 1, 1, -9/8>,
    <t + 1, 2, 3/8>,
    <t^2 + 1, 1, 3/8*t - 1/2>,
    <t^2 + 1, 2, 1/4>,
    <t^4 + 1, 1, 3/4*t^3 - 3/4*t + 1>
]
> PartialFractionDecomposition(X*Denom([1,1,2,4]));
[
    <1, 1, t^2 - t>,
    <t^2 + 1, 1, 1/2*t>,
    <t^4 + 1, 1, 1/2*t^3 - t^2 + 1/2*t>
]
> (1/2*t^3 - t^2 + 1/2*t)/(1+t^4) + 1/2*t/(1+t^2);
(t^5 - t^4 + t^3 - t^2 + t)/(t^6 + t^4 + t^2 + 1)
> X*Denom([1,1,2,4])-$1;
t^2 - t
> (1/2*t^3 - t^2 + 1/2*t)/(1+t^4) + 1/2*t/(1+t^2);
(t^5 - t^4 + t^3 - t^2 + t)/(t^6 + t^4 + t^2 + 1)
> X-$1/Denom([1,1,2,4]);
t/(t^7 - t^6 - t^5 + t^4 - t^3 + t^2 + t - 1)
> $1/(1+t);
t/(t^8 - 2*t^6 + 2*t^2 - 1)
> X := Qorb(8,[1,3,4],0);
> (1/2*t^3 - t^2 + 1/2*t)/(1+t^4) + 1/2*t/(1+t^2);
(t^5 - t^4 + t^3 - t^2 + t)/(t^6 + t^4 + t^2 + 1)
> 
> 
> 
> X;
(t^8 - t^7 + t^6)/(t^14 - 2*t^13 + t^12 - t^10 + 2*t^9 - t^8 - t^6 + 2*t^5 - t^4
    + t^2 - 2*t + 1)
> Denom([1,1,2,4,8]);
-t^16 + 2*t^15 - 2*t^13 + 2*t^12 - 2*t^11 + 2*t^9 - 2*t^7 + 2*t^5 - 2*t^4 + 
    2*t^3 - 2*t + 1
> Denom([1,1,4,8]);
t^14 - 2*t^13 + t^12 - t^10 + 2*t^9 - t^8 - t^6 + 2*t^5 - t^4 + t^2 - 2*t + 1
> PartialFractionDecomposition(X*Denom([1,1,1,1]));
[
    <t + 1, 1, -9/8>,
    <t + 1, 2, 3/8>,
    <t^2 + 1, 1, 3/8*t - 1/2>,
    <t^2 + 1, 2, 1/4>,
    <t^4 + 1, 1, 3/4*t^3 - 3/4*t + 1>
]
> $1[5,3]/$1[5,1]
> ;
(3/4*t^3 - 3/4*t + 1)/(t^4 + 1)
> $1*(1-t^8);
-3/4*t^7 + 3/4*t^5 - t^4 + 3/4*t^3 - 3/4*t + 1
> X;
(t^8 - t^7 + t^6)/(t^14 - 2*t^13 + t^12 - t^10 + 2*t^9 - t^8 - t^6 + 2*t^5 - t^4
    + t^2 - 2*t + 1)
> Denom([1,1,1,8]);
t^11 - 3*t^10 + 3*t^9 - t^8 - t^3 + 3*t^2 - 3*t + 1
> Qorb(4,[1,3],4)/(1-t^4);
-t^5/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <t + 1, 1, -3/4>,
    <t + 1, 2, 1/4>,
    <t^2 + 1, 1, -1/4*t + 1>,
    <t^2 + 1, 2, -1/2>
]
> BB8 := [A : A in BB | 8 in A];
> BB8134 := [A : A in BB8 | [8,1,3,4] in Bask(A)];
> #BB8134;
164
> n:=0;
> n:=n+1; A:=BB8134[n]; A; Bask(A); PC(A);
[ 1, 1, 3, 4, 8, 17 ]
[
    [ 3, 1, 1, 1 ],
    [ 8, 1, 3, 4 ]
]
[
    [ 4, 1, 3 ]
]
[
    (2*t^7 + 3*t^6 + 3*t^5 + 3*t^4 + 2*t^3)/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 
        - 2*t^4 + t^2 - 2*t + 1)
]
> X:=PC(A)[1];
> PartialFractionDecomposition(X*Denom([1,1,1,1]));
[
    <1, 1, 2*t - 1>,
    <t + 1, 1, 3/4>,
    <t + 1, 2, -1/4>,
    <t^2 + 1, 1, -7/4*t + 1>,
    <t^2 + 1, 2, -1/2>
]
> Qorb(4,[1,3],4)/(1-t^4);
-t^5/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
> PartialFractionDecomposition(X*Denom([1,1,1,1]));
[
    <1, 1, 2*t - 1>,
    <t + 1, 1, 3/4>,
    <t + 1, 2, -1/4>,
    <t^2 + 1, 1, -7/4*t + 1>,
    <t^2 + 1, 2, -1/2>
]
> Qorb(4,[1,3],4)/(1-t^4);
-t^5/(t^10 - 2*t^9 + t^8 - 2*t^6 + 4*t^5 - 2*t^4 + t^2 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <t + 1, 1, -3/4>,
    <t + 1, 2, 1/4>,
    <t^2 + 1, 1, -1/4*t + 1>,
    <t^2 + 1, 2, -1/2>
]
> X-Qorb(4,[1,3],4)/(1-t^4);
(2*t^5 + 3*t^4 + 2*t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <1, 1, 2*t - 1>,
    <t + 1, 1, 3/2>,
    <t + 1, 2, -1/2>,
    <t^2 + 1, 1, -3/2*t>
]
> Qorb(2,[1,1],2)/(1-t^4);
-t^3/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <t + 1, 1, -1>,
    <t + 1, 2, 1/2>,
    <t^2 + 1, 1, 1/2>
]
> X-Qorb(4,[1,3],4)/(1-t^4)-Qorb(2,[1,1],2)/(1-t^4);;
(2*t^5 + 3*t^4 + 3*t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> X-Qorb(4,[1,3],4)/(1-t^4)+Qorb(2,[1,1],2)/(1-t^4);;
(2*t^4 + t^3)/(t^7 - 3*t^6 + 3*t^5 - t^4 - t^3 + 3*t^2 - 3*t + 1)
> X-Qorb(4,[1,3],4)/(1-t^4)+Qorb(2,[1,1],2)/(1-t^2);;
(t^5 + 3*t^4 + t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> X-Qorb(4,[1,3],4)/(1-t^4);
(2*t^5 + 3*t^4 + 2*t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <1, 1, 2*t - 1>,
    <t + 1, 1, 3/2>,
    <t + 1, 2, -1/2>,
    <t^2 + 1, 1, -3/2*t>
]
> Qorb(2,[1,1],2)/(1-t^4);
-t^3/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <t + 1, 1, -1>,
    <t + 1, 2, 1/2>,
    <t^2 + 1, 1, 1/2>
]
> X-Qorb(4,[1,3],4)/(1-t^4)+Qorb(2,[1,1],2)/(1-t^2);
(t^5 + 3*t^4 + t^3)/(t^8 - 2*t^7 + 2*t^5 - 2*t^4 + 2*t^3 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <1, 1, t + 1>,
    <t + 1, 1, -3/2>,
    <t + 1, 2, 1/2>,
    <t^2 + 1, 1, -3/2*t>
]
> Qorb(2,[1,1],2)/(1-t^2);
-t^3/(t^6 - 2*t^5 - t^4 + 4*t^3 - t^2 - 2*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <1, 1, -t + 2>,
    <t + 1, 1, -3>,
    <t + 1, 2, 1>
]
> X-Qorb(4,[1,3],4)/(1-t^4)+1/2*Qorb(2,[1,1],2)/(1-t^2);
3/2*t^3/(t^6 - 4*t^5 + 7*t^4 - 8*t^3 + 7*t^2 - 4*t + 1)
> PartialFractionDecomposition($1*Denom([1,1,1,1]));
[
    <1, 1, 3/2*t>,
    <t^2 + 1, 1, -3/2*t>
]
> 
> .

Total time: 10.679 seconds, Total memory usage: 8.72MB