: integration : Macros in libraries : gkz

## integral-k1

```[[f1 ... fm] [v1 ... vn] [v1 w1 ... vp wp] k1] integral0
[[g1 ... gq],[e1,...,er]]
poly|string f1 ...fm; string v1 ... vn;
string v1 ... vp; integer w1 ... wp;
integer k1;
poly g1 ... gq; poly e1, ..., er;
f1 ... fm are annihilors, v1 ... vn are variables,
w1 is the weight of the variable v1, ...
k1 is the maximal degree of the filtration: maximal integral root
of b-function. cf. intwbf
g1, ..., gq are integral. e1, ..., er are basis of the free module to which
the g1, ..., gq belong.
THE ORDERS OF INTEGRAL VARIABLES MUST BE SAME BOTH IN THE SECOND AND
THE THIRD ARGUMENTS. INTEGRAL VARIABLES MUST APPEAR FIRST.
Example 1: [[(x-y) (Dx+Dy)] [(y) (x)] [(y) -1 (Dy) 1] 1] integral-k1
Example 2: [[(x (x-1)) (x)] annfs 0 get [(x)] [(x) -1 (Dx) 1] 1] integral-k1
Example 3: [[ (Dt- (2 t x1 + x2)) (Dx1 - t^2) (Dx2 - t) ]
[(t) (x1) (x2)] [(t) -1 (Dt) 1] 0] integral-k1
The resulting ideal annihilates f(x1,x2)=int(x1*t^2+x2*t,dt)
```

Nobuki Takayama 平成22年2月8日