   : intersection : Macros in libraries : integral-k1

## integration

``` [[f1 f2 ...] [t1 t2 ...] [vars params] [k0 k1 limitdeg ]] integration
[ 0-th cohomology group,  (-1)-th cohomology group, .... ]

[[f1 f2 ...] [t1 t2 ...] [vars params] limitdeg] integration

Integration of the D-ideal [f1 f2 ...] to t1=0, t2=0, ... is computed.
vars is a list of the variables and params is a list of parameters.
k0 is the minimum integral root of the b-function and k1 is the maximum
integral root of the b-function. If these values are not given and
they are small, then they are automatically computed. The program returns
0-th, ..., -limitdeg-th cohomology groups.
[vars params] and [k0 k1 deg] are optional arguments.
If vars and params are not given, the values of the global variables
BFvarlist and BFparlist will be used.
The operator restriciton will be used after the laplace transformation.

For the algorithm, see math.AG/9805006, http://xxx.langl.gov

Example 1:
[[(x (x-1)) (x) ] annfs 0 get       [(x)] [[(x)] [ ]]] integration ::
Example 2:
[ [(Dt - (3 t^2-x)) (Dx + t)] [(t)]      [[(t) (x)] [ ]] 0] integration ::
Example 3:
[ [[(Dt - (3 t^2-x)) (0)] [ (Dx + t) (0)]] [(t)]      [[(t) (x)] [ ]] 0] integration ::
In case of vector input, INTEGRAL VARIABLES MUST APPEAR FIRST
in the list of variable. We are using wbfRoots to get the roots of
b-functions, so we can use only generic weight vector for now.
```

Nobuki Takayama 平成17年2月10日