# Singular

##### 7.7.7.0. ivMis2Base
Procedure from library `fpadim.lib` (see fpadim_lib).

Usage:
ivMis2Base(M); M a list of intvecs

Return:
ideal, a K-base of the given algebra

Purpose:
Computing the K-base out of given mistletoes

Assume:
- The mistletoes have to be ordered lexicographically -> OrdMisLex.
Otherwise there might some elements missing.
- basering is a Letterplace ring.
- mistletoes are stored as intvecs, as described in the overview

Example:
 ```LIB "fpadim.lib"; ring r = 0,(x,y),dp; def R = makeLetterplaceRing(5); // constructs a Letterplace ring R; ==> // coefficients: QQ ==> // number of vars : 10 ==> // block 1 : ordering a ==> // : names x(1) y(1) x(2) y(2) x(3) y(3) x(4) y(4) x(\ 5) y(5) ==> // : weights 1 1 1 1 1 1 1 1 \ 1 1 ==> // block 2 : ordering dp ==> // : names x(1) y(1) ==> // block 3 : ordering dp ==> // : names x(2) y(2) ==> // block 4 : ordering dp ==> // : names x(3) y(3) ==> // block 5 : ordering dp ==> // : names x(4) y(4) ==> // block 6 : ordering dp ==> // : names x(5) y(5) ==> // block 7 : ordering C setring R; // sets basering to Letterplace ring intvec i1 = 1,2; intvec i2 = 2,1,2; // the mistletoes are xy and yxy, which are already ordered lexicographically list L = i1,i2; ivMis2Base(L); // returns the basis of the factor algebra ==> [1]: ==> 2 ==> [2]: ==> 2,1 ==> [3]: ==> 2,1,2 ==> [4]: ==> 1 ==> [5]: ==> 1,2 ==> [6]: ==> 0 ```