type Lp
- implementing the Lp-grading group
SYNOPSIS:
Given a weight sequence (p
1
,..,p
t
), the Lp-group is the rank one abelian group generated by x
1
,..,x
t
subject to the relations
p
1
x
1
= p
2
x
2
= ... = p
t
x
t
=: c .
c is called the "canonical element" in Lp.
Each element x in Lp has a unique presentation in "normal form":
x=l
1
x
1
+ ... +l
t
x
t
+l
c
,
with integers l
1
,..,l
t
,l such that 0<=l
i
<p
i
.
These elements are encoded as lists with t+1 entries: [l
1
,..,l
t
,l] . They need not be entered in normal form; so when entering such an element you are allowed to enter a list consisting of t+1 arbitrary integers.
So, for instance, if the weight sequence entered is (2,3,5), then [1,-1,8,2] would encode the element x
1
- x
2
+ 8 x
3
+ 2 c . Note, however, that even if you wish to enter an element where you specify only the multiplicities of the generators - for instance 2 x
1
- 7 x
2
+ 14 x
3
- you have to key in a list of t+1 (in our example t+1=4) integers, then setting the t+1 entry to 0 (so [2,-7,14,0] for our example; not(!) [2,-7,14]).
The command "NF" computes the normal form corresponding to this element. - All operations defined on Lp (cf. to
tubular/Lp
for a complete list of these) return their results in normal form.
SEE ALSO:
tubular/Lp
,
Lp_shift
BACK TO:
start page of the crep online manual
,
tubular