FUNCTION: wp - test a unit form for weak positivity

CALLING SEQUENCE:
wp(q)
wp(q,rt)
wp(q,rt,r)

PARAMETERS:
q - a unit form
rt - an optional parameter evaluating to a name
r - an optional parameter evaluating to 'a' or 'A'

SYNOPSIS:

• wp uses a program and algorithm of Hans von Hoehne to test, whether the unit form q given as first argument is weakly positive.

• In case, the function is called with excatly one argument (wich then has to be the unit form q), wp will return the value 'false' if q is not weakly positive, and, if q is weakly positive, will return a pair [s,t] of non-negative integers, s being the number of all positive 1-roots of q, t the number of all sincere 1-roots.

• In case the function is called with more then one argument, it will return the value 'true' if its first argument, the unit form q is weakly positive and the value 'false' otherwise.

• In case the unit form q is weakly positive and a second argument rt is given this argument will be used to return a table of positive 1-roots of the unit form q. If no third argument r is given, or if the third argument r evalutes to 'A', this table will consist of all sincere positive 1-roots of q. If the argument r evalutes to 'a', rt will be assigend a list of all positive 1-roots of q.

EXAMPLES:

> a:=[4,[[1,2,3,4]]];

> q:=titsform(a);

> wp(q);

> wp(q,'rt');

> print(rt);

> wp(q,'rt','a');

> print(rt);

> wp(q,'rt','A');

> print(rt);