misc.at

is_nonnegative

test if an integer is even, or a rational is an integer

also in this file at line 9

is_positive 2 overloads

test if a ratvec is in fact a vec (integers)

also defined in coherent_irreducible.at

is_nonnegative

also in this file at line 4

%

transform ParamPol into a list of (Split,Param) pairs; previously built-in

also defined in basic.at, extParamPol.at, polynomial.at

int_part

int_part and s_part of a ParamPol, s.t. P=int_part(P)+s*s_part(P)

also defined in basic.at, K_types.at

s_part

also defined in basic.at, K_types.at

param

simpler syntax for param command: param(G,3,...) for param(KGB(G,3),...)

finalize

replace non-final parameter with ParamPol
this function used to return a [Param] instead, with coefficients ignored

also in this file at line 29

Finalize

finalize

will fail on an empty list

also in this file at line 24

# 3 overloads

evaluate at s=t for t integer (or rational?): replace w=a+bs with a+bt

would seem to make sense only if t^2=1, so if either t=1 or t=-1

with integer coefficients

also defined in basic.at, W_reps.at, cells.at

fiber_partition

ss_rank

also defined in affine.at

root_length

is_simple_root

simple_imaginary_subsystem

simple (co)roots

simple_real_subsystem

simple (co)roots

to_binary

generate_all_binary

generate_all_subsets 3 overloads

generate all subsets of a set of integers

generate all subsets of a set of vectors

all 2^n subsets of a set of rational vectors

is_proper_subset

A is a proper subset of B

also defined in parameters.at

complement

complement of A in B

also defined in basic.at, parameters.at

prettyPrint 2 overloads

nicer display of Splits

nice output of ParamPol:
prettyPrint the coefficients, print terms in order of x

box 2 overloads

Cartesian power (#height)^rank, lists of length rank of numbers <height

converted from [vec] to [[int]]

Cartesian product (#heights[0])*(#heights[1])*...*(heights~[0])

converted

flatten

delete_trailing_zeros

delete trailing zeros, a.k.a. |strip_to_partition| from combinatorics.at

delete_leading_zeros

not_a_root 2 overloads

for logical convenience

all_root_index 2 overloads

index of root in list of all roots

also defined in tits_centralizer.at

simple_root_index 2 overloads

index of root in list of simple roots

pm_simple_root_index 2 overloads

return 0...n-1=simple root index of alpha (if positive simple) or -alpha (if negative simple)
or -1 to indicate an error

sgn 2 overloads

sgn(alpha)alpha is positive

also defined in Weylgroup.at

height 2 overloads

alpha>0: height(alpha)=sum of coefficients of simple roots
alpha<0: height(alpha)=height(-alpha)(

also defined in basic.at

roots_of_height

list roots of given height

max_height

also defined in basic.at

roots_by_height

all roots, sorted by height

root_string 2 overloads

return (p,q) where
alpha+p\beta is a root (maximal such p)
alpha-q\beta is a root (maximal such q)

set root_string(RootDatum rd, vec alpha, vec beta)=(int,int):
assert(not alpha=-beta,"alpha=-beta");
let x = first(for i:4 do  not is_root(rd,alpha+i*beta) od) then
y = first(for i:4 do not  is_root(rd,alpha-i*beta) od) in (x-1,y-1)

posroot_as_sum_of_simple

write a positive root as a sum of simple roots

root_as_sum_of_simple

write any root as sum of simple or sum of (-simple)

simple_root_summand

alpha>0: return alpha_1  (alpha_1 simple) so alpha= alpha_1+(other simple roots...)
alpha<0: return -alpha_1 (alpha_1 simple) so alpha=-alpha_1-(other simple roots...)