Script File

`GK_dimension.at`

Source

atlas-scripts/GK_dimension.at (70 lines)

Definitions

Loads

<basic.at
<tensor_product.at { |dimension@ParamPol| }

Loaded by

none of the other all.at files

Definitions in source order

`dim_K_types_std_upto`

L6dim_K_types_std_upto (Param p, int n) = int

largest k so that b^k<=n

sum of dimensions of K-types up to given height

`truncate`

L9truncate (ParamPol P, int n) = ParamPol

terms of ParamPol of height <=n (with multiplicity)

also defined in truncated_induction.at

`slice`

L14slice (ParamPol P, int n)

terms of ParamPol of height =n (with multiplicity)

estimating GK dimension of module X
X_n=K-types of height <=n

L18

dim(X_n)= cn^d  d=GK-dimension
dim(X_2^n)= c2^dn
dim(X_2^(n-1))= c2^d(n-1)
dim(X_2^n)/ dim(X_(2^(n-1))
dim(X_2^n)/X_x^(n-1))= c2^dn/c2^d(n-1)=2^d
d=log_2(dim(X_2^n)/X_2^(n-1))

L20

`rounded_log_2`

L29rounded_log_2 (rat r) = int

`sort_K_types_by_log_2_height`

L35sort_K_types_by_log_2_height (KTypePol P, int exp) = [KTypePol]

separate terms of |P| coarsely by height

`growth`

L44growth ([KTypePol] list) = [int]

estimate GK dimension
list[k]: KTypePol all terms with rounded_log_2(height)=k
estimate: log_2(dim(list[k+1])/dim(list[k])

`growth_std`

L65growth_std (Param p, int n) = [int]

estimate growth of standard module up to height 2^n

`growth_irr`

L69growth_irr (Param p, int n) = [int]

estimate growth of irreducible module up to height 2^n

Generated from atlas-scripts at commit 7e1b958 (2026-09-17).