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meataxe: simplify ngens / orig_ngens handling
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@fingolfin
fingolfin committed Nov 9, 2024
1 parent 08ae33c commit e87a79f
Showing 1 changed file with 42 additions and 80 deletions.
122 changes: 42 additions & 80 deletions lib/meataxe.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -390,18 +390,14 @@ end );
## It is returned as a list of normed vectors.
## If the optional third argument is present, then only the first ngens
## matrices in the list are used.
SMTX.SpinnedBasis:=function( arg )
local v, matrices, ngens, zero,ldim,step,
ans, dim, subdim, leadpos, w, i, j, k, l, m,F;
SMTX.SpinnedBasis:=function( v, matrices, F, ngens... )
local zero, ldim, step, ans, dim, subdim, leadpos, w, i, j, k, l, m;

if Length(arg) < 3 or Length(arg) > 4 then
if Length(ngens) > 1 then
Error("Usage: SpinnedBasis( v, matrices, F, [ngens] )");
fi;
v:=arg[1];
matrices:=arg[2];
F:=arg[3];
if Length(arg) = 4 then
ngens:=arg[4];
if Length(ngens) = 1 then
ngens:=ngens[1];

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if ngens <= 0 or ngens > Length(matrices) then
ngens:=Length(matrices);
fi;
Expand Down Expand Up @@ -449,7 +445,6 @@ SMTX.SpinnedBasis:=function( arg )
# apply generator m to submodule generator i
w:=ShallowCopy(ans[i] * m);
# try to express w in terms of existing submodule generators
j:=1;
for j in [1..subdim] do
k:=w[leadpos[j]];
if k <> zero then
Expand Down Expand Up @@ -965,7 +960,7 @@ SMTX.RAND_ELM_LIMIT:=5000;
## is not an end-user function but only called internally
SMTX.IrreducibilityTest:=function( module )
local matrices, tmatrices, ngens, ans, M, mat, g1, g2, maxdeg,
newgenlist, coefflist, orig_ngens, zero,
newgenlist, coefflist, zero,
N, NT, v, subbasis, fac, sfac, pol, orig_pol, q, dim, ndim, i,
l, trying, deg, facno, bestfacno, F, count, R, rt0,idmat,
pfac1, pfac2, quotRem, pfr, idemp, M2, mat2, mat3;
Expand All @@ -981,8 +976,7 @@ SMTX.IrreducibilityTest:=function( module )
fi;
matrices:=ShallowCopy(module.generators);
dim:=SMTX.Dimension(module);
ngens:=Length(matrices);
orig_ngens:=ngens;
ngens:=Length(module.generators);
F:=SMTX.Field(module);
zero:=Zero(F);
R:=PolynomialRing(F);
Expand Down Expand Up @@ -1099,7 +1093,7 @@ SMTX.IrreducibilityTest:=function( module )

Info(InfoMeatAxe,5,"Evaluated nullspace. Dimension = ",
ndim,". Time = ",Runtime()-rt0,".");
subbasis:=SMTX.SpinnedBasis(v, matrices, F,orig_ngens);
subbasis:=SMTX.SpinnedBasis(v, module.generators, F);
Info(InfoMeatAxe,5,"Spun up vector. Dimension = ",
Length(subbasis),". Time = ",Runtime()-rt0,".");
if Length(subbasis) < dim then
Expand All @@ -1113,16 +1107,14 @@ SMTX.IrreducibilityTest:=function( module )
# module is definitely irreducible.
mat:=TransposedMat(mat);
if Length(tmatrices)=0 then
for i in [1..orig_ngens] do
Add(tmatrices, TransposedMat(matrices[i]));
od;
tmatrices := List(module.generators, TransposedMat);
fi;
Info(InfoMeatAxe,5,"Transposed matrices. Time = ",
Runtime()-rt0,".");
NT:=NullspaceMat(mat);
Info(InfoMeatAxe,5,"Evaluated nullspace. Dimension = ",
Length(NT),". Time = ",Runtime()-rt0, ".");
subbasis:=SMTX.SpinnedBasis(NT[1],tmatrices,F,orig_ngens);
subbasis:=SMTX.SpinnedBasis(NT[1],tmatrices,F);
Info(InfoMeatAxe,5,"Spun up vector. Dimension = ",
Length(subbasis),". Time = ",Runtime()-rt0, ".");
if Length(subbasis) < dim then
Expand All @@ -1134,7 +1126,7 @@ SMTX.IrreducibilityTest:=function( module )
# that way, but we'll certainly get a proper submodule.
v:=SMTX.OrthogonalVector(subbasis);
SMTX.SetSubbasis(module,
SMTX.SpinnedBasis(v,matrices,F,orig_ngens));
SMTX.SpinnedBasis(v,module.generators,F));

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ans:=false;
else
ans:=true;
Expand Down Expand Up @@ -1179,7 +1171,7 @@ SMTX.IrreducibilityTest:=function( module )
mat3:=mat2*M2*mat2;
v:=v*(M*mat3 - mat3*M);
# This vector might lie in a proper subspace!
subbasis:=SMTX.SpinnedBasis(v, matrices, F,orig_ngens);
subbasis:=SMTX.SpinnedBasis(v, module.generators, F);
Info(InfoMeatAxe,5,"Spun up vector. Dimension = ",
Length(subbasis),". Time = ",Runtime()-rt0,".");
if Length(subbasis) < dim and Length(subbasis) <> 0 then
Expand Down Expand Up @@ -1238,7 +1230,7 @@ end;
## Returns false if module is irreducible.
SMTX.RandomIrreducibleSubGModule:=function( module )
local ranSub, subbasis, submodule, subbasis2, submodule2,
F, el, M, fac, N, i, matrices, ngens, genpair;
F, el, M, fac, N, i, matrices, genpair;

if not SMTX.IsMTXModule(module) then
return Error("Argument of RandomIrreducibleSubGModule is not a module.");
Expand Down Expand Up @@ -1299,12 +1291,10 @@ SMTX.RandomIrreducibleSubGModule:=function( module )
# Only the actual algebra element and its nullspace have to be recomputed
# This code is essentially from IsomorphismGModule
matrices:=ShallowCopy(submodule2.generators);
ngens:=Length(matrices);
for genpair in el[1] do
ngens:=ngens + 1;
matrices[ngens]:=matrices[genpair[1]] * matrices[genpair[2]];
Add(matrices, matrices[genpair[1]] * matrices[genpair[2]]);

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od;
M:=ImmutableMatrix(F,Sum([1..ngens], i-> el[2][i] * matrices[i]));
M:=ImmutableMatrix(F,Sum([1..Length(matrices)], i-> el[2][i] * matrices[i]));

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SMTX.SetAlgElMat(submodule2,M);
N:=NullspaceMat(SMTX_Value(fac,M,M^0));
SMTX.SetAlgElNullspaceVec(submodule2,N[1]);
Expand All @@ -1324,7 +1314,7 @@ end;
## irreducible, and the degree of the relevant field extension otherwise.
## This is needed for testing for equivalence of modules.
SMTX.GoodElementGModule:=function( module )
local matrices, ngens, M, mat, N, newgenlist, coefflist,
local matrices, M, mat, N, newgenlist, coefflist,
fac, pol, oldpol, q, deg, i, l,
trying, dim, mindim, F, R, count, rt0, idmat;

Expand All @@ -1347,7 +1337,6 @@ local matrices, ngens, M, mat, N, newgenlist, coefflist,

dim:=SMTX.Dimension(module);
matrices:=ShallowCopy(module.generators);
ngens:=Length(matrices);
F:=SMTX.Field(module);
R:=PolynomialRing(F);

Expand All @@ -1367,8 +1356,7 @@ local matrices, ngens, M, mat, N, newgenlist, coefflist,
fi;
Info(InfoMeatAxe,5,"Choosing random element number ",count,".");

M:=SMTX.SMCoRaEl(matrices,ngens,newgenlist,dim,F);
ngens:=Length(matrices);
M:=SMTX.SMCoRaEl(matrices,Length(matrices),newgenlist,dim,F);

coefflist:=M[2];
pol:=M[3];
Expand Down Expand Up @@ -2025,13 +2013,12 @@ end;
## composition factor.
##
SMTX.Distinguish:=function( cf, i )
local el, genpair, ngens, orig_ngens, mat, matsi, mats, M, idmat,
local el, genpair, ngens, mat, matsi, mats, M, idmat,
dim, F, fac, p, q, oldp, found, extdeg, j, k,
lcf, lf, x, y, wno, deg, trying, N, fact, R;

lcf:=Length(cf);
ngens:=Length(cf[1][1].generators);
orig_ngens:=ngens;
F:=SMTX.Field(cf[1][1]);
R:=PolynomialRing(F);
matsi:=ShallowCopy(cf[i][1].generators);
Expand All @@ -2051,11 +2038,9 @@ SMTX.Distinguish:=function( cf, i )
mats:=ShallowCopy(cf[j][1].generators);
dim:=SMTX.Dimension(cf[j][1]);
for genpair in el[1] do
ngens:=ngens + 1;
mats[ngens]:=mats[genpair[1]] * mats[genpair[2]];
Add(mats, mats[genpair[1]] * mats[genpair[2]]);
od;
M:=ImmutableMatrix(F,Sum([1..ngens], k -> el[2][k] * mats[k]));
ngens:=orig_ngens;
M:=ImmutableMatrix(F,Sum([1..Length(mats)], k -> el[2][k] * mats[k]));
mat:=SMTX_Value(fact, M, M^0);
if RankMat(mat) < dim then
found:=false;
Expand Down Expand Up @@ -2084,11 +2069,10 @@ SMTX.Distinguish:=function( cf, i )
while y = x and ngens > 1 do y:=Random(1, ngens); od;
Add(el[1], [x, y]);
ngens:=ngens + 1;
matsi[ngens]:=matsi[x] * matsi[y];
Add(matsi, matsi[x] * matsi[y]);

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fi;
# Now take the new random element
el[2]:=[];
for j in [1..ngens] do el[2][j]:=Random(F); od;
el[2]:=List([1..ngens], j -> Random(F));

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# First evaluate on cf[i][1].
M:=ImmutableMatrix(F,Sum([1..ngens], k -> el[2][k] * matsi[k]));
p:=CharacteristicPolynomialMatrixNC(F,M,1);
Expand Down Expand Up @@ -2144,12 +2128,10 @@ SMTX.Distinguish:=function( cf, i )
if j <> i and found then
mats:=ShallowCopy(cf[j][1].generators);
dim:=SMTX.Dimension(cf[j][1]);
ngens:=orig_ngens;
for genpair in el[1] do
ngens:=ngens + 1;
mats[ngens]:=mats[genpair[1]] * mats[genpair[2]];
Add(mats, mats[genpair[1]] * mats[genpair[2]]);

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od;
M:=ImmutableMatrix(F,Sum([1..ngens], k -> el[2][k] * mats[k]));
M:=ImmutableMatrix(F,Sum([1..Length(mats)], k -> el[2][k] * mats[k]));

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mat:=SMTX_Value(fact, M, M^0);
if RankMat(mat) < dim then
found:=false;
Expand Down Expand Up @@ -2177,35 +2159,30 @@ end;
## cf[i][1] is calculated and returned - i.e. if cf[i][2] = 1.
##
SMTX.MinimalSubGModule:=function( module, cf, i )
local el, genpair, ngens, orig_ngens, mat, mats, M, F,
local el, genpair, mat, mats, M, F,
k, N, fact;

if SMTX.IsMTXModule(module) = false then
return Error("First argument is not a module.");
fi;

ngens:=Length(module.generators);
orig_ngens:=ngens;
F:=SMTX.Field(module);

# Apply the alg. el. of factor i to module
el:=SMTX.AlgEl(cf[i][1]);
mats:=ShallowCopy(module.generators);
for genpair in el[1] do
ngens:=ngens + 1;
mats[ngens]:=mats[genpair[1]] * mats[genpair[2]];
Add(mats, mats[genpair[1]] * mats[genpair[2]]);

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od;

M:=ImmutableMatrix(F,Sum([1..ngens], k -> el[2][k] * mats[k]));
M:=ImmutableMatrix(F,Sum([1..Length(mats)], k -> el[2][k] * mats[k]));

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# Now throw away extra generators of module
for k in [orig_ngens + 1..ngens] do
Unbind(mats[k]);
od;
ngens:=orig_ngens;
mats:=ShallowCopy(module.generators);

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fact:=SMTX.AlgElCharPolFac(cf[i][1]);
mat:=SMTX_Value(fact, M,M^0);
N:=NullspaceMat(mat);
return SMTX.SpinnedBasis(N[1], mats,F, ngens);
return SMTX.SpinnedBasis(N[1], mats, F);

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end;

Expand All @@ -2225,7 +2202,7 @@ end;
##
SMTX.IsomorphismComp:=function(module1, module2, action)
local matrices, matrices1, matrices2, F, dim, swapmodule, genpair,
swapped, orig_ngens, i, j, el, p, fac, ngens, M, mat, v1, v2, v,
swapped, i, j, el, p, fac, M, mat, v1, v2, v,
N, basis, basis1, basis2;

if SMTX.IsMTXModule(module1) = false then
Expand Down Expand Up @@ -2264,9 +2241,7 @@ SMTX.IsomorphismComp:=function(module1, module2, action)
SMTX.GoodElementGModule(module1);
matrices1:=module1.generators;
matrices2:=ShallowCopy(module2.generators);
ngens:=Length(matrices1);
orig_ngens:=ngens;
if ngens <> Length(matrices2) then
if Length(matrices1) <> Length(matrices2) then
Error("GModules have different numbers of defining matrices.");
fi;

Expand All @@ -2279,15 +2254,12 @@ SMTX.IsomorphismComp:=function(module1, module2, action)
Info(InfoMeatAxe,2,"Extending generating set for second module.");
el:=SMTX.AlgEl(module1);
for genpair in el[1] do
ngens:=ngens + 1;
matrices2[ngens]:=matrices2[genpair[1]] * matrices2[genpair[2]];
Add(matrices2, matrices2[genpair[1]] * matrices2[genpair[2]]);
od;
M:=ImmutableMatrix(F,Sum([1..ngens], i -> el[2][i] * matrices2[i]));
M:=ImmutableMatrix(F,Sum([1..Length(matrices2)], i -> el[2][i] * matrices2[i]));
# Having done that, we no longer want the extra generators of module2,
# so we throw them away again.
for i in [orig_ngens + 1..ngens] do
Unbind(matrices2[i]);
od;
matrices2:=ShallowCopy(module2.generators);

Info(InfoMeatAxe,2,
"Calculating characteristic polynomial for second module.");
Expand Down Expand Up @@ -2375,7 +2347,7 @@ end;
##
SMTX.Homomorphisms:= function(m1, m2)

local F, ngens, orig_ngens, mats1, mats2, dim1, dim2, m1bas, imbases,
local F, mats1, mats2, dim1, dim2, m1bas, imbases,
el, genpair, fac, mat, N, imlen, subdim, leadpos, vec, imvecs,
numrels, rels, leadposrels, newrels, bno, genno, colno, rowno,
zero, looking, ans, i, j, k;
Expand All @@ -2391,8 +2363,7 @@ SMTX.Homomorphisms:= function(m1, m2)
fi;
mats1:=m1.generators;
mats2:=ShallowCopy(m2.generators);
ngens:=Length(mats1);
if ngens <> Length(mats2) then
if Length(mats1) <> Length(mats2) then
return Error("GModules have different numbers of generators.");
fi;

Expand Down Expand Up @@ -2425,19 +2396,14 @@ SMTX.Homomorphisms:= function(m1, m2)
# store a basis in imbases.

Info(InfoMeatAxe,2,"Extending generating set for second module.");
orig_ngens:=ngens;
el:=SMTX.AlgEl(m1);
for genpair in el[1] do
ngens:=ngens + 1;
mats2[ngens]:=mats2[genpair[1]] * mats2[genpair[2]];
Add(mats2, mats2[genpair[1]] * mats2[genpair[2]]);
od;
mat:=ImmutableMatrix(F,Sum([1..ngens], i -> el[2][i] * mats2[i]));
mat:=ImmutableMatrix(F,Sum([1..Length(mats2)], i -> el[2][i] * mats2[i]));
# Having done that, we no longer want the extra generators of m2,
# so we throw them away again.
for i in [orig_ngens + 1..ngens] do
Unbind(mats2[i]);
od;
ngens:=orig_ngens;
mats2:=ShallowCopy(m2.generators);

fac:=SMTX.AlgElCharPolFac(m1);
mat:=SMTX_Value(fac, mat,mat^0);
Expand Down Expand Up @@ -2482,17 +2448,13 @@ SMTX.Homomorphisms:= function(m1, m2)
Info(InfoMeatAxe,2,"Starting spinning.");
bno:=1;
while bno <= subdim do
for genno in [1..ngens] do
for genno in [1..Length(mats1)] do
# apply generator no. genno to submodule generator bno
vec:=m1bas[bno] * mats1[genno];
# and do the same to the images
imvecs:=[];
for i in [1..imlen] do
imvecs[i]:=imbases[i][bno] * mats2[genno];
od;
imvecs:=List([1..imlen], i -> imbases[i][bno] * mats2[genno]);
# try to express w in terms of existing submodule generators
# make same changes to images
j:=1;
for j in [1..subdim] do
k:=vec[leadpos[j]];
if k <> zero then
Expand Down

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