exponent vector overflow, restarting #95
Comments
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In this case I "fixed" the issue by changing to a different term ordering (the computation is now done instantly!), however the questions still stand. |
Yes.
At the moment there is no such feature. The algorithm in Groebner.jl is very much more efficient for |
No, the error was with
Thanks, good to know. |
Ah.. it is interesting that it is slow with |
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The code is for finding the eigenvalues of a family of matrices. Here it is, in case you're interested: # An attempt at finding the eigenvalue with largest magnitude of some
# large matrices defined by a small number of parameters. Inspired by
# this post on Julia's Discourse:
#
# https://discourse.julialang.org/t/strategy-for-finding-eigenvalues-of-an-infinite-banded-matrix/106513/3?u=nsajko
#
# The idea is to use the characteristic polynomial and other known
# relations for constructing a system of polynomial equations, which
# could perhaps be solved using Gröbner bases, as implemented in the
# Groebner.jl Julia package, given enough additional relations.
#
# The relations that are currently in use are *not* restrictive enough
# for obtaining a finite set of solutions for the eigenvalues. Trying
# to think of other relations to add to the system.
# In Mason's problem, the parameters are all negative. Here they're all
# positive instead. This is OK because, for any matrix `M`, the
# eigenvalues of `-M` are just the eigenvalues of `M`, but with
# all signs reversed.
# Parameters, they define the elements of the matrix: `a`, `b`, `c₀`,
# `c₁`, `c₂`. `x` is the indeterminate representing an eigenvalue.
module EigenMasonEquations
import LinearAlgebra, LinearAlgebraX, MultivariatePolynomials
const MP = MultivariatePolynomials
const NT = NTuple{n,Any} where {n}
square(x) = x*x
"""
An equation that represents the inequality `0 ≤ target`. `scratch`
should be a dedicated variable, used just in this equation.
"""
is_ordered_after_zero(::typeof(≤), target, scratch) =
square(scratch) - target
"""
An equation that represents the inequality `0 < target`. `scratch`
should be a dedicated variable, used just in this equation.
"""
is_ordered_after_zero(::typeof(<), target, scratch) =
square(scratch) * target - true
is_ordered_after_zero(
r::R, ::Type{T}, target, scratch,
) where {R<:Union{typeof(≤),typeof(<)}, T} =
is_ordered_after_zero(r, target, scratch + zero(T))
"""
An equation that represents the inequality `l o r`. `scratch`
should be a variable dedicated just for this equation.
"""
are_ordered(
o::R, ::Type{T}, l, r, scratch,
) where {R<:Union{typeof(≤),typeof(<)}, T} =
is_ordered_after_zero(o, T, r - l, scratch)
"""
An equation that represents the Laguerre–Samuelson inequality for the
polynomial `p` with indeterminate `x`.
`scratch` should be a variable dedicated just for this equation.
"""
function laguerre_samuelson_inequality(::Type{I}, p, x, scratch) where {I}
n = MP.maxdegree(p, x)
coef = let p = p, x = x
i -> MP.coefficient(p, x^i, (x,))
end
isone(coef(n)) || error("polynomial not monic")
a_nm1 = coef(n - 1)
a_nm2 = coef(n - 2)
c0 = I(n)::I
c1 = I(n - 1)::I
c2 = I(2*n)::I
are_ordered(
≤, I,
square(c0*x + a_nm1),
c1*(c1*square(a_nm1) - c2*a_nm2),
scratch,
)
end
uniform_scaling_matrix(x, n) = (LinearAlgebra.Diagonal ∘ fill)(x, n)
function characteristic_polynomial(m, x)
n = LinearAlgebra.checksquare(m)
LinearAlgebraX.detx(m - uniform_scaling_matrix(x, n))
end
symmetric_setindex!(m::LinearAlgebra.Symmetric, v, i, j) =
m[begin + i, begin + j] = v
function symmetric_setindex!(m::AbstractMatrix, v, i, j)
m[begin + i, begin + j] = v
m[begin + j, begin + i] = v
end
function symmetric_set_diagonal!(m, j, x)
n = LinearAlgebra.checksquare(m)
(j ∈ 0:(n - 1)) || error("`j` out of bounds")
for i ∈ 0:(n - 1 - j)
symmetric_setindex!(m, x, i, i + j)
end
end
new_square_zero_matrix(::Type{T}, n) where {T} = zeros(T, n, n)
function the_matrix(::Type{I}, n, ab::NT{2}, c::NT{m}) where {I, m}
T = (eltype ∘ promote)(zero(I), ab..., c...)
ret = new_square_zero_matrix(T, n)
c! = let r = ret, c = c
i -> symmetric_set_diagonal!(r, 2*i, c[begin + i])
end
for i ∈ Base.OneTo(m)
c!(i - 1)
end
(a, b) = ab
if 0 < n
symmetric_setindex!(ret, a, 0, 0)
if 1 < n
symmetric_setindex!(ret, a, 1, 1)
symmetric_setindex!(ret, b, 0, 1)
end
end
LinearAlgebra.issymmetric(ret) || error("matrix not symmetric")
S = LinearAlgebra.Symmetric
S(ret)::S{T}
end
the_polynomial(::Type{I}, n, x, ab::NT{2}, c::NT{m}) where {I, m} =
characteristic_polynomial(the_matrix(I, n, ab, c), x)
struct Variables{
m, X, AB<:NT{2}, CF, CR<:NT{m}, SAB<:NT{2}, SCF, SCR<:NT{m},
LS, OA, OC, OAB, OBA, OCC1<:NT{m}, OCC2<:Tuple,
}
x::X
ab::AB
c_first::CF
c_rest::CR
sign_ab::SAB
sign_c_first::SCF
sign_c_rest::SCR
laguerre_samuelson::LS
order_a::OA
order_c::OC
order_ab::OAB
order_ba::OBA
order_cc1::OCC1
order_cc2::OCC2
end
function the_equations(
::Type{I}, n, vars::Variables{c_rest_len},
) where {I, c_rest_len}
is_pos = (l, s) -> is_ordered_after_zero(<, I, l, s)
greater_than = (l, r, s) -> are_ordered(<, I, l, r, s)
greater_or_eq = (l, r, s) -> are_ordered(≤, I, l, r, s)
p = the_polynomial(I, n, vars.x, vars.ab, (vars.c_first, vars.c_rest...))
s_ab = map(is_pos, vars.ab, vars.sign_ab)
s_c_first = is_pos(vars.c_first, vars.sign_c_first)
s_c_rest = map(is_pos, vars.c_rest, vars.sign_c_rest)
ls = laguerre_samuelson_inequality(I, p, vars.x, vars.laguerre_samuelson)
# Theorem 4.8 from *Eigenvalues of Nonnegative Symmetric Matrices*, 1974,
# Miroslav Fiedler, 10.1016/0024-3795(74)90031-7
#
# Only necessarily holds for the greatest eigenvalue; i.e., if we assume
# these equations hold, we're potentially losing all other eigenvalues.
o_a = greater_or_eq(first(vars.ab), vars.x, vars.order_a)
o_c = greater_or_eq(vars.c_first , vars.x, vars.order_c)
mag_fac_small = I(2)
mag_fac_big = I(1000)
# Some equations specific to Mason's problem
#
# * b < a
# * a,b have similar magnitudes: a ≤ mag_fac_small*b
# * c_first is of greater magnitude than any of c_rest
# * all c_rest values have similar magnitudes
occ1 = let ge = greater_or_eq, cf = vars.c_first, cr = vars.c_rest,
cc = vars.order_cc1
i -> ge(mag_fac_big*(cr[i]), cf, cc[i])
end
occ2 = let ge = greater_or_eq, cr = vars.c_rest, cc = vars.order_cc2
function(i)
j = i - 1
k = j >>> true
a = cr[begin + k]
b = cr[begin + k + 1]
if iseven(j)
ge(a, mag_fac_small*b, cc[i])
else
ge(b, mag_fac_small*a, cc[i])
end
end
end
(va, vb) = vars.ab
spec = (
greater_than(vb, va, vars.order_ab),
greater_or_eq(va, mag_fac_small*vb, vars.order_ba),
ntuple(occ1, Val(c_rest_len))...,
ntuple(occ2, Val(2*(c_rest_len - 1)))...,
)
ret = (p, s_ab..., s_c_first, s_c_rest..., ls, o_a, o_c, spec...)
collect(ret)
end
end
import Groebner, DynamicPolynomials, TypedPolynomials
const GRB = Groebner
const POL = DynamicPolynomials
const EME = EigenMasonEquations
my_groebner_(::Type{I}, n, vars; kwargs...) where {I} =
GRB.groebner((collect ∘ EME.the_equations)(I, n, vars); kwargs...)
function default_vars()
POL.@polyvar x c₀ c₀ₛ l aₒ c₀ₒ abₒ baₒ
v_ab = POL.@polyvar a b
v_c_rest = POL.@polyvar c₁ c₂
v_sign_ab = POL.@polyvar aₛ bₛ
v_sign_c = POL.@polyvar c₁ₛ c₂ₛ
v_cc1 = POL.@polyvar q₁ q₂
v_cc2 = POL.@polyvar r₁ r₂
EME.Variables(
x, v_ab, c₀, v_c_rest, v_sign_ab, c₀ₛ, v_sign_c, l, aₒ, c₀ₒ,
abₒ, baₒ, v_cc1, v_cc2,
)
end
my_groebner_(::Type{I}, n; kwargs...) where {I} = my_groebner_(I, n, default_vars(); kwargs...)
my_groebner_2(::Type{I}, n) where {I} = my_groebner_(I, n, ordering = GRB.DegLex())
my_groebner_3(::Type{I}, n) where {I} = my_groebner_(I, n, ordering = GRB.DegRevLex())
my_groebner(n) = my_groebner_3(BigInt, n) |
|
Thanks for sharing the example! I will try to look at it this weekend. Unfortunately at the moment if I do ERROR: LoadError: polynomial not monic
Stacktrace:
[1] error(s::String)
@ Base .\error.jl:35
[2] laguerre_samuelson_inequality(#unused#::Type{BigInt}, p::DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, BigInt}, x::DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, scratch::DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}})
@ Main.EigenMasonEquations C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:48
[3] the_equations(#unused#::Type{BigInt}, n::Int64, vars::Main.EigenMasonEquations.Variables{2, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}})
@ Main.EigenMasonEquations C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:154
[4] call_composed(fs::Tuple{typeof(Main.EigenMasonEquations.the_equations)}, x::Tuple{DataType, Int64, Main.EigenMasonEquations.Variables{2, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}}}, kw::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ Base .\operators.jl:1035
[5] call_composed(fs::Tuple{typeof(collect), typeof(Main.EigenMasonEquations.the_equations)}, x::Tuple{DataType, Int64, Main.EigenMasonEquations.Variables{2, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}}}, kw::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ Base .\operators.jl:1034
[6] (::ComposedFunction{typeof(collect), typeof(Main.EigenMasonEquations.the_equations)})(::Type, ::Vararg{Any}; kw::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ Base .\operators.jl:1031
[7] ComposedFunction
@ .\operators.jl:1031 [inlined]
[8] my_groebner_(::Type{BigInt}, n::Int64, vars::Main.EigenMasonEquations.Variables{2, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}, Tuple{DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}, DynamicPolynomials.Variable{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}}; kwargs::Base.Pairs{Symbol,
Groebner.DegRevLex{Nothing}, Tuple{Symbol}, NamedTuple{(:ordering,), Tuple{Groebner.DegRevLex{Nothing}}}})
@ Main C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:208
[9] my_groebner_
@ C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:208 [inlined]
[10] #my_groebner_#4
@ C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:237 [inlined]
[11] my_groebner_
@ C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:237 [inlined]
[12] my_groebner_3
@ C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:241 [inlined]
[13] my_groebner(n::Int64)
@ Main C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:243
[14] top-level scope
@ C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:245
in expression starting at C:\data\projects\gbgb\Groebner.jl\experimental\linear-algebra\stuff:245 |
|
Ah, yes, the |
|
Oh, I see, thanks |
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While trying to find a Groebner basis, a message like this is output:
Does this mean that my computation is restarting completely, from scratch?
I don't know what is an exponent vector, but I wonder whether there's a way to increase the exponent size in advance, before starting the computation. Otherwise there's a lot of wasted computational effort, if the computation restarts multiple times each time I start the process.
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