feat: Groebner Walk #3131

welpj · 2023-12-21T12:35:46Z

Hello @ederc ,
I finished the first step of the migration of the Groebner Walk to the Oscar.jl library and already talked to @afkafkafk13 about it.

This PR includes:

Gröbner Walk
Perturbed Gröbner Walk
Fractal Walk
Generic Walk
Tran´s version of the Groebner Walk

There probably are several improvements necessary, for example in the use of IdealGens: I don't know the handling of IdealGens in detail, @jankoboehm do you have any hints for improvements?

At the moment the tests take less than two minutes, but I was thinking of adding another bigger Ideal for testing the whole algorithms. @fingolfin, would that be appropriate? Are there further limits on RAM consumption?

I'm happy for any hint to beautify the code.

Thank you
Jordi

fingolfin

Thank you for your contribution. A bunch of quick comments added inline. Top level:

Please do not use tabs at all (see also https://docs.oscar-system.org/dev/DeveloperDocumentation/styleguide/).
adding multi minute / multi GB tests that are run every time is very problematic. Aren't there easier examples? They don't need to be "mathematically interesting" (interesting slow examples should be there, but not as part of the CI tests).

fingolfin · 2023-12-21T13:16:26Z

src/Rings/walk.jl

@@ -0,0 +1,1724 @@
+using Oscar


This is not the way to go about it if you want to integrate this code into Oscar. Instead, add the code into a subdirectory of experimental -- please read https://docs.oscar-system.org/dev/Experimental/intro/ for details.

fingolfin · 2023-12-21T13:19:20Z

src/Rings/walk.jl

@@ -0,0 +1,1724 @@
+using Oscar
+
+global infoLevel = 0


A global like this is a no-go.

An alternative would be to use @vprint and friends in your code, see https://www.thofma.com/Hecke.jl/stable/features/macros/#verbosity-macros for details (and also you can grep through our code to see examples using it).

fingolfin · 2023-12-21T13:19:36Z

src/Rings/walk.jl

+		groebnerwalk(
+			I::MPolyIdeal; 
+			startOrder::MonomialOrdering = default_ordering(base_ring(I)),
+			targetOrder::Symbol = lex(base_ring(I)),
+			walktype::Symbol = :standard,
+			perturbationDegree::Int = 2,
+		)


Should be indented by four spaces, not tabs

fingolfin · 2023-12-21T13:45:37Z

src/Rings/walk.jl

+			walktype::Symbol = :standard,
+			perturbationDegree::Int = 2,
+		)
+Compute a reduced Groebner basis w.r.t. to a monomial order by converting it using the Groebner Walk.


There must be an empty line between the function signatures and the text documenting it.

fingolfin · 2023-12-21T13:46:45Z

src/Rings/walk.jl

+Standard Walk (:standard) computes the Walk like it´s presented in Cox, Little & O´Shea (2005).
+Generic Walk (:generic) computes the Walk like it´s presented in Fukuda, Jensen, Lauritzen & Thomas (2005).
+Perturbed Walk (:perturbed, with p = degree of the perturbation) computes the Walk like it´s presented in Amrhein, Gloor & Küchlin (1997).
+Tran´s Walk (:tran) computes the Walk like it´s presented in Tran (2000).
+Fractal Walk (:fractalcombined) computes the Walk like it´s presented in Amrhein & Gloor (1998) with multiple extensions. The target monomial order has to be lex. This version uses the Buchberger Algorithm to skip weight vectors with entries bigger than Int32.
+Fractal Walk (:fractal) computes the Walk like it´s presented in Amrhein & Gloor (1998). Pertubes only the target vector.


Suggested change

Standard Walk (:standard) computes the Walk like it´s presented in Cox, Little & O´Shea (2005).

Generic Walk (:generic) computes the Walk like it´s presented in Fukuda, Jensen, Lauritzen & Thomas (2005).

Perturbed Walk (:perturbed, with p = degree of the perturbation) computes the Walk like it´s presented in Amrhein, Gloor & Küchlin (1997).

Tran´s Walk (:tran) computes the Walk like it´s presented in Tran (2000).

Fractal Walk (:fractalcombined) computes the Walk like it´s presented in Amrhein & Gloor (1998) with multiple extensions. The target monomial order has to be lex. This version uses the Buchberger Algorithm to skip weight vectors with entries bigger than Int32.

Fractal Walk (:fractal) computes the Walk like it´s presented in Amrhein & Gloor (1998). Pertubes only the target vector.

Standard Walk (:standard) computes the Walk like it´s presented in Cox, Little & O´Shea (2005).

- Generic Walk (:generic) computes the Walk as presented in Fukuda, Jensen, Lauritzen & Thomas (2005).

- Perturbed Walk (:perturbed, with p = degree of the perturbation) computes the Walk ass presented in Amrhein, Gloor & Küchlin (1997).

- Tran's Walk (:tran) computes the Walk like as presented in Tran (2000).

- Fractal Walk (:fractalcombined) computes the Walk like as presented in Amrhein & Gloor (1998) with multiple extensions. The target monomial order has to be lex. This version uses the Buchberger algorithm to skip weight vectors with entries bigger than Int32.

- Fractal Walk (:fractal) computes the Walk as presented in Amrhein & Gloor (1998). Perturbs only the target vector.

fingolfin · 2023-12-21T14:19:03Z

src/Rings/walk.jl

+	d0 = 0
+	for g in Singular.gens(G)
+		temp = deg(g, n)
+		if d0 < temp
+			d0 = temp
+		end
+	end


Suggested change

d0 = 0

for g in Singular.gens(G)

temp = deg(g, n)

if d0 < temp

d0 = temp

end

end

d0 = maximum(g -> deg(g, n), gens(g))

fingolfin · 2023-12-21T14:20:02Z

src/Rings/walk.jl

+	M = 0
+	for i ∈ 1:n
+		for j ∈ 1:n
+			temp = T[i, j]
+			if M < temp
+				M = temp
+			end
+		end
+	end


Suggested change

M = 0

for i ∈ 1:n

for j ∈ 1:n

temp = T[i, j]

if M < temp

M = temp

end

end

end

M = maximum(T)

fingolfin · 2023-12-21T14:20:10Z

src/Rings/walk.jl

+	w = d^(n - 1) * T[1, :]
+	for i ∈ 2:n
+		w = w + d^(n - i) * T[i, :]
+	end


Suggested change

w = d^(n - 1) * T[1, :]

for i ∈ 2:n

w = w + d^(n - i) * T[i, :]

end

w = sum(i -> d^(n - i) * T[i, :], 1:n)

Both versions are somewhat inefficient because they keep recomputing powers of d. Better would be something like this (could be slightly buggy but you should get the gist):

Suggested change

w = d^(n - 1) * T[1, :]

for i ∈ 2:n

w = w + d^(n - i) * T[i, :]

end

w = T[n, :]

e = one(d)

for i in 1:n-1

e *= d

w += e * T[n-i, :]

end

fingolfin · 2023-12-21T14:20:25Z

src/Rings/walk.jl

+		return true
+	end
+	return false
+end


File should end in a newline

Suggested change

end

end

fingolfin · 2023-12-21T14:21:52Z

src/Rings/walk.jl

+		if size(collect(Singular.coefficients(g)))[1] > 2
+			return true
+		end
+		if size(collect(Singular.coefficients(g)))[1] == 2
+			counter = counter + 1
+		end


Don't compute things twice

Suggested change

if size(collect(Singular.coefficients(g)))[1] > 2

return true

end

if size(collect(Singular.coefficients(g)))[1] == 2

counter = counter + 1

end

s = size(collect(Singular.coefficients(g)))[1]

s > 2 && return true

if s == 2

counter += 1

end

fingolfin · 2024-04-03T10:15:09Z

@afkafkafk13 just explained that someone else in Berlin (@ooinaruhugh) is working on Gröbner walk stuff and is building on top of this to produce new code (they will probably open a new PR for that, but let's keep this one open for now as reference).

fingolfin · 2024-07-17T10:04:12Z

Closing this in favor of PR #3821 which borrows some code from here but is under active development.

welpj added 2 commits December 19, 2023 22:50

feat:groebnerwalk

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feat: doc

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fingolfin requested changes Dec 21, 2023

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ooinaruhugh mentioned this pull request Jun 3, 2024

experimental: Gröbner Walk #3821

Merged

fingolfin closed this Jul 17, 2024

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feat: Groebner Walk #3131

feat: Groebner Walk #3131

welpj commented Dec 21, 2023 •

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fingolfin commented Apr 3, 2024

fingolfin commented Jul 17, 2024

-	w = d^(n - 1) * T[1, :]
-	for i ∈ 2:n
-		w = w + d^(n - i) * T[i, :]
-	end
+    w = T[n, :]
+	e = one(d)
+	for i in 1:n-1
+	    e *= d
+		w += e * T[n-i, :]
+	end

feat: Groebner Walk #3131

feat: Groebner Walk #3131

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welpj commented Dec 21, 2023 • edited Loading

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fingolfin commented Apr 3, 2024

fingolfin commented Jul 17, 2024

welpj commented Dec 21, 2023 •

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