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Mathematica package to check boundedness of general Higgs potentials.

License: BSD 3-Clause "New" or "Revised" License

Mathematica 99.95% MATLAB 0.05%

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boundedfrombelow's Issues

Custom potential

I added a simple example to BFB and tried to run it,
At first I used your definition of polynomials

polyn
and I got this error
err1

and in terminal;

(base) asus@layla:~/BoundedFromBelow$ mathematica 
/usr/share/Macaulay2/Core/enginering.m2:451:15:(1):[9]: error: can't promote number to ring
/usr/share/Macaulay2/Core/enginering.m2:459:38:(1):[8]: --back trace--
/usr/share/Macaulay2/Core/classes.m2:58:53:(1):[7]: --back trace--
/usr/share/Macaulay2/Core/enginering.m2:641:40:(1):[6]: --back trace--
script.m2:3:47:(3):[5]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:113:27:(1):[5]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:106:18:(1):[4]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:126:41:(1):[3]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:129:6:(1):[2]: --back trace--
/home/dan/src/M2/M2.git/M2/Macaulay2/m2/startup.m2.in:547:63:(0):[1]: --back trace--
/home/dan/src/M2/M2.git/M2/Macaulay2/m2/startup.m2.in:668:6:(0): --back trace--
error in RunMacaulay2Script: script ended with bad exit code

Then I used my definition of polynomials;
mydef

and I got this error
myerr

and in terminal;

(base) asus@layla:~/BoundedFromBelow$ mathematica 
/usr/share/Macaulay2/Core/methods.m2:37:35:(1):[18]: error: no method found for applying ring to:
                              3           2
     argument   :  {{- 4eig*x1  + lsh*x1*s }} (of class List)
/usr/share/Macaulay2/Core/methods.m2:133:19:(1):[17]: --back trace--
/usr/share/Macaulay2/Core/matrix1.m2:182:75:(1):[14]: --back trace--
/usr/share/Macaulay2/Core/matrix1.m2:186:11:(1):[13]: --back trace--
/usr/share/Macaulay2/Core/matrix1.m2:281:35:(1):[12]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:119:80:(1):[11]: --back trace--
/usr/share/Macaulay2/Resultants.m2:82:43:(2):[9]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:119:80:(1):[7]: --back trace--
/usr/share/Macaulay2/Core/option.m2:16:8:(1):[6]: --back trace--
script.m2:4:18:(3):[5]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:113:27:(1):[5]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:106:18:(1):[4]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:126:41:(1):[3]: --back trace--
/usr/share/Macaulay2/Core/setup.m2:129:6:(1):[2]: --back trace--
/home/dan/src/M2/M2.git/M2/Macaulay2/m2/startup.m2.in:547:63:(0):[1]: --back trace--
/home/dan/src/M2/M2.git/M2/Macaulay2/m2/startup.m2.in:668:6:(0): --back trace--
error in RunMacaulay2Script: script ended with bad exit code

Thanks
Layla

Originally posted by @Layla-Kalhor in #1 (comment)

Some errors in my BFB code

Dear all,
Thanks for your useful package specially in HEP.

I have installed BFB, according to "README.md" in this package.

- my mathematica version is 11.2.0.0

- I have installed Macaulay2, according to this site "https://faculty.math.illinois.edu/Macaulay2/"
when I type M2 in terminal, I have this message:

Macaulay2, version 1.16
with packages: ConwayPolynomials, Elimination, IntegralClosure, InverseSystems,
               LLLBases, MinimalPrimes, PrimaryDecomposition, ReesAlgebra,
               TangentCone, Truncations

I think, my problem is the lack of Resultants package!!
Screenshot from 2020-11-10 11-24-22
because when I want to load this packge, I have a warning:

i1 : loadPackage "Resultants"
--warning: symbol "resultant" in Elimination.Dictionary is shadowed by a symbol in Resultants.Dictionary
--  use the synonym Elimination$resultant
--warning: symbol "discriminant" in Elimination.Dictionary is shadowed by a symbol in Resultants.Dictionary
--  use the synonym Elimination$discriminant

- I tried to install Resultants according to "README.md", but this page didn't open for(to) me
https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2-1.10/share/doc/Macaulay2/Resultants/html/

- when I want to run Test.nb, I have an error in the

eigvals = DeleteDuplicates[eig /. Solve[retval[["Resultant"]] == 0, eig]]

my error is
Screenshot from 2020-11-10 11-47-20

- I downloaded "BoundedFromBelow-master" and I unzipped this file. and there are other .m files in this directory,
I also modify the file config.m

Thanks for your time and attention

Positivity Test

Dear Marcel,

constraints on parameters
I looked at your article and thesis again, I am a little confused about positivity test and constraints for(on) parameters.
Let me see if I've got it right...
The eigenvalues must be positive for boundedness potential from below, then according to this eigenvalues I can get some constraints on parameters.

For example consider this simple potential;

potential = -mu*h^2 + lh*h^4 + ms*s^2 + lsh*h^2*s^2 + ls*s^4;

I have 4 eigenvalues according to BFB package;

eigvals = DeleteDuplicates[eig /. Solve[retval[["Resultant"]] == 0, eig]]

{lh, ls, 1/2 (lh + ls - Sqrt[lh^2 - 2 lh ls + ls^2 + lsh^2]), 
 1/2 (lh + ls + Sqrt[lh^2 - 2 lh ls + ls^2 + lsh^2])}

and we know that eigenvalues must be positive, so;

lh>0,
ls>0,
1/2 (lh + ls - Sqrt[lh^2 - 2 lh ls + ls^2 + lsh^2])>0, 
1/2 (lh + ls + Sqrt[lh^2 - 2 lh ls + ls^2 + lsh^2])}>0

and I can find constraints on parameters.

positivity test
In last issue, you mentioned and had some examples about positivity test.

PositivityTest[2*x^4 - 1*x^2*y^2 + 2*y^4, {x, y}]
PositivityTest[-2*x^4 + 1*x^2*y^2 + 2*y^4, {x, y}]
PositivityTest[0*x^4 + 1*x^2*y^2 + 2*y^4, {x, y}]

and in the definition, you wrote "Tests a given Higgs potential for postive (semi)definiteness on large field values."

PositivityTest[potential, variables, (parameters), (options)]

In Positivity Test, I myself must give some numbers to parameters?
For example lh = 0.129, ls = 3, lsh = 2, and run it?
And for last question, where is the output of Positivity Test?
I think it is very obvious and Positivity Test is not necessary, am I wrong?
I am a little confused about this!!!

Best Wishes
Layla

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