TristanVaccon

load("mora3.py")
load("tropical_F5.py")

##################################
#             Tools              #
#                                #
################################## 


def Single_Newton_Polytope(f,R):

TristanVaccon

from copy import*

##################################
#             Tools              #
#                                #
##################################    


def Tate_LT(f,R,w):
    r"""

TristanVaccon

from copy import*

##################################
#        Linear preliminary      #
#                                #
##################################    

def diagonalisable_in_glnZp_with_blocks_growing_valuation_random_eigenvalues(dim=6,blocks=[2,1,3],p=5,prec=10):    
    R = Zp(p,prec)
    diag0 = [[R.random_element() for i in range(blocks[u])] for u in range(len(blocks))]

TristanVaccon

r"""

This module implements the tropicalF5+FGLM technique to compute lex basis over fields with valuation. 




REFERENCES:

.. [F02] Jean-Charles Faugère. *A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)*.  In Proceedings of the 2002 international symposium on Symbolic and algebraic computation, ISSAC '02, pages 75-83, New York, NY, USA, 2002. ACM. 

TristanVaccon

#%cython

#This module implements a variant of the F4 algorithm to compute (approximate)
#Groebner bases for Tate algebras.

#AUTHOR:

#- Tristan Vaccon (2018)

TristanVaccon

#This module implements a variant of the F4 algorithm to compute (approximate)
#Groebner bases for Tate algebras.

#AUTHOR:

#- Tristan Vaccon (2018-2019)


#*****************************************************************************
#  Copyright (C) 2018-2019 Tristan Vaccon <tristan.vaccon@unilim.fr>

TristanVaccon

r"""

Educational Versions of the F5 Algorithm to compute tropical Groebner bases.

We have followed [F02], [AP11] [EF17] and [VY17].

No attempt was made to optimize the algorithm as the emphasis of
these implementations is to obtain an as clean and easy presentation as possible. To compute a
Groebner basis in Sage efficiently use the
:meth:`sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal.groebner_basis()`

TristanVaccon

r"""

Educational Versions of the F5 Algorithm to compute tropical Groebner bases.

We have followed [F02], [AP11] [EF17] and [VY17].

No attempt was made to optimize the algorithm as the emphasis of
these implementations is to obtain an as clean and easy presentation as possible. To compute a
Groebner basis in Sage efficiently use the
:meth:`sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal.groebner_basis()`

TristanVaccon

##################################################
#                Matrix tools                    #
##################################################


def Make_Macaulay_Matrix_sparse_dict(list_poly, monom):
    r"""

    Build the Macaulay matrix for the polynomials of degree d in list_poly. It is represented as a couple of a matrix and the list of the signatures of its rows, assuming compatibility.
    The matrix is sparse.

TristanVaccon

"""
This module implements Groebner bases computation via Matrix-F5 algorithm.

Computations over finite-precision complete discrete valuation field are available with the option "weak" in F5M.
Computations of tropical Groebner bases are available via the tropical option of F5M.

AUTHOR:

- Tristan Vaccon (2013-07)
"""