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MinMaxgd[$\gamma,\delta$] - Data processing tools to handle periodic series in semiring

The MinmaxGD Library is developed in C++

A web-based experimental version is available at the following address:

snippets of code

/*declaration of two monomials*/
m1 = gd(1,4);
m2 = gd(2,5);

/*print the monomial */
print m1;
print m2;

/*sum of two monomials */
r0 = m1+m2;
print r0;

/* product of two monomials */
r1 = m1*m2;
print r1;

/*right and left residuation of two monomials */
r2 = m1/m2;
r3 = m1\m2;
print r2;
print r3;

/* Causality projection */
r2 = prcaus(r2);
print r2;

/*star operation */
r4 = star(r3);
print r4;

/*polynomial declaration*/
p1 = poly((1,2)(2,5)(5,9));
p2 = poly((1,1)(2,6)(4,8));

print p1;
print p2;

/*sum of two polynomials */
r1 = p1 + p2;
print r1;

/*product of two polynomials */
r2 = p1 * p2;
print r2;

/*right and left residuation of two polynomials */
r3 = p1/p2;
r4 = p1 \ p2;

print r3;
print r4;

/*causality projection of polynomial*/
r5 = prcaus(r3);
print r5;

/*star operation of polynomial */
r6 = star(r5);
print r6;

/* serie declaration */
s1 = series((1,2)(3,6)(5,8),(6,9),(1,4));
s2 = series((1,1),(2,4)(5,8),(2,2));

print s1;
print s2;

/*sum of two series */
s = s1 + s2;
print s;

/*product of two series */
s = s1 * s2;
print s;

/*right and left residuation of two series*/
sr = s1 / s2;
sl = s2 \ s1;

print sr;
print sl;

/*causality projection of serie */
sr = prcaus(sr);
print sr;

/*star operation on serie */
st = star(sr);
print st;

/* Declaration of matrices */

smatrix M1(2,2),M2(2,2);

M1(1,1) = gd(1,4);
M1(1,2) = gd(2,5);
M1(2,2) = gd(3,5);

M2(1,1) = gd(1,1);
M2(1,2) = gd(4,5);

print M1;
print M2;

/*sum of two matrices */
M = M1 + M1;
print M;

/*product of two matrices */
M = M1*M2;
print M;

/*right and left residuation of two matrices */
Mr = M1 / M2;
Ml = M1 \ M2;

print Mr;
print Ml;

/* start operation of matrix */
Ms = star(M1);
print Ms;

/* concatenation of matrices */
Mc = [M1,M2];
print Mc;

Mr = [M1;M2];
print Mr;

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