# Changeset a0b5e2 in git

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Timestamp:
Sep 20, 2010, 6:47:00 PM (13 years ago)
Branches:
(u'spielwiese', '8d54773d6c9e2f1d2593a28bc68b7eeab54ed529')
Children:
50b025ceafb1c25958940abd4fee0a82510cba8e
Parents:
dec1024e771ce38246bebbcab5f04dba4465e82d
Message:
```the pending changes for monomial.lib

git-svn-id: file:///usr/local/Singular/svn/trunk@13231 2c84dea3-7e68-4137-9b89-c4e89433aadc```
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• ## Singular/LIB/monomial.lib

 rdec1024 (radical, intersection, quotient...). LITERATURE: Miller, Ezra  and Sturmfels, Bernd: Combinatorial Commutative Algebra, Springer 2004 PROCEDURES: isMonomial(id);       checks whether an ideal id is monomial isirreducibleMon(id); checks whether a monomial ideal id is irreducible isartinianMon(id);    checks whether a monomial ideal id is artininan isgenericMon(id);     checks whether a monomial ideal id is generic isgenericMon(id);     checks whether a monomial ideal id is generic, i.e., no two  minimal generators of it agree in the exponent of any variable that actually appears in both of them. dimMon(id);           dimension of a monomial ideal id irreddecMon(id,..);   computes the irreducible decomposition of a monomial " USAGE:    checkIdeal (I); I ideal. RETURN:   1, if ideal is generated by monomials; 0, otherwise. RETURN:   1, if the given generators of I are monomials; 0, otherwise. " // Aqui NO estoy quitando el caso de que el ideal sea el trivial. USAGE:    quotientIdealMon(I,f); I ideal, f polynomial. RETURN:   an ideal, the quotient ideal I:(f). ASSUME:   I is an ideal generated by a list of monomials and f is a monomial ASSUME:   I is an ideal given by a list of monomials and f is a monomial of the basering. " // Si no tienen el mismo numero de generadores, no pueden ser iguales; ya // que vienen dados por el sistema minimal de generadores. if (size(I) <> size(J)) if (ncols(I) <> ncols(J)) { return(0); " USAGE:    isMinimal (I); I ideal. RETURN:   1, if the generators of I are the minimal ones; RETURN:   1, if the given generators of I are the minimal ones; 0 & minimal generators of I, otherwise. ASSUME:   I is an ideal of the basering generated by monomials. ASSUME:   I is an ideal of the basering given by monomial generators. " { I = J; i--; sizI = size(I); sizI = ncols(I); } } RETURN:   a list, 1 & the minimal generators of I, if I is a monomial ideal; 0, otherwise. ASSUME:   I is an ideal of the basering which is not generated by ASSUME:   I is an ideal of the basering whose given generators are not monomials. NOTE:     this procedure is NOT Grobner free and should be used only if the ideal has non-monomial generators (use first checkIdeal) given generators are not monomials. (use first checkIdeal) " { "USAGE:    minbaseMon (I); I ideal. RETURN:   an ideal, the minimal monomial generators of I. (-1 if the generators of I are not monomials) (-1 if the given generators of I are not monomials) ASSUME:   I is an  ideal generated by a list of monomials of the basering. EXAMPLE:  example minbaseMon; shows an example. if (control == 0) { return (-1); ERROR ("the ideal is not monomial"); } // Quitamos los ceros del sistema de generadores. ASSUME:   I,J are monomial ideals of the basering. NOTE:     the minimal monomial generating set is returned. USING THE SINGULAR COMMAND 'intersect' IS USUALLY FASTER EXAMPLE:  example intersectMon; shows some examples " { ERROR ("the second ideal is not monomial."); return (-1); } else } // Generico sizI = size(I); sizI = ncols(I); if (genericlist[1] == 0) { { expartI = leadexp(artI[1]); if (size(artI) <> 1) { artI = artI[2..size(artI)]; if (ncols(artI) <> 1) { artI = artI[2..ncols(artI)]; } // Hay que distinguir T_1 y T_2. Para ello se comparar vectores { artI = sort(artI)[1]; int sizartI = size(artI); int sizartI = ncols(artI); for (i = 1 ; i <= sizartI - 1 ; i ++) { poly comp; intvec exp; int sizIrred = size(irredDec); int sizIrred = ncols(irredDec); ideal auxIdeal; for (i = 1 ; i <= sizIrred ; i ++) (returns -1 if I is not a monomial ideal). ASSUME:   I is a monomial ideal of the basering k[x(1)..x(n)]. NOTE:     This procesure returns the irreducible decomposition of I. NOTE:     This procedure returns the irreducible decomposition of I, i.e., the unique irredundant decomposition of I into irreducible monomial ideals. One may call the procedure with different algorithms using the optional argument 'alg': (returns -1 if I is not a monomial ideal). ASSUME:   I is a monomial ideal of the basering k[x(1)..x(n)]. NOTE:     This procesure returns a minimal primary decomposition of I. NOTE:     This procedure returns a minimal primary decomposition of I. One may call the procedure with different algorithms using the optional argument 'alg':
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