[380a17b] | 1 | /////////////////////////////////////////////////////////////////////////// |
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[3686937] | 2 | version="version schreyer.lib 4.0.0.0 Jun_2013 "; // $Id$ |
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[4c6c938] | 3 | category="General purpose"; |
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| 4 | info=" |
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[789d6f] | 5 | LIBRARY: schreyer.lib Helpers for computing a Schreyer resolution in @code{derham.lib} |
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[4c6c938] | 6 | AUTHOR: Oleksandr Motsak <U@D>, where U={motsak}, D={mathematik.uni-kl.de} |
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[789d6f] | 7 | KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy |
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[b1645e] | 8 | OVERVIEW: |
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[370468] | 9 | @* The library contains helper procedures for computing a Schreyer resoltion (cf. [SFO]), |
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| 10 | originally meant to be used by @code{derham.lib} (which requires resolutions over the homogenized Weyl algebra). |
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| 11 | The library works both in the commutative and non-commutative setting (cf. [MO]). |
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[43e3e7] | 12 | Here, we call a free resolution a Schreyer resolution if each syzygy module is given by a Groebner basis |
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[b1645e] | 13 | with respect to the corresponding Schreyer ordering. |
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[370468] | 14 | A Schreyer resolution can be much bigger than a minimal resolution of the same module, but may be easier to construct. |
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| 15 | @* The input for the resolution computations is a set of vectors @code{M} in form of a module over some basering @code{R}. |
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[b1645e] | 16 | The ring @code{R} may be non-commutative, in which case the ring ordering should be global. |
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| 17 | @* These procedures produce/work with partial Schreyer resolutions of @code{(R^rank(M))/M} in form of |
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| 18 | a ring (endowed with a special ring ordering that will be extended in the course of a resolution computation) |
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| 19 | containing a list of modules @code{RES} and a module @code{MRES}: |
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[370468] | 20 | @* The list of modules @code{RES} contains the images of maps (also called syzygy modules) substituting the |
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[43e3e7] | 21 | computed beginning of a Schreyer resolution, that is, each syzygy module is given by a Groebner basis |
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| 22 | with respect to the corresponding Schreyer ordering. |
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[b1645e] | 23 | @* The list @code{RES} starts with a zero map given by @code{rank(M)} zero generators indicating that the image of |
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| 24 | the first differential map is zero. The second map @code{RES[2]} is given by @code{M}, which indicates that |
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[370468] | 25 | the resolution of @code{(R^rank(M))/M} is being computed. |
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[b1645e] | 26 | @* The module @code{MRES} is a direct sum of modules from @code{RES} and thus comprises all computed differentials. |
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| 27 | @* Syzygies are shifted so that @code{gen(i)} is mapped to @code{MRES[i]} under the differential map. |
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[370468] | 28 | @* The Schreyer ordering succesively extends the starting module ordering on @code{M} (defined in Singular by the basering @code{R}) |
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[b1645e] | 29 | and is extended to higher syzygies using the following definition: |
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| 30 | @* a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ), |
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| 31 | @* where @code{d(a)} is the image of a under the differential (given by @code{MRES}), |
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[370468] | 32 | and @code{comp(a)} is the module component, for any module terms @code{a} and @code{b} from the same higher syzygy module. |
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[b1645e] | 33 | REFERENCES: |
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| 34 | [SFO] Schreyer, F.O.: Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrassschen Divisionssatz, |
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| 35 | Master's thesis, Univ. Hamburg, 1980. |
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| 36 | [MO] Motsak, O.: Non-commutative Computer Algebra with applications: Graded commutative algebra and related |
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| 37 | structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010 |
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| 38 | |
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| 39 | NOTE: requires the dynamic or built-in module @code{syzextra} |
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[4c6c938] | 40 | |
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| 41 | PROCEDURES: |
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[b1645e] | 42 | Sres(M,len) compute Schreyer resolution of module M of maximal length len |
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| 43 | Ssyz(M) compute Schreyer resolution of module M of length 1 |
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| 44 | Scontinue(len) extend currently active resolution by (at most) len syszygies |
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[4c6c938] | 45 | "; |
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| 46 | |
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| 47 | static proc prepareSyz( module I, list # ) |
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| 48 | { |
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| 49 | int i; |
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| 50 | int k = 0; |
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| 51 | int r = nrows(I); |
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| 52 | int c = ncols(I); |
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| 53 | |
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| 54 | |
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| 55 | if( size(#) > 0 ) |
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| 56 | { |
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| 57 | if( typeof(#[1]) == "int" || typeof(#[1]) == "bigint" ) |
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| 58 | { |
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| 59 | k = #[1]; |
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| 60 | } |
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| 61 | } |
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| 62 | |
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| 63 | if( k < r ) |
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| 64 | { |
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| 65 | "// *** Wrong k: ", k, " < nrows: ", r, " => setting k = r = ", r; |
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| 66 | k = r; |
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| 67 | } |
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| 68 | |
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| 69 | // "k: ", k; "c: ", c; "I: ", I; |
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| 70 | |
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| 71 | for( i = c; i > 0; i-- ) |
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| 72 | { |
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| 73 | I[i] = I[i] + gen(k + i); |
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| 74 | } |
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| 75 | |
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| 76 | // DetailedPrint(I); |
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| 77 | |
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| 78 | return(I); |
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| 79 | } |
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| 80 | |
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| 81 | static proc separateSyzGB( module J, int c ) |
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| 82 | { |
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| 83 | module II, G; vector v; int i; |
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| 84 | |
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| 85 | J = simplify(J, 2); |
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| 86 | |
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| 87 | for( i = ncols(J); i > 0; i-- ) |
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| 88 | { |
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| 89 | v = J[i]; |
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| 90 | if( leadcomp(v) > c ) |
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| 91 | { |
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| 92 | II[i] = v; |
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| 93 | } else |
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| 94 | { |
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| 95 | G[i] = v; // leave only gen(i): i <= c |
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| 96 | } |
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| 97 | } |
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| 98 | |
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| 99 | II = simplify(II, 2); |
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| 100 | G = simplify(G, 2); |
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| 101 | |
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| 102 | return (list(G, II)); |
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| 103 | } |
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| 104 | |
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| 105 | static proc splitSyzGB( module J, int c ) |
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| 106 | { |
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| 107 | module JJ; vector v, vv; int i; |
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| 108 | |
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| 109 | for( i = ncols(J); i > 0; i-- ) |
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| 110 | { |
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| 111 | v = J[i]; |
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| 112 | |
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| 113 | vv = 0; |
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| 114 | |
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| 115 | while( leadcomp(v) <= c ) |
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| 116 | { |
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| 117 | vv = vv + lead(v); |
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| 118 | v = v - lead(v); |
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| 119 | } |
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| 120 | |
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| 121 | J[i] = vv; |
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| 122 | JJ[i] = v; |
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| 123 | } |
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| 124 | |
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| 125 | J = simplify(J, 2); |
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| 126 | JJ = simplify(JJ, 2); |
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| 127 | |
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| 128 | return (list(J, JJ)); |
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| 129 | } |
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| 130 | |
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| 131 | |
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| 132 | static proc Sinit(module M) |
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| 133 | { |
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| 134 | def @save = basering; |
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| 135 | |
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| 136 | int @DEBUG = !system("with", "ndebug"); |
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| 137 | if( @DEBUG ) |
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| 138 | { |
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| 139 | "Sinit::Input"; |
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| 140 | type(M); |
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| 141 | DetailedPrint(M); |
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| 142 | attrib(M); |
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| 143 | } |
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| 144 | |
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| 145 | int @RANK = nrows(M); int @SIZE = ncols(M); |
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| 146 | |
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| 147 | int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?! |
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| 148 | |
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| 149 | if( !@IS_A_SB ) |
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| 150 | { |
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| 151 | M = std(M); // this should be faster than computing std in S (later on) |
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| 152 | } |
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| 153 | |
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| 154 | def S = MakeInducedSchreyerOrdering(1); // 1 puts history terms to the back |
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| 155 | // TODO: NOTE: +1 causes trouble to Singular interpreter!!!??? |
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| 156 | setring S; // a new ring with a Schreyer ordering |
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| 157 | |
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| 158 | if( @DEBUG ) |
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| 159 | { |
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| 160 | "Sinit::StartingISRing"; |
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| 161 | basering; |
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| 162 | // DetailedPrint(basering); |
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| 163 | } |
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| 164 | |
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| 165 | // Setup the leading syzygy^{-1} module to zero: |
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| 166 | module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0)); |
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| 167 | |
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| 168 | module MRES = Z; |
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| 169 | |
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| 170 | list RES; RES[1] = Z; |
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| 171 | |
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| 172 | module F = freemodule(@RANK); |
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| 173 | intvec @V = deg(F[1..@RANK]); |
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| 174 | |
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| 175 | module M = imap(@save, M); |
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[f37467] | 176 | |
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[4c6c938] | 177 | attrib(M, "isHomog", @V); |
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| 178 | attrib(M, "isSB", 1); |
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| 179 | |
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| 180 | |
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| 181 | if( @DEBUG ) |
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| 182 | { |
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| 183 | "Sinit::SB_Input: "; |
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| 184 | type(M); |
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| 185 | attrib(M); |
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| 186 | attrib(M, "isHomog"); |
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| 187 | DetailedPrint(M); |
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| 188 | } |
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| 189 | |
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[f37467] | 190 | if( @DEBUG ) |
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[4c6c938] | 191 | { |
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[f37467] | 192 | // 0^th syz. property |
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| 193 | if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 ) |
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| 194 | { |
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| 195 | transpose( transpose(M) * transpose(MRES) ); |
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| 196 | "transpose( transpose(M) * transpose(MRES) ) != 0!!!"; |
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| 197 | $ |
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| 198 | } |
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[4c6c938] | 199 | } |
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| 200 | |
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| 201 | RES[size(RES)+1] = M; // list of all syzygy modules |
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| 202 | MRES = MRES, M; |
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| 203 | |
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| 204 | attrib(MRES, "isHomog", @V); |
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| 205 | |
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| 206 | attrib(S, "InducionLeads", lead(M)); |
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| 207 | attrib(S, "InducionStart", @RANK); |
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| 208 | |
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| 209 | if( @DEBUG ) |
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| 210 | { |
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| 211 | "Sinit::MRES"; |
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| 212 | DetailedPrint(MRES); |
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| 213 | attrib(MRES, "isHomog"); |
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| 214 | attrib(S); |
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| 215 | } |
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| 216 | |
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| 217 | export RES; |
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| 218 | export MRES; |
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| 219 | return (S); |
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| 220 | } |
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| 221 | |
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| 222 | static proc Sstep() |
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| 223 | { |
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| 224 | int @DEBUG = !system("with", "ndebug"); |
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| 225 | |
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| 226 | if( @DEBUG ) |
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| 227 | { |
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| 228 | "Sstep::NextInducedRing"; |
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| 229 | DetailedPrint(basering); |
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| 230 | |
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| 231 | attrib(basering, "InducionLeads"); |
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| 232 | attrib(basering, "InducionStart"); |
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| 233 | |
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| 234 | GetInducedData(); |
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| 235 | } |
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| 236 | |
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| 237 | // syzygy step: |
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| 238 | |
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| 239 | /* |
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| 240 | // is initial weights are all zeroes! |
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| 241 | def L = lead(M); |
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| 242 | intvec @V = deg(M[1..ncols(M)]); @W; @V; @W = @V; attrib(L, "isHomog", @W); |
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| 243 | SetInducedReferrence(L, @RANK, 0); |
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| 244 | */ |
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| 245 | |
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| 246 | // def L = lead(MRES); |
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| 247 | // @W = @W, @V; |
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| 248 | // attrib(L, "isHomog", @W); |
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| 249 | |
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| 250 | |
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| 251 | // General setting: |
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| 252 | // SetInducedReferrence(MRES, 0, 0); // limit: 0! |
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| 253 | int @l = size(RES); |
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| 254 | |
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| 255 | module M = RES[@l]; |
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| 256 | |
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| 257 | module L = attrib(basering, "InducionLeads"); |
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| 258 | int limit = attrib(basering, "InducionStart"); |
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| 259 | |
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| 260 | // L; limit; |
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| 261 | |
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| 262 | int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?! |
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| 263 | |
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| 264 | /* |
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| 265 | if( @RANK != nrows(M) ) |
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| 266 | { |
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| 267 | type(MRES); |
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| 268 | @RANK; |
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| 269 | type(M); |
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| 270 | pause(); |
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| 271 | } |
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| 272 | */ |
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| 273 | |
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| 274 | intvec @W = attrib(M, "isHomog"); |
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| 275 | intvec @V = deg(M[1..ncols(M)]); |
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| 276 | @V = @W, @V; |
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| 277 | |
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| 278 | if( @DEBUG ) |
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| 279 | { |
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| 280 | "Sstep::NextInput: "; |
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| 281 | M; |
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[7fe9f8b] | 282 | deg(M[1..ncols(M)]); // no use of @W :(? |
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[4c6c938] | 283 | @RANK; |
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| 284 | DetailedPrint(MRES); |
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[7fe9f8b] | 285 | attrib(MRES, "isHomog"); @W; |
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| 286 | deg(MRES[1..ncols(MRES)]); |
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[4c6c938] | 287 | } |
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| 288 | |
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| 289 | |
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| 290 | |
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| 291 | SetInducedReferrence(L, limit, 0); |
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| 292 | |
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| 293 | def K = prepareSyz(M, @RANK); |
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| 294 | // K; |
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| 295 | |
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| 296 | // attrib(K, "isHomog", @V); DetailedPrint(K, 1000); |
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| 297 | |
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| 298 | // pause(); |
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| 299 | |
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| 300 | K = idPrepare(K, @RANK); // std(K); // ? |
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| 301 | K = simplify(K, 2); |
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| 302 | |
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| 303 | // K; |
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| 304 | |
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| 305 | module N = separateSyzGB(K, @RANK)[2]; // 1^st syz. module: vectors which start in lower part (comp >= @RANK) |
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| 306 | |
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| 307 | // "N_0: "; N; DetailedPrint(N, 10); |
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[7fe9f8b] | 308 | |
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| 309 | // basering; print(@V); type(N); |
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| 310 | // attrib(N, "isHomog", @V); // TODO: fix "wrong weights"!!!? deg is wrong :((( |
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| 311 | N = std(N); |
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[4c6c938] | 312 | attrib(N, "isHomog", @V); |
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| 313 | |
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| 314 | // N; |
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| 315 | |
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[f37467] | 316 | if( @DEBUG ) |
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[4c6c938] | 317 | { |
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[f37467] | 318 | if( size(N) > 0 ) |
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[4c6c938] | 319 | { |
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[f37467] | 320 | // next syz. property |
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| 321 | if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 ) |
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| 322 | { |
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| 323 | MRES; |
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[4c6c938] | 324 | |
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[f37467] | 325 | "N: "; N; DetailedPrint(N, 10); |
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[4c6c938] | 326 | |
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[f37467] | 327 | "K:"; K; DetailedPrint(K, 10); |
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[4c6c938] | 328 | |
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[f37467] | 329 | "RANKS: ", @RANK; |
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[4c6c938] | 330 | |
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[f37467] | 331 | "transpose( transpose(N) * transpose(MRES) ) != 0!!!"; |
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| 332 | transpose( transpose(N) * transpose(MRES) ); |
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[4c6c938] | 333 | |
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[f37467] | 334 | "transpose(N) * transpose(MRES): "; |
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| 335 | transpose(N) * transpose(MRES); |
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| 336 | DetailedPrint(module(_), 2); |
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| 337 | $ |
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| 338 | } |
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[4c6c938] | 339 | } |
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| 340 | } |
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| 341 | |
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| 342 | RES[@l + 1] = N; // list of all syzygy modules |
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| 343 | |
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| 344 | MRES = MRES, N; |
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| 345 | attrib(MRES, "isHomog", @V); |
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| 346 | |
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| 347 | |
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| 348 | L = L, lead(N); |
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| 349 | attrib(basering, "InducionLeads", L); |
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| 350 | |
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| 351 | if( @DEBUG ) |
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| 352 | { |
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| 353 | "Sstep::NextSyzOutput: "; |
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| 354 | DetailedPrint(N); |
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| 355 | attrib(N, "isHomog"); |
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| 356 | } |
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| 357 | |
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| 358 | } |
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| 359 | |
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| 360 | proc Scontinue(int l) |
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[33694c] | 361 | "USAGE: Scontinue(int len) |
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| 362 | RETURN: nothing, instead it changes the currently active resolution |
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| 363 | PURPOSE: extends the currently active resolution by at most len syzygies |
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[b1645e] | 364 | ASSUME: must be used within a ring returned by Sres or Ssyz |
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[4c6c938] | 365 | EXAMPLE: example Scontinue; shows an example |
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| 366 | " |
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| 367 | { |
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| 368 | def data = GetInducedData(); |
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| 369 | |
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| 370 | if( (!defined(RES)) || (!defined(MRES)) || (typeof(data) != "list") || (size(data) != 2) ) |
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| 371 | { |
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| 372 | ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz"); |
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| 373 | } |
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| 374 | for (; (l != 0) && (size(RES[size(RES)]) > 0); l-- ) |
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| 375 | { |
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| 376 | Sstep(); |
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| 377 | } |
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| 378 | } |
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| 379 | example |
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| 380 | { "EXAMPLE:"; echo = 2; |
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| 381 | ring r; |
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| 382 | module M = maxideal(1); M; |
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| 383 | def S = Ssyz(M); setring S; S; |
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| 384 | "Only the first syzygy: "; |
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| 385 | RES; MRES; |
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| 386 | "More syzygies: "; |
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| 387 | Scontinue(10); |
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| 388 | RES; MRES; |
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| 389 | } |
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| 390 | |
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| 391 | proc Ssyz(module M) |
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[33694c] | 392 | "USAGE: Ssyz(module M) |
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| 393 | RETURN: ring, containing a Schreyer resolution |
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[b1645e] | 394 | PURPOSE: computes a Schreyer resolution of M of length 1 (see the library overview) |
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| 395 | SEE ALSO: Sres |
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[4c6c938] | 396 | EXAMPLE: example Ssyz; shows an example |
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| 397 | " |
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| 398 | { |
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| 399 | def S = Sinit(M); setring S; |
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| 400 | |
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| 401 | Sstep(); // NOTE: what if M is zero? |
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| 402 | |
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| 403 | return (S); |
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| 404 | } |
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| 405 | example |
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| 406 | { "EXAMPLE:"; echo = 2; |
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| 407 | ring r; |
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| 408 | module M = maxideal(1); M; |
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| 409 | def S = Ssyz(M); setring S; S; |
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| 410 | "Only the first syzygy: "; |
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| 411 | RES; |
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| 412 | MRES; // Note gen(i) |
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| 413 | kill S; |
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| 414 | setring r; kill M; |
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| 415 | |
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| 416 | module M = 0; |
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| 417 | def S = Ssyz(M); setring S; S; |
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| 418 | "Only the first syzygy: "; |
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| 419 | RES; |
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| 420 | MRES; |
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| 421 | } |
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| 422 | |
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| 423 | proc Sres(module M, int l) |
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[33694c] | 424 | "USAGE: Sres(module M, int len) |
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| 425 | RETURN: ring, containing a Schreyer resolution |
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[b1645e] | 426 | PURPOSE: computes a Schreyer resolution of M of length at most len (see the library overview) |
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| 427 | NOTE: If given len is zero then nvars(basering) + 1 is used instead. |
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| 428 | SEE ALSO: Ssyz |
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[4c6c938] | 429 | EXAMPLE: example Sres; shows an example |
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| 430 | " |
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| 431 | { |
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| 432 | def S = Sinit(M); setring S; |
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| 433 | |
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| 434 | if (l == 0) |
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| 435 | { |
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| 436 | l = nvars(basering) + 1; // not really an estimate...?! |
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| 437 | } |
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| 438 | |
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| 439 | Sstep(); l = l - 1; |
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| 440 | |
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| 441 | Scontinue(l); |
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| 442 | |
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| 443 | return (S); |
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| 444 | } |
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| 445 | example |
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| 446 | { "EXAMPLE:"; echo = 2; |
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| 447 | ring r; |
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| 448 | module M = maxideal(1); M; |
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| 449 | def S = Sres(M, 0); setring S; S; |
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| 450 | RES; |
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| 451 | MRES; |
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| 452 | kill S; |
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| 453 | setring r; kill M; |
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| 454 | |
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| 455 | def A = nc_algebra(-1,0); setring A; |
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| 456 | ideal Q = var(1)^2, var(2)^2, var(3)^2; |
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| 457 | qring SCA = twostd(Q); |
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| 458 | basering; |
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| 459 | |
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| 460 | module M = maxideal(1); |
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| 461 | def S = Sres(M, 2); setring S; S; |
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| 462 | RES; |
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| 463 | MRES; |
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| 464 | } |
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| 465 | |
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| 466 | |
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| 467 | |
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[6b6c82] | 468 | // ================================================================== // |
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| 469 | |
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| 470 | |
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| 471 | LIB "general.lib"; // for sort |
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| 472 | |
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[e89ff5] | 473 | /* static proc Tail(def M) // DONE: in C++ (dyn. module: syzextra)! |
---|
[6b6c82] | 474 | { |
---|
| 475 | int i = ncols(M); def m; |
---|
| 476 | while (i > 0) |
---|
| 477 | { |
---|
| 478 | m = M[i]; |
---|
[e89ff5] | 479 | m = m - lead(m); // m = tail(m) |
---|
| 480 | M[i] = m; |
---|
[6b6c82] | 481 | i--; |
---|
| 482 | } |
---|
| 483 | return (M); |
---|
[e89ff5] | 484 | }*/ |
---|
| 485 | |
---|
[8b78ee] | 486 | /* static */ |
---|
| 487 | proc MySort(def M) |
---|
| 488 | { |
---|
| 489 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 490 | { |
---|
| 491 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 492 | } else |
---|
| 493 | { |
---|
| 494 | int @DEBUG = !system("with", "ndebug"); |
---|
| 495 | } |
---|
| 496 | |
---|
[8b368ff] | 497 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
[8b78ee] | 498 | { |
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[8b368ff] | 499 | int @KERCHECK = attrib(basering, "KERCHECK"); |
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[8b78ee] | 500 | } else |
---|
| 501 | { |
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[8b368ff] | 502 | int @KERCHECK = @DEBUG; // TODO: @SYZCHECK:( |
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[8b78ee] | 503 | } |
---|
| 504 | |
---|
| 505 | |
---|
| 506 | if( @DEBUG ) |
---|
| 507 | { |
---|
| 508 | "MySort:: Input: "; M; |
---|
| 509 | } |
---|
| 510 | |
---|
| 511 | def @N = M; Sort_c_ds(@N); |
---|
| 512 | |
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[8b368ff] | 513 | if( @KERCHECK ) |
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[8b78ee] | 514 | { |
---|
| 515 | def iv = sort(lead(M), "c,ds", 1)[2]; // ,1 => reversed! // TODO: not needed? |
---|
| 516 | def @M = M; |
---|
| 517 | @M = M[iv]; |
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| 518 | |
---|
| 519 | // 0^th syz. property |
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[8b368ff] | 520 | if(size(@N) * size(@M) > 0 ) |
---|
| 521 | { |
---|
| 522 | if( size(module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) )) > 0 ) |
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[8b78ee] | 523 | { |
---|
| 524 | "@M:"; @M; |
---|
| 525 | "@N:"; @N; |
---|
| 526 | |
---|
| 527 | "module( matrix(@N) - matrix(@M) ): "; |
---|
| 528 | module( matrix(@N) - matrix(@M) ); |
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| 529 | |
---|
[8b368ff] | 530 | "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!"; |
---|
[8b78ee] | 531 | $ |
---|
| 532 | } |
---|
[8b368ff] | 533 | } |
---|
[8b78ee] | 534 | } |
---|
| 535 | |
---|
| 536 | if( @DEBUG ) |
---|
| 537 | { |
---|
| 538 | "MySort:: Ouput: "; @N; |
---|
| 539 | } |
---|
| 540 | |
---|
| 541 | return (@N); |
---|
| 542 | } |
---|
| 543 | |
---|
[6b6c82] | 544 | |
---|
[4b2e47] | 545 | /* static */ proc SSinit(def M) |
---|
[6b6c82] | 546 | { |
---|
| 547 | if( (typeof(M) != "module") && (typeof(M) != "ideal") ) |
---|
| 548 | { |
---|
| 549 | ERROR("Sorry: need an ideal or a module for input"); |
---|
| 550 | } |
---|
| 551 | |
---|
| 552 | // TODO! DONE? |
---|
| 553 | def @save = basering; |
---|
| 554 | |
---|
| 555 | int @DEBUG = !system("with", "ndebug"); |
---|
[8e650e] | 556 | |
---|
| 557 | if( typeof( attrib(SSinit, "DEBUG") ) == "int" ) |
---|
| 558 | { |
---|
| 559 | @DEBUG = attrib(SSinit, "DEBUG"); |
---|
| 560 | } |
---|
| 561 | |
---|
| 562 | int @SYZCHECK = @DEBUG; |
---|
| 563 | |
---|
| 564 | if( typeof( attrib(SSinit, "SYZCHECK") ) == "int" ) |
---|
| 565 | { |
---|
| 566 | @SYZCHECK = attrib(SSinit, "SYZCHECK"); |
---|
| 567 | } |
---|
[8b368ff] | 568 | |
---|
| 569 | int @KERCHECK = @SYZCHECK; |
---|
| 570 | |
---|
| 571 | if( typeof( attrib(SSinit, "KERCHECK") ) == "int" ) |
---|
| 572 | { |
---|
| 573 | @KERCHECK = attrib(SSinit, "KERCHECK"); |
---|
| 574 | } |
---|
| 575 | |
---|
[6b6c82] | 576 | if( @DEBUG ) |
---|
| 577 | { |
---|
| 578 | "SSinit::Input"; |
---|
| 579 | type(M); |
---|
[4b2e47] | 580 | // DetailedPrint(M); |
---|
[6b6c82] | 581 | attrib(M); |
---|
| 582 | } |
---|
| 583 | |
---|
| 584 | int @RANK = nrows(M); int @SIZE = ncols(M); |
---|
| 585 | |
---|
| 586 | int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?! |
---|
| 587 | |
---|
| 588 | if( !@IS_A_SB ) |
---|
| 589 | { |
---|
| 590 | def opts = option(get); |
---|
| 591 | option(redSB); option(redTail); |
---|
| 592 | M = std(M); |
---|
| 593 | option(set, opts); |
---|
| 594 | kill opts; |
---|
| 595 | } else |
---|
| 596 | { |
---|
| 597 | M = simplify(M, 2 + 4 + 32); |
---|
| 598 | } |
---|
| 599 | |
---|
[8b78ee] | 600 | def @N = MySort(M); // TODO: replace with inplace sorting!!! |
---|
| 601 | def LEAD = lead(@N); |
---|
| 602 | |
---|
| 603 | if( @SYZCHECK ) |
---|
| 604 | { |
---|
| 605 | def @LEAD = lead(M); |
---|
| 606 | |
---|
| 607 | // sort wrt neg.deg.rev.lex! |
---|
| 608 | intvec iv_ds = sort(@LEAD, "c,ds", 1)[2]; // ,1 => reversed! |
---|
| 609 | |
---|
| 610 | M = M[iv_ds]; // sort M wrt ds on current leading terms |
---|
| 611 | @LEAD = @LEAD[iv_ds]; |
---|
| 612 | |
---|
| 613 | // 0^th syz. property |
---|
| 614 | if( size(module( matrix(@N) - matrix(M) )) > 0 ) |
---|
| 615 | { |
---|
| 616 | "M:"; M; |
---|
| 617 | "@N:"; @N; |
---|
| 618 | |
---|
| 619 | "module( matrix(@N) - matrix(M) ): "; |
---|
| 620 | module( matrix(@N) - matrix(M) ); |
---|
[6b6c82] | 621 | |
---|
[8b78ee] | 622 | "ERROR: wrong sorting (in SSnit): @N != M!!!"; |
---|
| 623 | $ |
---|
| 624 | } |
---|
| 625 | |
---|
| 626 | // 0^th syz. property |
---|
| 627 | if( size(module( matrix(@LEAD) - matrix(LEAD) )) > 0 ) |
---|
| 628 | { |
---|
| 629 | "LEAD:"; LEAD; |
---|
| 630 | "@LEAD:"; @LEAD; |
---|
| 631 | |
---|
| 632 | "module( matrix(@LEAD) - matrix(LEAD) ): "; |
---|
| 633 | module( matrix(@LEAD) - matrix(LEAD) ); |
---|
| 634 | |
---|
| 635 | "ERROR: wrong sorting (in SSnit): @LEAD != LEAD!!!"; |
---|
| 636 | $ |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | } |
---|
[6b6c82] | 640 | |
---|
[8b78ee] | 641 | M = @N; |
---|
| 642 | |
---|
| 643 | |
---|
| 644 | |
---|
[6b6c82] | 645 | |
---|
| 646 | def TAIL = Tail(M); |
---|
| 647 | |
---|
| 648 | intvec @DEGS = deg(M[1..@SIZE]); // store actuall degrees of input elements |
---|
| 649 | |
---|
| 650 | // TODO: what about real modules? weighted ones? |
---|
| 651 | |
---|
| 652 | list @l = ringlist(@save); |
---|
| 653 | |
---|
| 654 | int @z = 0; ideal @m = maxideal(1); intvec @wdeg = deg(@m[1..ncols(@m)]); |
---|
| 655 | |
---|
| 656 | // NOTE: @wdeg will be ignored anyway :( |
---|
| 657 | @l[3] = list(list("C", @z), list("lp", @wdeg)); |
---|
| 658 | |
---|
| 659 | kill @z, @wdeg; // since these vars are ring independent! |
---|
| 660 | |
---|
| 661 | def S = ring(@l); // --MakeInducedSchreyerOrdering(1); |
---|
| 662 | |
---|
| 663 | module F = freemodule(@RANK); |
---|
| 664 | intvec @V = deg(F[1..@RANK]); |
---|
| 665 | |
---|
| 666 | setring S; // ring with an easy divisibility test ("C, lex") |
---|
| 667 | |
---|
| 668 | if( @DEBUG ) |
---|
| 669 | { |
---|
[fdde6ce] | 670 | "SSinit::NewRing(C, lex)"; |
---|
[6b6c82] | 671 | basering; |
---|
[7b7c2c] | 672 | DetailedPrint(basering); |
---|
[6b6c82] | 673 | } |
---|
| 674 | |
---|
| 675 | // Setup the leading syzygy^{-1} module to zero: |
---|
| 676 | module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0)); |
---|
| 677 | |
---|
| 678 | module MRES = Z; |
---|
| 679 | |
---|
| 680 | list RES; RES[1] = Z; |
---|
| 681 | list LRES; LRES[1] = Z; |
---|
| 682 | list TRES; TRES[1] = Z; |
---|
| 683 | |
---|
| 684 | def M = imap(@save, M); |
---|
[f37467] | 685 | |
---|
[6b6c82] | 686 | attrib(M, "isHomog", @V); |
---|
| 687 | attrib(M, "isSB", 1); |
---|
| 688 | attrib(M, "degrees", @DEGS); |
---|
| 689 | |
---|
| 690 | def LEAD = imap(@save, LEAD); |
---|
[f37467] | 691 | |
---|
[6b6c82] | 692 | attrib(LEAD, "isHomog", @V); |
---|
| 693 | attrib(LEAD, "isSB", 1); |
---|
| 694 | |
---|
| 695 | def TAIL = imap(@save, TAIL); |
---|
| 696 | |
---|
| 697 | if( @DEBUG ) |
---|
| 698 | { |
---|
| 699 | "SSinit::(sorted) SB_Input: "; |
---|
| 700 | type(M); |
---|
| 701 | attrib(M); |
---|
| 702 | attrib(M, "isHomog"); |
---|
[4b2e47] | 703 | // DetailedPrint(M); |
---|
[6b6c82] | 704 | } |
---|
| 705 | |
---|
[b0ca43c] | 706 | if( @SYZCHECK ) |
---|
[6b6c82] | 707 | { |
---|
[f37467] | 708 | // 0^th syz. property |
---|
| 709 | if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 ) |
---|
| 710 | { |
---|
| 711 | transpose( transpose(M) * transpose(MRES) ); |
---|
| 712 | "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!"; |
---|
| 713 | $ |
---|
| 714 | } |
---|
[6b6c82] | 715 | } |
---|
| 716 | |
---|
[7b7c2c] | 717 | RES [size(RES)+1] = M; // list of all syzygy modules |
---|
[6b6c82] | 718 | LRES[size(LRES)+1] = LEAD; // list of all syzygy modules |
---|
| 719 | TRES[size(TRES)+1] = TAIL; // list of all syzygy modules |
---|
| 720 | |
---|
| 721 | MRES = MRES, M; //? |
---|
| 722 | |
---|
[f37467] | 723 | attrib(MRES, "isHomog", @V); |
---|
| 724 | |
---|
[b0ca43c] | 725 | // attrib(S, "InducionStart", @RANK); |
---|
[8e650e] | 726 | |
---|
| 727 | |
---|
| 728 | if( typeof( attrib(SSinit, "LEAD2SYZ") ) == "int" ) |
---|
| 729 | { |
---|
| 730 | attrib(S, "LEAD2SYZ", attrib(SSinit, "LEAD2SYZ") ); |
---|
| 731 | } else |
---|
| 732 | { |
---|
| 733 | attrib(S, "LEAD2SYZ", 1); |
---|
| 734 | } |
---|
| 735 | |
---|
| 736 | if( typeof( attrib(SSinit, "TAILREDSYZ") ) == "int" ) |
---|
| 737 | { |
---|
| 738 | attrib(S, "TAILREDSYZ", attrib(SSinit, "TAILREDSYZ") ); |
---|
| 739 | } else |
---|
| 740 | { |
---|
| 741 | attrib(S, "TAILREDSYZ", 1); |
---|
| 742 | } |
---|
| 743 | |
---|
| 744 | |
---|
| 745 | if( typeof( attrib(SSinit, "HYBRIDNF") ) == "int" ) |
---|
| 746 | { |
---|
| 747 | attrib(S, "HYBRIDNF", attrib(SSinit, "HYBRIDNF") ); |
---|
| 748 | } else |
---|
| 749 | { |
---|
| 750 | attrib(S, "HYBRIDNF", 0); |
---|
| 751 | } |
---|
| 752 | |
---|
[fdde6ce] | 753 | attrib(S, "DEBUG", @DEBUG); |
---|
[b0ca43c] | 754 | attrib(S, "SYZCHECK", @SYZCHECK); |
---|
[8b368ff] | 755 | attrib(S, "KERCHECK", @KERCHECK); |
---|
[6b6c82] | 756 | |
---|
| 757 | if( @DEBUG ) |
---|
| 758 | { |
---|
| 759 | "SSinit::MRES"; |
---|
[4b2e47] | 760 | MRES; |
---|
| 761 | // DetailedPrint(MRES); |
---|
[6b6c82] | 762 | attrib(MRES, "isHomog"); |
---|
| 763 | attrib(S); |
---|
| 764 | } |
---|
| 765 | |
---|
| 766 | export RES; |
---|
| 767 | export MRES; |
---|
| 768 | export LRES; |
---|
| 769 | export TRES; |
---|
| 770 | return (S); |
---|
| 771 | } |
---|
| 772 | example |
---|
| 773 | { "EXAMPLE:"; echo = 2; |
---|
| 774 | ring R = 0, (w, x, y, z), dp; |
---|
| 775 | |
---|
| 776 | def M = maxideal(1); |
---|
| 777 | def S = SSinit(M); setring S; S; |
---|
| 778 | |
---|
| 779 | "Only the first initialization: "; |
---|
| 780 | RES; LRES; TRES; |
---|
| 781 | MRES; |
---|
| 782 | |
---|
| 783 | kill S; setring R; kill M; |
---|
| 784 | |
---|
| 785 | ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; |
---|
| 786 | def S = SSinit(M); setring S; S; |
---|
| 787 | |
---|
| 788 | "Only the first initialization: "; |
---|
| 789 | RES; LRES; TRES; |
---|
| 790 | MRES; |
---|
| 791 | |
---|
| 792 | kill S; setring R; kill M; |
---|
| 793 | } |
---|
| 794 | |
---|
[8f57c0] | 795 | |
---|
| 796 | LIB "poly.lib"; // for lcm |
---|
| 797 | |
---|
| 798 | |
---|
[f37467] | 799 | |
---|
| 800 | /// Compute L(Syz(L)) |
---|
| 801 | proc SSComputeLeadingSyzygyTerms(def L) |
---|
[8f57c0] | 802 | { |
---|
[fdde6ce] | 803 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 804 | { |
---|
| 805 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 806 | } else |
---|
| 807 | { |
---|
| 808 | int @DEBUG = !system("with", "ndebug"); |
---|
| 809 | } |
---|
[8f57c0] | 810 | |
---|
[7b7c2c] | 811 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 812 | { |
---|
| 813 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 814 | } else |
---|
| 815 | { |
---|
| 816 | int @SYZCHECK = @DEBUG; |
---|
| 817 | } |
---|
[8b368ff] | 818 | |
---|
| 819 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 820 | { |
---|
| 821 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 822 | } else |
---|
| 823 | { |
---|
| 824 | int @KERCHECK = @SYZCHECK; |
---|
| 825 | } |
---|
| 826 | |
---|
[8f57c0] | 827 | if( @DEBUG ) |
---|
| 828 | { |
---|
| 829 | "SSComputeLeadingSyzygyTerms::Input: "; |
---|
| 830 | L; |
---|
| 831 | } |
---|
| 832 | |
---|
[7b7c2c] | 833 | module SS = ComputeLeadingSyzygyTerms(L); |
---|
[8f57c0] | 834 | |
---|
[8b368ff] | 835 | if( @KERCHECK ) |
---|
[7b7c2c] | 836 | { |
---|
[8b78ee] | 837 | int i, j, r; |
---|
[7b7c2c] | 838 | int N = ncols(L); |
---|
| 839 | def a, b; |
---|
| 840 | poly aa, bb; |
---|
[8f57c0] | 841 | |
---|
[7b7c2c] | 842 | bigint c; |
---|
[8f57c0] | 843 | |
---|
[7b7c2c] | 844 | ideal M; |
---|
[4b2e47] | 845 | |
---|
[7b7c2c] | 846 | module S = 0; |
---|
[8f57c0] | 847 | |
---|
[7b7c2c] | 848 | for(i = 1; i <= N; i++) |
---|
[8f57c0] | 849 | { |
---|
[7b7c2c] | 850 | a = L[i]; |
---|
| 851 | c = leadcomp(a); |
---|
| 852 | r = int(c); |
---|
[8f57c0] | 853 | |
---|
[7b7c2c] | 854 | aa = leadmonomial(a); |
---|
| 855 | |
---|
| 856 | M = 0; |
---|
| 857 | |
---|
| 858 | for(j = i-1; j > 0; j--) |
---|
[8f57c0] | 859 | { |
---|
[7b7c2c] | 860 | b = L[j]; |
---|
| 861 | |
---|
| 862 | if( leadcomp(b) == c ) |
---|
[4b2e47] | 863 | { |
---|
[7b7c2c] | 864 | bb = leadmonomial(b); |
---|
[8f57c0] | 865 | |
---|
[7b7c2c] | 866 | M[j] = (lcm(aa, bb) / aa); |
---|
| 867 | } |
---|
[8f57c0] | 868 | } |
---|
[7b7c2c] | 869 | |
---|
| 870 | // TODO: add quotient relations here... |
---|
| 871 | |
---|
| 872 | M = simplify(M, 1 + 2 + 32); |
---|
| 873 | |
---|
[8b78ee] | 874 | M = MySort(M); |
---|
[7b7c2c] | 875 | |
---|
| 876 | S = S, M * gen(i); |
---|
[8f57c0] | 877 | } |
---|
| 878 | |
---|
[8b78ee] | 879 | S = MySort(simplify(S, 2)); |
---|
[8f57c0] | 880 | |
---|
[8b368ff] | 881 | if( size(S) * size(SS) > 0 ) |
---|
| 882 | { |
---|
[7b7c2c] | 883 | if( size(module(matrix(S) - matrix(SS))) > 0 ) |
---|
| 884 | { |
---|
[8b368ff] | 885 | "ERROR: SSComputeLeadingSyzygyTerms: S != SS "; |
---|
[8f57c0] | 886 | |
---|
[7b7c2c] | 887 | "basering: "; |
---|
| 888 | DetailedPrint(basering); |
---|
[8f57c0] | 889 | |
---|
[7b7c2c] | 890 | "S: "; S; |
---|
| 891 | DetailedPrint(S, 1); |
---|
| 892 | "SS: "; SS; |
---|
| 893 | DetailedPrint(SS, 1); |
---|
| 894 | |
---|
| 895 | "DIFF: "; |
---|
| 896 | print(matrix(S) - matrix(SS)); |
---|
| 897 | DetailedPrint(module(matrix(S) - matrix(SS)), 2); |
---|
| 898 | $ |
---|
| 899 | } |
---|
[8b368ff] | 900 | } |
---|
[7b7c2c] | 901 | } |
---|
[8f57c0] | 902 | |
---|
| 903 | |
---|
| 904 | if( @DEBUG ) |
---|
| 905 | { |
---|
| 906 | "SSComputeLeadingSyzygyTerms::Output: "; |
---|
[7b7c2c] | 907 | "SS: "; |
---|
| 908 | SS; |
---|
| 909 | } |
---|
| 910 | |
---|
[8b368ff] | 911 | if( size(SS) > 0 ) |
---|
| 912 | { |
---|
| 913 | attrib(SS, "isSB", 1); |
---|
| 914 | } |
---|
| 915 | |
---|
[7b7c2c] | 916 | return (SS); |
---|
[f37467] | 917 | } |
---|
| 918 | |
---|
| 919 | /// Compute Syz(L), where L is a monomial (leading) module |
---|
[74afe1f] | 920 | proc SSCompute2LeadingSyzygyTerms(def L) |
---|
[f37467] | 921 | { |
---|
[fdde6ce] | 922 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 923 | { |
---|
| 924 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 925 | } else |
---|
| 926 | { |
---|
| 927 | int @DEBUG = !system("with", "ndebug"); |
---|
| 928 | } |
---|
[f37467] | 929 | |
---|
[b0ca43c] | 930 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 931 | { |
---|
| 932 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 933 | } else |
---|
| 934 | { |
---|
| 935 | int @SYZCHECK = @DEBUG; |
---|
| 936 | } |
---|
[74afe1f] | 937 | |
---|
[8b368ff] | 938 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 939 | { |
---|
| 940 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 941 | } else |
---|
| 942 | { |
---|
| 943 | int @KERCHECK = @SYZCHECK; |
---|
| 944 | } |
---|
| 945 | |
---|
[74afe1f] | 946 | int @TAILREDSYZ = 1; |
---|
| 947 | if( typeof( attrib(basering, "TAILREDSYZ") ) == "int" ) |
---|
| 948 | { |
---|
| 949 | @TAILREDSYZ = attrib(basering, "TAILREDSYZ"); |
---|
| 950 | } |
---|
| 951 | |
---|
[b0ca43c] | 952 | |
---|
[f37467] | 953 | if( @DEBUG ) |
---|
| 954 | { |
---|
| 955 | "SSCompute2LeadingSyzygyTerms::Input: "; |
---|
| 956 | L; |
---|
| 957 | } |
---|
| 958 | |
---|
[d058ea] | 959 | module SS = Compute2LeadingSyzygyTerms(L); |
---|
[f37467] | 960 | |
---|
[d058ea] | 961 | if( @DEBUG ) |
---|
| 962 | { |
---|
| 963 | "SSCompute2LeadingSyzygyTerms::Syz(SS): "; SS; |
---|
| 964 | } |
---|
| 965 | |
---|
| 966 | if( @SYZCHECK ) |
---|
| 967 | { |
---|
| 968 | if( size(SS) > 0 and size(L) > 0 ) |
---|
| 969 | { |
---|
| 970 | if( size(module(transpose( transpose(SS) * transpose(L) ))) > 0 ) |
---|
| 971 | { |
---|
| 972 | transpose( transpose(SS) * transpose(L) ); |
---|
| 973 | "ERROR: transpose( transpose(SS) * transpose(L) ) != 0!!!"; |
---|
| 974 | $ |
---|
| 975 | } |
---|
| 976 | } |
---|
[8b368ff] | 977 | } |
---|
| 978 | |
---|
| 979 | if( @KERCHECK ) |
---|
| 980 | { |
---|
[f37467] | 981 | |
---|
[d058ea] | 982 | int i, j, r; |
---|
| 983 | int N = ncols(L); |
---|
| 984 | def a, b; |
---|
[f37467] | 985 | |
---|
[d058ea] | 986 | poly aa, bb, @lcm; |
---|
[f37467] | 987 | |
---|
[d058ea] | 988 | bigint c; |
---|
[f37467] | 989 | |
---|
[d058ea] | 990 | module M; |
---|
[f37467] | 991 | |
---|
[d058ea] | 992 | module S = 0; |
---|
[f37467] | 993 | |
---|
[d058ea] | 994 | for(i = 1; i <= N; i++) |
---|
[f37467] | 995 | { |
---|
[d058ea] | 996 | a = L[i]; |
---|
| 997 | // "a: ", a; |
---|
| 998 | c = leadcomp(a); |
---|
| 999 | r = int(c); |
---|
| 1000 | |
---|
| 1001 | aa = leadmonomial(a); |
---|
| 1002 | |
---|
| 1003 | M = 0; |
---|
[f37467] | 1004 | |
---|
[d058ea] | 1005 | for(j = i-1; j > 0; j--) |
---|
[f37467] | 1006 | { |
---|
[d058ea] | 1007 | b = L[j]; |
---|
| 1008 | // "b: ", b; |
---|
| 1009 | |
---|
| 1010 | if( leadcomp(b) == c ) |
---|
| 1011 | { |
---|
| 1012 | bb = leadmonomial(b); |
---|
| 1013 | @lcm = lcm(aa, bb); |
---|
[f37467] | 1014 | |
---|
[d058ea] | 1015 | M[j] = (@lcm / aa)* gen(i) - (@lcm / bb)* gen(j); |
---|
| 1016 | } |
---|
[f37467] | 1017 | } |
---|
| 1018 | |
---|
[d058ea] | 1019 | M = simplify(M, 2); |
---|
[f37467] | 1020 | |
---|
[d058ea] | 1021 | // TODO: add quotient relations here... |
---|
| 1022 | S = S, M; |
---|
| 1023 | } |
---|
[f37467] | 1024 | |
---|
[d058ea] | 1025 | if( @TAILREDSYZ ) |
---|
| 1026 | { |
---|
| 1027 | // Make sure that 2nd syzygy terms are not reducible by 1st |
---|
| 1028 | def opts = option(get); |
---|
| 1029 | option(redSB); option(redTail); |
---|
| 1030 | S = std(S); // binomial module |
---|
| 1031 | option(set, opts); |
---|
| 1032 | // kill opts; |
---|
| 1033 | } else |
---|
| 1034 | { |
---|
| 1035 | S = simplify(S, 2 + 32); |
---|
| 1036 | } |
---|
[f37467] | 1037 | |
---|
[d058ea] | 1038 | S = MySort(S); |
---|
[f37467] | 1039 | |
---|
[d058ea] | 1040 | if( @DEBUG ) |
---|
[f37467] | 1041 | { |
---|
[d058ea] | 1042 | "SSCompute2LeadingSyzygyTerms::Syz(S): "; S; |
---|
[f37467] | 1043 | } |
---|
[74afe1f] | 1044 | |
---|
| 1045 | if( size(module(matrix(S) - matrix(SS))) > 0 ) |
---|
| 1046 | { |
---|
[8b368ff] | 1047 | "ERROR: SSCompute2LeadingSyzygyTerms: S != SS "; |
---|
[74afe1f] | 1048 | |
---|
| 1049 | "basering: "; |
---|
| 1050 | DetailedPrint(basering); |
---|
| 1051 | |
---|
| 1052 | "S: "; S; |
---|
| 1053 | DetailedPrint(S, 2); |
---|
| 1054 | "SS: "; SS; |
---|
| 1055 | DetailedPrint(SS, 2); |
---|
| 1056 | |
---|
| 1057 | "DIFF: "; |
---|
| 1058 | print(matrix(S) - matrix(SS)); |
---|
| 1059 | DetailedPrint(module(matrix(S) - matrix(SS)), 4); |
---|
| 1060 | $ |
---|
| 1061 | } |
---|
[d058ea] | 1062 | } |
---|
| 1063 | |
---|
| 1064 | module S2 = Tail(SS); |
---|
| 1065 | SS = lead(SS); // (C,lp) on base ring! |
---|
[f37467] | 1066 | |
---|
| 1067 | if( @DEBUG ) |
---|
| 1068 | { |
---|
[d058ea] | 1069 | "SSCompute2LeadingSyzygyTerms::Output: "; SS; S2; |
---|
[f37467] | 1070 | } |
---|
| 1071 | |
---|
[d058ea] | 1072 | attrib(SS, "isSB", 1); |
---|
[f37467] | 1073 | |
---|
[d058ea] | 1074 | return (SS, S2); |
---|
[8f57c0] | 1075 | } |
---|
| 1076 | |
---|
[f37467] | 1077 | // -------------------------------------------------------- // |
---|
| 1078 | |
---|
[b2fb0c] | 1079 | /// TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz? |
---|
| 1080 | proc SSFindReducer(def product, def syzterm, def L, def T, list #) |
---|
[8f57c0] | 1081 | { |
---|
[fdde6ce] | 1082 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1083 | { |
---|
| 1084 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1085 | } else |
---|
| 1086 | { |
---|
| 1087 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1088 | } |
---|
[4b2e47] | 1089 | |
---|
[b2fb0c] | 1090 | |
---|
[4b2e47] | 1091 | if( @DEBUG ) |
---|
| 1092 | { |
---|
[b2fb0c] | 1093 | "SSFindReducer::Input: "; |
---|
[4b2e47] | 1094 | |
---|
[b2fb0c] | 1095 | "syzterm: ", syzterm; |
---|
| 1096 | "product: ", product; |
---|
[4b2e47] | 1097 | "L: ", L; |
---|
| 1098 | "T: ", T; |
---|
[fdde6ce] | 1099 | if( size(#) > 0 ) |
---|
| 1100 | { |
---|
| 1101 | "LSyz: ", #; |
---|
| 1102 | } |
---|
[4b2e47] | 1103 | } |
---|
| 1104 | |
---|
[b2fb0c] | 1105 | |
---|
| 1106 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1107 | { |
---|
| 1108 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1109 | } else |
---|
| 1110 | { |
---|
| 1111 | int @SYZCHECK = @DEBUG; |
---|
| 1112 | } |
---|
| 1113 | |
---|
| 1114 | if( @SYZCHECK && (syzterm != 0) ) |
---|
[4b2e47] | 1115 | { |
---|
[b2fb0c] | 1116 | def @@c = leadcomp(syzterm); int @@r = int(@@c); |
---|
| 1117 | def @@product = leadmonomial(syzterm) * L[@@r]; |
---|
| 1118 | |
---|
| 1119 | if( @@product != product) |
---|
| 1120 | { |
---|
| 1121 | "product: ", product, ", @@product: ", @@product; |
---|
| 1122 | "ERROR: 'syzterm' results in wrong product !!!???"; |
---|
| 1123 | $ |
---|
| 1124 | } |
---|
[4b2e47] | 1125 | } |
---|
| 1126 | |
---|
[b2fb0c] | 1127 | // def product = m * t; |
---|
[8f57c0] | 1128 | |
---|
[b2fb0c] | 1129 | bigint c = leadcomp(product); int r = int(c); |
---|
| 1130 | |
---|
| 1131 | def a, b, bb; |
---|
[8f57c0] | 1132 | |
---|
[b2fb0c] | 1133 | vector nf = [0]; |
---|
| 1134 | |
---|
| 1135 | // looking for an appropriate diviser |
---|
[4b2e47] | 1136 | for( int k = ncols(L); k > 0; k-- ) |
---|
| 1137 | { |
---|
| 1138 | a = L[k]; |
---|
| 1139 | // with the same mod. component |
---|
| 1140 | if( leadcomp(a) == c ) |
---|
| 1141 | { |
---|
| 1142 | b = - (leadmonomial(product) / leadmonomial(L[k])); |
---|
[b2fb0c] | 1143 | |
---|
| 1144 | // which divides the product: looking for the 1st appropriate one! |
---|
[4b2e47] | 1145 | if( b != 0 ) |
---|
| 1146 | { |
---|
[f37467] | 1147 | bb = b * gen(k); |
---|
[b2fb0c] | 1148 | |
---|
| 1149 | if (size(bb + syzterm) == 0) // cannot allow something like: a*gen(i) - a*gen(i) |
---|
| 1150 | { |
---|
| 1151 | nf = [0]; |
---|
| 1152 | } else |
---|
| 1153 | { |
---|
| 1154 | nf = bb; |
---|
| 1155 | } |
---|
[4b2e47] | 1156 | |
---|
[b2fb0c] | 1157 | // new syz. term should not be in <LS = #> |
---|
[fdde6ce] | 1158 | if( size(#) > 0 ) |
---|
| 1159 | { |
---|
| 1160 | if( typeof(#[1]) == "module" ) |
---|
| 1161 | { |
---|
| 1162 | nf = NF(bb, #[1]); |
---|
| 1163 | } |
---|
| 1164 | } |
---|
| 1165 | |
---|
[4b2e47] | 1166 | // while the complement (the fraction) is not reducible by leading syzygies |
---|
[b2fb0c] | 1167 | if( nf != 0 ) // nf must be == bb!!! |
---|
[4b2e47] | 1168 | { |
---|
[fdde6ce] | 1169 | /// TODO: save shortcut LM(m) * T[i] -> ? |
---|
| 1170 | |
---|
| 1171 | // choose ANY such reduction... (with the biggest index?) |
---|
[4b2e47] | 1172 | break; |
---|
| 1173 | } |
---|
| 1174 | } |
---|
| 1175 | } |
---|
| 1176 | } |
---|
[b2fb0c] | 1177 | if( @DEBUG ) |
---|
| 1178 | { |
---|
| 1179 | "SSFindReducer::Output: ", nf; |
---|
| 1180 | } |
---|
| 1181 | return (nf); |
---|
| 1182 | } |
---|
| 1183 | |
---|
| 1184 | |
---|
| 1185 | |
---|
| 1186 | |
---|
| 1187 | |
---|
| 1188 | /// TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? |
---|
| 1189 | proc SSReduceTerm(poly m, def t, def syzterm, def L, def T, list #) |
---|
| 1190 | { |
---|
| 1191 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1192 | { |
---|
| 1193 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1194 | } else |
---|
| 1195 | { |
---|
| 1196 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1197 | } |
---|
| 1198 | |
---|
| 1199 | |
---|
| 1200 | if( @DEBUG ) |
---|
| 1201 | { |
---|
| 1202 | "SSReduce::Input: "; |
---|
| 1203 | |
---|
| 1204 | "syzterm: ", syzterm; |
---|
| 1205 | "mult: ", m; |
---|
| 1206 | "term: ", t; |
---|
| 1207 | "L: ", L; |
---|
| 1208 | "T: ", T; |
---|
| 1209 | if( size(#) > 0 ) |
---|
| 1210 | { |
---|
| 1211 | "LSyz: ", #; |
---|
| 1212 | } |
---|
| 1213 | // "attrib(LS, 'isSB')", attrib(LS, "isSB"); |
---|
| 1214 | } |
---|
| 1215 | |
---|
| 1216 | |
---|
| 1217 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1218 | { |
---|
| 1219 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1220 | } else |
---|
| 1221 | { |
---|
| 1222 | int @SYZCHECK = @DEBUG; |
---|
| 1223 | } |
---|
| 1224 | |
---|
| 1225 | if( @SYZCHECK && (syzterm != 0) ) |
---|
| 1226 | { |
---|
| 1227 | def @@c = leadcomp(syzterm); int @@r = int(@@c); |
---|
| 1228 | poly @@m = leadmonomial(syzterm); def @@t = L[@@r]; |
---|
| 1229 | |
---|
| 1230 | if( (@@m != m) || (@@t != t)) |
---|
| 1231 | { |
---|
| 1232 | "m: ", m, ", t: ", t; |
---|
| 1233 | "@@m: ", @@m, ", @@t: ", @@t; |
---|
| 1234 | "ERROR: 'syzterm' results in wrong m * t !!!"; |
---|
| 1235 | $ |
---|
| 1236 | } |
---|
| 1237 | } |
---|
| 1238 | |
---|
| 1239 | vector s = [0]; |
---|
| 1240 | |
---|
| 1241 | if( size(t) > 0 ) |
---|
| 1242 | { |
---|
| 1243 | def product = m * t; |
---|
| 1244 | |
---|
| 1245 | s = SSFindReducer(product, syzterm, L, T, #); |
---|
| 1246 | |
---|
| 1247 | if( size(s) != 0 ) |
---|
| 1248 | { |
---|
| 1249 | poly b = leadmonomial(s); |
---|
| 1250 | |
---|
| 1251 | def c = leadcomp(s); int k = int(c); |
---|
| 1252 | |
---|
| 1253 | s = s + SSTraverseTail(b, T[k], L, T, #); // !!! |
---|
| 1254 | } |
---|
| 1255 | } |
---|
| 1256 | |
---|
[4b2e47] | 1257 | if( @DEBUG ) |
---|
| 1258 | { |
---|
[fdde6ce] | 1259 | "SSReduceTerm::Output: ", s; |
---|
[4b2e47] | 1260 | } |
---|
[b2fb0c] | 1261 | |
---|
[4b2e47] | 1262 | return (s); |
---|
[8f57c0] | 1263 | } |
---|
| 1264 | |
---|
[b2fb0c] | 1265 | |
---|
[fdde6ce] | 1266 | // TODO: store m * @tail -.-^-.-^-.--> ? |
---|
| 1267 | proc SSTraverseTail(poly m, def @tail, def L, def T, list #) |
---|
[4b2e47] | 1268 | { |
---|
[fdde6ce] | 1269 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1270 | { |
---|
| 1271 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1272 | } else |
---|
| 1273 | { |
---|
| 1274 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1275 | } |
---|
[4b2e47] | 1276 | |
---|
| 1277 | if( @DEBUG ) |
---|
| 1278 | { |
---|
| 1279 | "SSTraverse::Input: "; |
---|
[8f57c0] | 1280 | |
---|
[4b2e47] | 1281 | "mult: ", m; |
---|
[fdde6ce] | 1282 | "tail: ", @tail; // T[i]; |
---|
[4b2e47] | 1283 | |
---|
[fdde6ce] | 1284 | if( size(#) > 0 ) |
---|
| 1285 | { |
---|
| 1286 | "LSyz: "; #[1]; |
---|
| 1287 | } |
---|
[4b2e47] | 1288 | } |
---|
| 1289 | |
---|
| 1290 | vector s = 0; |
---|
| 1291 | |
---|
[fdde6ce] | 1292 | def @l; |
---|
| 1293 | |
---|
| 1294 | // iterate tail-terms in ANY order! |
---|
[4b2e47] | 1295 | while( size(@tail) > 0 ) |
---|
| 1296 | { |
---|
| 1297 | @l = lead(@tail); |
---|
[b2fb0c] | 1298 | s = s + SSReduceTerm(m, @l, [0], L, T, #); // :( |
---|
[4b2e47] | 1299 | @tail = @tail - @l; |
---|
| 1300 | } |
---|
| 1301 | |
---|
| 1302 | if( @DEBUG ) |
---|
| 1303 | { |
---|
[fdde6ce] | 1304 | "SSTraverseTail::Output: ", s; |
---|
[4b2e47] | 1305 | } |
---|
| 1306 | return (s); |
---|
| 1307 | } |
---|
[8f57c0] | 1308 | |
---|
[f37467] | 1309 | // -------------------------------------------------------- // |
---|
| 1310 | |
---|
| 1311 | // module (N, LL, TT) = SSComputeSyzygy(L, T); |
---|
| 1312 | // Compute Syz(L ++ T) = N = LL ++ TT |
---|
[fdde6ce] | 1313 | proc SSComputeSyzygy(def L, def T) |
---|
[6b6c82] | 1314 | { |
---|
[fdde6ce] | 1315 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1316 | { |
---|
| 1317 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1318 | } else |
---|
| 1319 | { |
---|
| 1320 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1321 | } |
---|
[8e650e] | 1322 | |
---|
| 1323 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1324 | { |
---|
| 1325 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1326 | } else |
---|
| 1327 | { |
---|
| 1328 | int @SYZCHECK = @DEBUG; |
---|
| 1329 | } |
---|
[8b368ff] | 1330 | |
---|
[fdde6ce] | 1331 | |
---|
[6b6c82] | 1332 | if( @DEBUG ) |
---|
| 1333 | { |
---|
| 1334 | "SSComputeSyzygy::Input"; |
---|
| 1335 | "basering: ", basering; attrib(basering); |
---|
| 1336 | // DetailedPrint(basering); |
---|
| 1337 | |
---|
[f37467] | 1338 | // "iCompShift: ", iCompShift; |
---|
[6b6c82] | 1339 | |
---|
| 1340 | "L: "; L; |
---|
| 1341 | "T: "; T; |
---|
| 1342 | } |
---|
| 1343 | |
---|
[fdde6ce] | 1344 | def a; bigint c; int r, k; poly aa; |
---|
[f37467] | 1345 | |
---|
[fdde6ce] | 1346 | int @LEAD2SYZ = 0; |
---|
| 1347 | if( typeof( attrib(basering, "LEAD2SYZ") ) == "int" ) |
---|
| 1348 | { |
---|
| 1349 | @LEAD2SYZ = attrib(basering, "LEAD2SYZ"); |
---|
| 1350 | } |
---|
[f37467] | 1351 | |
---|
[fdde6ce] | 1352 | int @TAILREDSYZ = 1; |
---|
| 1353 | if( typeof( attrib(basering, "TAILREDSYZ") ) == "int" ) |
---|
| 1354 | { |
---|
| 1355 | @TAILREDSYZ = attrib(basering, "TAILREDSYZ"); |
---|
| 1356 | } |
---|
[7b7c2c] | 1357 | |
---|
[b2fb0c] | 1358 | int @HYBRIDNF = 0; |
---|
| 1359 | if( typeof( attrib(basering, "HYBRIDNF") ) == "int" ) |
---|
| 1360 | { |
---|
| 1361 | @HYBRIDNF = attrib(basering, "HYBRIDNF"); |
---|
| 1362 | } |
---|
| 1363 | |
---|
| 1364 | module LL; |
---|
| 1365 | def a2; int r2; poly aa2; |
---|
| 1366 | |
---|
[fdde6ce] | 1367 | /// Get the critical leading syzygy terms |
---|
| 1368 | if( @LEAD2SYZ ) // & 2nd syz. term |
---|
| 1369 | { |
---|
[b2fb0c] | 1370 | module LL2; |
---|
[74afe1f] | 1371 | (LL, LL2) = SSCompute2LeadingSyzygyTerms(L); // ++ |
---|
[fdde6ce] | 1372 | } else |
---|
| 1373 | { |
---|
[b2fb0c] | 1374 | LL = SSComputeLeadingSyzygyTerms(L); |
---|
[fdde6ce] | 1375 | } |
---|
[4b2e47] | 1376 | |
---|
[b2fb0c] | 1377 | module TT, SYZ; def spoly; |
---|
[4b2e47] | 1378 | |
---|
| 1379 | if( size(LL) > 0 ) |
---|
[fdde6ce] | 1380 | { |
---|
| 1381 | list LS; |
---|
| 1382 | |
---|
[b2fb0c] | 1383 | if( @TAILREDSYZ) |
---|
[fdde6ce] | 1384 | { |
---|
| 1385 | LS = list(LL); |
---|
| 1386 | } |
---|
[b2fb0c] | 1387 | |
---|
[4b2e47] | 1388 | vector @tail; |
---|
[8f57c0] | 1389 | |
---|
[4b2e47] | 1390 | for(k = ncols(LL); k > 0; k-- ) |
---|
| 1391 | { |
---|
[f37467] | 1392 | // leading syz. term: |
---|
| 1393 | a = LL[k]; c = leadcomp(a); r = int(c); aa = leadmonomial(a); |
---|
[fdde6ce] | 1394 | // "A: ", a, " --->>>> ", aa, " **** [", r, "]: "; |
---|
[4b2e47] | 1395 | |
---|
[b2fb0c] | 1396 | // NF reduction: |
---|
| 1397 | if( !@HYBRIDNF ) |
---|
| 1398 | { |
---|
| 1399 | /// TODO: save shortcut (aa) * T[r] -> ? |
---|
| 1400 | @tail = SSTraverseTail(aa, T[r], L, T, LS); |
---|
| 1401 | // // @tail = SSTraverseTail(a, L, T, LS); |
---|
| 1402 | |
---|
| 1403 | // get the 2nd syzygy term... |
---|
| 1404 | |
---|
| 1405 | if( @LEAD2SYZ ) // with the 2nd syz. term: |
---|
| 1406 | { |
---|
| 1407 | a2 = LL2[k]; c = leadcomp(a2); r2 = int(c); aa2 = leadmonomial(a2); |
---|
| 1408 | |
---|
| 1409 | @tail = @tail + a2 + |
---|
| 1410 | /// TODO: save shortcut (aa2) * T[r2] -> ? |
---|
| 1411 | SSTraverseTail(aa2, T[r2], L, T, LS); |
---|
| 1412 | // // SSTraverseTail(a2, L, T, LS); |
---|
| 1413 | } else |
---|
| 1414 | { |
---|
| 1415 | @tail = @tail + |
---|
| 1416 | SSReduceTerm(aa, L[r], a, L, T, LS); |
---|
| 1417 | // // SSReduceTerm(a, L, T, LS); |
---|
| 1418 | } |
---|
[fdde6ce] | 1419 | } else |
---|
| 1420 | { |
---|
[b2fb0c] | 1421 | spoly = aa * T[r]; |
---|
| 1422 | |
---|
| 1423 | if( @LEAD2SYZ ) |
---|
| 1424 | { |
---|
| 1425 | a2 = LL2[k]; |
---|
| 1426 | } else |
---|
| 1427 | { |
---|
| 1428 | a2 = SSFindReducer( aa * L[r], a, L, T, LS); |
---|
| 1429 | } |
---|
| 1430 | |
---|
| 1431 | if ( (@SYZCHECK || @DEBUG) ) |
---|
| 1432 | { |
---|
| 1433 | if( size(a2) == 0 ) // if syzterm == 0!!!! |
---|
| 1434 | { |
---|
| 1435 | "ERROR: could not find the 2nd syzygy term during the hybrid NF!!!"; |
---|
| 1436 | $ |
---|
| 1437 | } |
---|
| 1438 | } |
---|
| 1439 | |
---|
| 1440 | c = leadcomp(a2); r2 = int(c); aa2 = leadmonomial(a2); |
---|
| 1441 | |
---|
| 1442 | spoly = spoly + aa2 * T[r2]; |
---|
| 1443 | @tail = a2; |
---|
| 1444 | |
---|
| 1445 | while (size(spoly) > 0) |
---|
| 1446 | { |
---|
| 1447 | a2 = SSFindReducer( lead(spoly), [0], L, T, LS); |
---|
| 1448 | spoly = Tail(spoly); |
---|
| 1449 | |
---|
| 1450 | if( size(a2) != 0) |
---|
| 1451 | { |
---|
| 1452 | c = leadcomp(a2); r2 = int(c); aa2 = leadmonomial(a2); |
---|
| 1453 | |
---|
| 1454 | spoly = spoly + aa2 * T[r2]; |
---|
| 1455 | @tail = @tail + a2; |
---|
| 1456 | } |
---|
| 1457 | } |
---|
| 1458 | |
---|
| 1459 | } |
---|
[f37467] | 1460 | |
---|
[4b2e47] | 1461 | TT[k] = @tail; |
---|
| 1462 | SYZ[k] = a + @tail; |
---|
| 1463 | } |
---|
[8f57c0] | 1464 | } |
---|
[6b6c82] | 1465 | |
---|
| 1466 | if( @DEBUG ) |
---|
| 1467 | { |
---|
| 1468 | "SSComputeSyzygy::Output"; |
---|
| 1469 | |
---|
| 1470 | "SYZ: "; SYZ; |
---|
| 1471 | "LL: "; LL; |
---|
| 1472 | "TT: "; TT; |
---|
| 1473 | } |
---|
| 1474 | |
---|
| 1475 | return (SYZ, LL, TT); |
---|
| 1476 | } |
---|
| 1477 | |
---|
| 1478 | // resolution/syzygy step: |
---|
| 1479 | static proc SSstep() |
---|
| 1480 | { |
---|
[b0ca43c] | 1481 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1482 | { |
---|
| 1483 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1484 | } else |
---|
| 1485 | { |
---|
| 1486 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1487 | } |
---|
| 1488 | |
---|
| 1489 | |
---|
| 1490 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1491 | { |
---|
| 1492 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1493 | } else |
---|
| 1494 | { |
---|
| 1495 | int @SYZCHECK = @DEBUG; |
---|
| 1496 | } |
---|
[6b6c82] | 1497 | |
---|
| 1498 | if( @DEBUG ) |
---|
| 1499 | { |
---|
| 1500 | "SSstep::NextInducedRing"; |
---|
| 1501 | "basering: ", basering; attrib(basering); |
---|
| 1502 | } |
---|
| 1503 | |
---|
| 1504 | /* |
---|
| 1505 | // is initial weights are all zeroes! |
---|
| 1506 | def L = lead(M); |
---|
| 1507 | intvec @V = deg(M[1..ncols(M)]); @W; @V; @W = @V; attrib(L, "isHomog", @W); |
---|
| 1508 | SetInducedReferrence(L, @RANK, 0); |
---|
| 1509 | */ |
---|
| 1510 | |
---|
| 1511 | // def L = lead(MRES); |
---|
| 1512 | // @W = @W, @V; |
---|
| 1513 | // attrib(L, "isHomog", @W); |
---|
| 1514 | |
---|
| 1515 | |
---|
| 1516 | // General setting: |
---|
| 1517 | // SetInducedReferrence(MRES, 0, 0); // limit: 0! |
---|
| 1518 | int @l = size(RES); |
---|
| 1519 | |
---|
| 1520 | def M = RES[@l]; |
---|
| 1521 | |
---|
| 1522 | def L = LRES[@l]; |
---|
| 1523 | def T = TRES[@l]; |
---|
| 1524 | |
---|
| 1525 | |
---|
| 1526 | //// TODO: wrong !!!!! |
---|
| 1527 | int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?! |
---|
| 1528 | |
---|
| 1529 | |
---|
| 1530 | |
---|
| 1531 | /* |
---|
| 1532 | if( @RANK != nrows(M) ) |
---|
| 1533 | { |
---|
| 1534 | type(MRES); |
---|
| 1535 | @RANK; |
---|
| 1536 | type(M); |
---|
| 1537 | pause(); |
---|
| 1538 | } |
---|
| 1539 | */ |
---|
| 1540 | |
---|
| 1541 | intvec @W = attrib(M, "isHomog"); intvec @V = attrib(M, "degrees"); @V = @W, @V; |
---|
| 1542 | |
---|
| 1543 | if( @DEBUG ) |
---|
| 1544 | { |
---|
| 1545 | "Sstep::NextInput: "; |
---|
| 1546 | M; |
---|
| 1547 | L; |
---|
| 1548 | @V; |
---|
| 1549 | @RANK; |
---|
[4b2e47] | 1550 | // DetailedPrint(MRES); |
---|
[6b6c82] | 1551 | attrib(MRES, "isHomog"); |
---|
| 1552 | } |
---|
| 1553 | |
---|
| 1554 | |
---|
| 1555 | // TODO: N = SYZ( M )!!! |
---|
[f37467] | 1556 | module N, LL, TT; |
---|
| 1557 | (N, LL, TT) = SSComputeSyzygy(/*M, */L, T/*, @RANK*/); |
---|
| 1558 | |
---|
| 1559 | // shift syz.comp by @RANK: |
---|
| 1560 | module Z; |
---|
| 1561 | Z = 0; Z[@RANK] = 0; Z = Z, transpose(LL); LL = transpose(Z); |
---|
| 1562 | Z = 0; Z[@RANK] = 0; Z = Z, transpose(TT); TT = transpose(Z); |
---|
| 1563 | Z = 0; Z[@RANK] = 0; Z = Z, transpose(N); N = transpose(Z); |
---|
[6b6c82] | 1564 | |
---|
| 1565 | |
---|
[b0ca43c] | 1566 | if( @SYZCHECK ) |
---|
[6b6c82] | 1567 | { |
---|
[b0ca43c] | 1568 | if( size(N) > 0 ) |
---|
[6b6c82] | 1569 | { |
---|
[f37467] | 1570 | // next syz. property |
---|
| 1571 | if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 ) |
---|
| 1572 | { |
---|
| 1573 | "MRES", MRES; |
---|
[6b6c82] | 1574 | |
---|
[f37467] | 1575 | "N: "; N; // DetailedPrint(N, 2); |
---|
[6b6c82] | 1576 | |
---|
[f37467] | 1577 | "LL:"; LL; // DetailedPrint(LL, 1); |
---|
| 1578 | "TT:"; TT; // DetailedPrint(TT, 10); |
---|
[6b6c82] | 1579 | |
---|
[f37467] | 1580 | "RANKS: ", @RANK; |
---|
[6b6c82] | 1581 | |
---|
[f37467] | 1582 | "transpose( transpose(N) * transpose(MRES) ) != 0!!!"; |
---|
| 1583 | transpose( transpose(N) * transpose(MRES) ); |
---|
[6b6c82] | 1584 | |
---|
[f37467] | 1585 | "transpose(N) * transpose(MRES): "; |
---|
| 1586 | transpose(N) * transpose(MRES); |
---|
| 1587 | // DetailedPrint(module(_), 2); |
---|
| 1588 | $ |
---|
| 1589 | } |
---|
[6b6c82] | 1590 | } |
---|
| 1591 | } |
---|
[f37467] | 1592 | |
---|
| 1593 | attrib(N, "isHomog", @V); |
---|
| 1594 | |
---|
| 1595 | // TODO: correct the following: |
---|
| 1596 | intvec @DEGS = deg(N[1..ncols(N)]); // no mod. comp. weights :( |
---|
| 1597 | |
---|
| 1598 | |
---|
| 1599 | attrib(N, "degrees", @DEGS); |
---|
[6b6c82] | 1600 | |
---|
| 1601 | RES[@l + 1] = N; // list of all syzygy modules |
---|
| 1602 | LRES[@l + 1] = LL; // list of all syzygy modules |
---|
| 1603 | TRES[@l + 1] = TT; // list of all syzygy modules |
---|
| 1604 | |
---|
| 1605 | MRES = MRES, N; |
---|
[f37467] | 1606 | |
---|
[6b6c82] | 1607 | attrib(MRES, "isHomog", @V); |
---|
| 1608 | |
---|
| 1609 | // L = L, lead(N); attrib(basering, "InducionLeads", L); |
---|
| 1610 | |
---|
| 1611 | if( @DEBUG ) |
---|
| 1612 | { |
---|
| 1613 | "SSstep::NextSyzOutput: "; |
---|
[f37467] | 1614 | N; |
---|
[4b2e47] | 1615 | // DetailedPrint(N); |
---|
[6b6c82] | 1616 | attrib(N); |
---|
| 1617 | } |
---|
| 1618 | |
---|
| 1619 | } |
---|
| 1620 | |
---|
| 1621 | proc SScontinue(int l) |
---|
| 1622 | "USAGE: SScontinue(l) |
---|
| 1623 | RETURN: nothing, instead it changes RES and MRES variables in the current ring |
---|
| 1624 | PURPOSE: computes further (at most l) syzygies |
---|
| 1625 | NOTE: must be used within a ring returned by Sres or Ssyz. RES and MRES are |
---|
| 1626 | explained in Sres |
---|
| 1627 | EXAMPLE: example Scontinue; shows an example |
---|
| 1628 | " |
---|
| 1629 | { |
---|
| 1630 | |
---|
| 1631 | /// TODO! |
---|
| 1632 | // def data = GetInducedData(); |
---|
| 1633 | |
---|
| 1634 | if( (!defined(RES)) || (!defined(MRES)) ) /* || (typeof(data) != "list") || (size(data) != 2) */ |
---|
| 1635 | { |
---|
| 1636 | ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz"); |
---|
| 1637 | } |
---|
| 1638 | for (; (l != 0) && (size(RES[size(RES)]) > 0); l-- ) |
---|
| 1639 | { |
---|
| 1640 | SSstep(); |
---|
| 1641 | } |
---|
| 1642 | } |
---|
| 1643 | example |
---|
| 1644 | { "EXAMPLE:"; echo = 2; |
---|
| 1645 | ring r; |
---|
| 1646 | module M = maxideal(1); M; |
---|
| 1647 | def S = SSsyz(M); setring S; S; |
---|
| 1648 | "Only the first syzygy: "; |
---|
| 1649 | RES; MRES; |
---|
| 1650 | "More syzygies: "; |
---|
| 1651 | SScontinue(10); |
---|
| 1652 | RES; MRES; |
---|
| 1653 | } |
---|
| 1654 | |
---|
| 1655 | proc SSsyz(def M) |
---|
| 1656 | "USAGE: SSsyz(M) |
---|
| 1657 | RETURN: ring, containing a list of modules RES and a module MRES |
---|
| 1658 | PURPOSE: computes the first syzygy module of M (wrt some Schreyer ordering)? |
---|
| 1659 | NOTE: The output is explained in Sres |
---|
| 1660 | EXAMPLE: example Ssyz; shows an example |
---|
| 1661 | " |
---|
| 1662 | { |
---|
| 1663 | if( (typeof(M) != "module") && (typeof(M) != "ideal") ) |
---|
| 1664 | { |
---|
| 1665 | ERROR("Sorry: need an ideal or a module for input"); |
---|
| 1666 | } |
---|
| 1667 | |
---|
| 1668 | def SS = SSinit(M); setring SS; |
---|
| 1669 | |
---|
| 1670 | SSstep(); // NOTE: what if M is zero? |
---|
| 1671 | |
---|
| 1672 | return (SS); |
---|
| 1673 | } |
---|
| 1674 | example |
---|
| 1675 | { "EXAMPLE:"; echo = 2; |
---|
| 1676 | ring r; |
---|
| 1677 | |
---|
| 1678 | /* ideal M = 0; |
---|
| 1679 | def S = SSsyz(M); setring S; S; |
---|
| 1680 | "Only the first syzygy: "; |
---|
| 1681 | RES; LRES; TRES; |
---|
| 1682 | MRES; |
---|
| 1683 | |
---|
| 1684 | kill S; setring r; kill M; |
---|
| 1685 | */ |
---|
| 1686 | |
---|
[7b7c2c] | 1687 | ideal M = maxideal(1); M; |
---|
[b2fb0c] | 1688 | |
---|
[4b2e47] | 1689 | def S = SSres(M, 0); setring S; S; |
---|
[6b6c82] | 1690 | MRES; |
---|
[8b368ff] | 1691 | print(_); |
---|
[f37467] | 1692 | RES; |
---|
[6b6c82] | 1693 | |
---|
| 1694 | kill S; setring r; kill M; |
---|
| 1695 | |
---|
| 1696 | kill r; |
---|
| 1697 | |
---|
| 1698 | ring R = 0, (w, x, y, z), dp; |
---|
| 1699 | ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; |
---|
| 1700 | |
---|
[4b2e47] | 1701 | def S = SSres(M, 0); setring S; S; |
---|
[f37467] | 1702 | ""; |
---|
| 1703 | LRES; |
---|
| 1704 | ""; |
---|
[8b368ff] | 1705 | TRES; |
---|
| 1706 | ""; |
---|
| 1707 | MRES; |
---|
| 1708 | print(_); |
---|
| 1709 | RES; |
---|
[6b6c82] | 1710 | } |
---|
| 1711 | |
---|
| 1712 | proc SSres(def M, int l) |
---|
| 1713 | "USAGE: SSres(I, l) |
---|
| 1714 | RETURN: ring, containing a list of modules RES and a module MRES |
---|
| 1715 | PURPOSE: computes (at most l) syzygy modules of M wrt the classical Schreyer |
---|
| 1716 | induced ordering with gen(i) > gen(j) if i > j, provided both gens |
---|
| 1717 | are from the same syzygy level.??? |
---|
| 1718 | NOTE: RES contains the images of maps subsituting the beginning of the |
---|
| 1719 | Schreyer free resolution of baseRing^r/M, while MRES is a sum of |
---|
| 1720 | these images in a big free sum, containing all the syzygy modules. |
---|
| 1721 | The syzygy modules are shifted so that gen(i) correspons to MRES[i]. |
---|
| 1722 | The leading zero module RES[0] indicates the fact that coker of the |
---|
| 1723 | first map is zero. The number of zeroes inducates the rank of input. |
---|
| 1724 | NOTE: If l == 0 then l is set to be nvars(basering) + 1 |
---|
| 1725 | EXAMPLE: example SSres; shows an example |
---|
| 1726 | " |
---|
| 1727 | { |
---|
| 1728 | if( (typeof(M) != "module") && (typeof(M) != "ideal") ) |
---|
| 1729 | { |
---|
| 1730 | ERROR("Sorry: need an ideal or a module for input"); |
---|
| 1731 | } |
---|
| 1732 | |
---|
| 1733 | def SS = SSinit(M); setring SS; |
---|
| 1734 | |
---|
| 1735 | if (l == 0) |
---|
| 1736 | { |
---|
| 1737 | l = nvars(basering) + 1; // not really an estimate...?! |
---|
| 1738 | } |
---|
| 1739 | |
---|
| 1740 | SSstep(); l = l - 1; |
---|
| 1741 | |
---|
| 1742 | SScontinue(l); |
---|
| 1743 | |
---|
| 1744 | return (SS); |
---|
| 1745 | } |
---|
| 1746 | example |
---|
| 1747 | { "EXAMPLE:"; echo = 2; |
---|
| 1748 | ring r; |
---|
| 1749 | module M = maxideal(1); M; |
---|
| 1750 | def S = SSres(M, 0); setring S; S; |
---|
| 1751 | RES; |
---|
| 1752 | MRES; |
---|
| 1753 | kill S; |
---|
| 1754 | setring r; kill M; |
---|
| 1755 | |
---|
| 1756 | def A = nc_algebra(-1,0); setring A; |
---|
| 1757 | ideal Q = var(1)^2, var(2)^2, var(3)^2; |
---|
| 1758 | qring SCA = twostd(Q); |
---|
| 1759 | basering; |
---|
| 1760 | |
---|
| 1761 | module M = maxideal(1); |
---|
| 1762 | def S = SSres(M, 2); setring S; S; |
---|
| 1763 | RES; |
---|
| 1764 | MRES; |
---|
| 1765 | } |
---|
| 1766 | |
---|
| 1767 | |
---|
[4c6c938] | 1768 | |
---|
| 1769 | static proc loadme() |
---|
| 1770 | { |
---|
| 1771 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1772 | |
---|
| 1773 | if( @DEBUG ) |
---|
| 1774 | { |
---|
| 1775 | |
---|
| 1776 | "ndebug?: ", system("with", "ndebug"); |
---|
| 1777 | "om_ndebug?: ", system("with", "om_ndebug"); |
---|
| 1778 | |
---|
| 1779 | listvar(Top); |
---|
| 1780 | listvar(Schreyer); |
---|
| 1781 | } |
---|
| 1782 | // listvar(Syzextra); listvar(Syzextra_g); |
---|
| 1783 | |
---|
| 1784 | if( !defined(DetailedPrint) ) |
---|
| 1785 | { |
---|
[b5d6f0] | 1786 | if( 1 ) |
---|
[4c6c938] | 1787 | { |
---|
| 1788 | |
---|
| 1789 | if( @DEBUG ) |
---|
| 1790 | { |
---|
| 1791 | "Loading the Release version!"; |
---|
| 1792 | } |
---|
| 1793 | load("syzextra.so"); |
---|
| 1794 | |
---|
| 1795 | if( @DEBUG ) |
---|
| 1796 | { |
---|
| 1797 | listvar(Syzextra); |
---|
| 1798 | } |
---|
[ff12c6] | 1799 | |
---|
| 1800 | exportto(Top, Syzextra::ClearContent); |
---|
| 1801 | exportto(Top, Syzextra::ClearDenominators); |
---|
[7b7c2c] | 1802 | |
---|
| 1803 | exportto(Schreyer, Syzextra::m2_end); |
---|
[4c6c938] | 1804 | |
---|
| 1805 | // export Syzextra; |
---|
| 1806 | |
---|
| 1807 | // exportto(Schreyer, Syzextra::noop); |
---|
| 1808 | exportto(Schreyer, Syzextra::DetailedPrint); |
---|
[4b2e47] | 1809 | exportto(Schreyer, Syzextra::leadmonomial); |
---|
[4c6c938] | 1810 | exportto(Schreyer, Syzextra::leadcomp); |
---|
| 1811 | // exportto(Schreyer, Syzextra::leadrawexp); |
---|
| 1812 | // exportto(Schreyer, Syzextra::ISUpdateComponents); |
---|
| 1813 | exportto(Schreyer, Syzextra::SetInducedReferrence); |
---|
| 1814 | exportto(Schreyer, Syzextra::GetInducedData); |
---|
[71e402] | 1815 | // exportto(Schreyer, Syzextra::GetAMData); |
---|
[4c6c938] | 1816 | // exportto(Schreyer, Syzextra::SetSyzComp); |
---|
| 1817 | exportto(Schreyer, Syzextra::MakeInducedSchreyerOrdering); |
---|
| 1818 | // exportto(Schreyer, Syzextra::MakeSyzCompOrdering); |
---|
| 1819 | exportto(Schreyer, Syzextra::idPrepare); |
---|
| 1820 | // exportto(Schreyer, Syzextra::reduce_syz); |
---|
| 1821 | // exportto(Schreyer, Syzextra::p_Content); |
---|
| 1822 | |
---|
[f63b13] | 1823 | exportto(Schreyer, Syzextra::ProfilerStart); exportto(Schreyer, Syzextra::ProfilerStop); |
---|
| 1824 | |
---|
[e89ff5] | 1825 | exportto(Schreyer, Syzextra::Tail); |
---|
[7b7c2c] | 1826 | exportto(Schreyer, Syzextra::ComputeLeadingSyzygyTerms); |
---|
[74afe1f] | 1827 | exportto(Schreyer, Syzextra::Compute2LeadingSyzygyTerms); |
---|
[8b78ee] | 1828 | exportto(Schreyer, Syzextra::Sort_c_ds); |
---|
[4c6c938] | 1829 | } |
---|
[b5d6f0] | 1830 | /* |
---|
[4c6c938] | 1831 | else |
---|
| 1832 | { |
---|
| 1833 | if( @DEBUG ) |
---|
| 1834 | { |
---|
| 1835 | "Loading the Debug version!"; |
---|
| 1836 | } |
---|
| 1837 | |
---|
[b5d6f0] | 1838 | load("syzextra.so"); |
---|
[4c6c938] | 1839 | |
---|
| 1840 | if( @DEBUG ) |
---|
| 1841 | { |
---|
| 1842 | listvar(Syzextra_g); |
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| 1843 | } |
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| 1844 | |
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[ff12c6] | 1845 | exportto(Top, Syzextra_g::ClearContent); |
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| 1846 | exportto(Top, Syzextra_g::ClearDenominators); |
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| 1847 | |
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[7b7c2c] | 1848 | exportto(Schreyer, Syzextra_g::m2_end); |
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| 1849 | |
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[4c6c938] | 1850 | // export Syzextra_g; |
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| 1851 | // exportto(Schreyer, Syzextra_g::noop); |
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| 1852 | exportto(Schreyer, Syzextra_g::DetailedPrint); |
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[4b2e47] | 1853 | exportto(Schreyer, Syzextra_g::leadmonomial); |
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[4c6c938] | 1854 | exportto(Schreyer, Syzextra_g::leadcomp); |
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| 1855 | // exportto(Schreyer, Syzextra_g::leadrawexp); |
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| 1856 | // exportto(Schreyer, Syzextra_g::ISUpdateComponents); |
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| 1857 | exportto(Schreyer, Syzextra_g::SetInducedReferrence); |
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| 1858 | exportto(Schreyer, Syzextra_g::GetInducedData); |
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[71e402] | 1859 | // exportto(Schreyer, Syzextra_g::GetAMData); |
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[4c6c938] | 1860 | // exportto(Schreyer, Syzextra_g::SetSyzComp); |
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| 1861 | exportto(Schreyer, Syzextra_g::MakeInducedSchreyerOrdering); |
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| 1862 | // exportto(Schreyer, Syzextra_g::MakeSyzCompOrdering); |
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| 1863 | exportto(Schreyer, Syzextra_g::idPrepare); |
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| 1864 | // exportto(Schreyer, Syzextra_g::reduce_syz); |
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| 1865 | // exportto(Schreyer, Syzextra_g::p_Content); |
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| 1866 | |
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[f63b13] | 1867 | exportto(Schreyer, Syzextra_g::ProfilerStart); exportto(Schreyer, Syzextra_g::ProfilerStop); |
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| 1868 | |
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[e89ff5] | 1869 | exportto(Schreyer, Syzextra_g::Tail); |
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[8b78ee] | 1870 | exportto(Schreyer, Syzextra_g::ComputeLeadingSyzygyTerms); |
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[74afe1f] | 1871 | exportto(Schreyer, Syzextra_g::Compute2LeadingSyzygyTerms); |
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[8b78ee] | 1872 | exportto(Schreyer, Syzextra_g::Sort_c_ds); |
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| 1873 | |
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[4c6c938] | 1874 | } |
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[b5d6f0] | 1875 | */ |
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[4c6c938] | 1876 | |
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| 1877 | exportto(Top, DetailedPrint); |
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| 1878 | exportto(Top, GetInducedData); |
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| 1879 | |
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| 1880 | if( @DEBUG ) |
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| 1881 | { |
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| 1882 | listvar(Top); |
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| 1883 | listvar(Schreyer); |
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| 1884 | } |
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| 1885 | } |
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| 1886 | |
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| 1887 | if( !defined(GetInducedData) ) |
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| 1888 | { |
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[b5d6f0] | 1889 | ERROR("Sorry but we are missing the dynamic module (syzextra.so)..."); |
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[4c6c938] | 1890 | } |
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| 1891 | |
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| 1892 | } |
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| 1893 | |
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| 1894 | static proc mod_init() |
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| 1895 | { |
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| 1896 | loadme(); |
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| 1897 | } |
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| 1898 | |
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| 1899 | |
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| 1900 | proc testallSexamples() |
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| 1901 | { |
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| 1902 | example Ssyz; |
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| 1903 | example Scontinue; |
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| 1904 | example Sres; |
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| 1905 | } |
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[6b6c82] | 1906 | |
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| 1907 | proc testallSSexamples() |
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| 1908 | { |
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| 1909 | example SSsyz; |
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| 1910 | example SScontinue; |
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| 1911 | example SSres; |
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| 1912 | } |
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| 1913 | |
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[4c6c938] | 1914 | example |
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| 1915 | { "EXAMPLE:"; echo = 2; |
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| 1916 | testallSexamples(); |
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[6b6c82] | 1917 | testallSSexamples(); |
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[ff12c6] | 1918 | } |
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[c1931a4] | 1919 | |
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| 1920 | proc TestSSres(def M) |
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| 1921 | { |
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| 1922 | "-------------------------------------"; |
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| 1923 | "options: ", attrib(SSinit, "LEAD2SYZ"), attrib(SSinit, "TAILREDSYZ"), attrib(SSinit, "HYBRIDNF"), ": "; |
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| 1924 | int t = timer; |
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| 1925 | def S = SSres(M, 0); |
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| 1926 | int tt = timer; |
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| 1927 | /* |
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| 1928 | setring S; |
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| 1929 | |
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| 1930 | MRES; |
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| 1931 | RES; |
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| 1932 | ""; |
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| 1933 | LRES; |
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| 1934 | ""; |
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| 1935 | TRES; |
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| 1936 | */ |
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| 1937 | kill S; |
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| 1938 | "0-----------------------------------0 => ", tt - t; |
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| 1939 | } |
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| 1940 | |
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| 1941 | |
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| 1942 | proc TestSSresAttribs(def M) |
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| 1943 | { |
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| 1944 | |
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| 1945 | // the following 2 setups are bad for AGR@101n3d002s004%1:((( |
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| 1946 | // attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
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| 1947 | // attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
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| 1948 | |
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| 1949 | attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
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| 1950 | attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
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| 1951 | |
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| 1952 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
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| 1953 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
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| 1954 | |
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| 1955 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
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| 1956 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
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| 1957 | } |
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| 1958 | |
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| 1959 | |
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| 1960 | proc testALLA() |
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| 1961 | { |
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| 1962 | attrib(SSinit, "SYZCHECK", 1); // TODO: only for now!! |
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[8b368ff] | 1963 | attrib(SSinit, "KERCHECK", 0); // TODO: only for now!! |
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[c1931a4] | 1964 | |
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| 1965 | ring r; r; ideal M = maxideal(1); M; |
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| 1966 | TestSSresAttribs(M); |
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| 1967 | kill r; |
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| 1968 | |
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| 1969 | ring r = 0, (a, b, c, d), lp; r; ideal M = maxideal(1); M; |
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| 1970 | TestSSresAttribs(M); |
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| 1971 | kill r; |
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| 1972 | |
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| 1973 | ring R = 0, (w, x, y, z), dp; R; |
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| 1974 | ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; M; |
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| 1975 | TestSSresAttribs(M); |
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| 1976 | kill R; |
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| 1977 | |
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| 1978 | |
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| 1979 | ring AGR = (101), (a, b, c, d), dp; AGR; |
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| 1980 | // simple: AGR@101n3d002s004%1: |
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| 1981 | ideal M = c*d, b*d, a*d, c^2-d^2, b*c, a*c, b^2-d^2, a*b, a^2-d^2; |
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| 1982 | M; |
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| 1983 | TestSSresAttribs(M); |
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| 1984 | |
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| 1985 | |
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| 1986 | // medium: AGR@101n3d004s009%1; |
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| 1987 | ideal M = a*b+7*a*c-16*b*c-27*a*d+37*b*d-2*c*d, d^3, c*d^2, b*d^2, a*d^2, c^2*d, b*c*d, a*c*d, b^2*d, a^2*d, c^3, b*c^2, a*c^2, b^2*c, a^2*c, b^3, a^3; |
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| 1988 | M; |
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| 1989 | TestSSresAttribs(M); |
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| 1990 | |
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| 1991 | /* |
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| 1992 | // lengthy: AGR@101n3d008s058%3, toooo long!!! :(((( |
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| 1993 | ideal M = 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|
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| 1994 | M; |
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| 1995 | TestSSresAttribs(M); |
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| 1996 | */ |
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| 1997 | kill AGR; |
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| 1998 | |
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| 1999 | ring r = 0, (a, b, c, d, e, f), dp; r; ideal M = maxideal(1); M; |
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| 2000 | TestSSresAttribs(M); |
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| 2001 | kill r; |
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| 2002 | } |
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| 2003 | |
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| 2004 | // TODO: betti!!! |
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