[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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[2c16b8] | 141 | // DetailedPrint(M); |
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[4c6c938] | 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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[2c16b8] | 187 | // DetailedPrint(M); |
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[4c6c938] | 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)! |
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[6b6c82] | 474 | { |
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| 475 | int i = ncols(M); def m; |
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| 476 | while (i > 0) |
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| 477 | { |
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| 478 | m = M[i]; |
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[e89ff5] | 479 | m = m - lead(m); // m = tail(m) |
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| 480 | M[i] = m; |
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[6b6c82] | 481 | i--; |
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| 482 | } |
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| 483 | return (M); |
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[e89ff5] | 484 | }*/ |
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| 485 | |
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[8b78ee] | 486 | /* static */ |
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| 487 | proc MySort(def M) |
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[f6c459] | 488 | " |
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| 489 | Sorts the given ideal or module wrt >_{(c, ds)} (.<.<.<.<) |
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| 490 | NOTE: inplace?? |
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| 491 | " |
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[8b78ee] | 492 | { |
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| 493 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
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| 494 | { |
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| 495 | int @DEBUG = attrib(basering, "DEBUG"); |
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| 496 | } else |
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| 497 | { |
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[2c16b8] | 498 | int @DEBUG = 0; // !system("with", "ndebug"); |
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[8b78ee] | 499 | } |
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| 500 | |
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[8b368ff] | 501 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
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[8b78ee] | 502 | { |
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[8b368ff] | 503 | int @KERCHECK = attrib(basering, "KERCHECK"); |
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[8b78ee] | 504 | } else |
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| 505 | { |
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[f6c459] | 506 | int @KERCHECK = @DEBUG; |
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[8b78ee] | 507 | } |
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| 508 | |
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| 509 | |
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| 510 | if( @DEBUG ) |
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| 511 | { |
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| 512 | "MySort:: Input: "; M; |
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| 513 | } |
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| 514 | |
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[210d1b] | 515 | def @N = M; |
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[8b78ee] | 516 | |
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[210d1b] | 517 | if( size(M) > 0 ) |
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[8b78ee] | 518 | { |
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[210d1b] | 519 | Sort_c_ds(@N); |
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| 520 | |
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| 521 | if( @KERCHECK ) |
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[8b78ee] | 522 | { |
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[210d1b] | 523 | def iv = sort(lead(M), "c,ds", 1)[2]; // ,1 => reversed! // TODO: not needed? |
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| 524 | def @M = M; |
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| 525 | @M = M[iv]; |
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[8b78ee] | 526 | |
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[210d1b] | 527 | // 0^th syz. property |
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| 528 | if( (size(@N) + size(@M)) > 0 ) |
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| 529 | { |
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| 530 | if( size(module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) )) > 0 ) |
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| 531 | { |
---|
| 532 | "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!"; |
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| 533 | |
---|
| 534 | "@M:"; @M; |
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| 535 | "@N:"; @N; |
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[8b78ee] | 536 | |
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[210d1b] | 537 | "module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) ): "; |
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| 538 | module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) ); |
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| 539 | |
---|
| 540 | "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!"; |
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| 541 | $ |
---|
| 542 | } |
---|
| 543 | } |
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[8b78ee] | 544 | } |
---|
| 545 | } |
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| 546 | |
---|
| 547 | if( @DEBUG ) |
---|
| 548 | { |
---|
| 549 | "MySort:: Ouput: "; @N; |
---|
| 550 | } |
---|
| 551 | |
---|
| 552 | return (@N); |
---|
| 553 | } |
---|
| 554 | |
---|
[6b6c82] | 555 | |
---|
[f6c459] | 556 | static proc SSinit(def M) |
---|
[6b6c82] | 557 | { |
---|
| 558 | if( (typeof(M) != "module") && (typeof(M) != "ideal") ) |
---|
| 559 | { |
---|
| 560 | ERROR("Sorry: need an ideal or a module for input"); |
---|
| 561 | } |
---|
| 562 | |
---|
| 563 | // TODO! DONE? |
---|
| 564 | def @save = basering; |
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| 565 | |
---|
| 566 | int @DEBUG = !system("with", "ndebug"); |
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[8e650e] | 567 | |
---|
| 568 | if( typeof( attrib(SSinit, "DEBUG") ) == "int" ) |
---|
| 569 | { |
---|
| 570 | @DEBUG = attrib(SSinit, "DEBUG"); |
---|
| 571 | } |
---|
| 572 | |
---|
| 573 | int @SYZCHECK = @DEBUG; |
---|
| 574 | |
---|
| 575 | if( typeof( attrib(SSinit, "SYZCHECK") ) == "int" ) |
---|
| 576 | { |
---|
| 577 | @SYZCHECK = attrib(SSinit, "SYZCHECK"); |
---|
| 578 | } |
---|
[8b368ff] | 579 | |
---|
[f6c459] | 580 | int @KERCHECK = @DEBUG; |
---|
[8b368ff] | 581 | |
---|
| 582 | if( typeof( attrib(SSinit, "KERCHECK") ) == "int" ) |
---|
| 583 | { |
---|
| 584 | @KERCHECK = attrib(SSinit, "KERCHECK"); |
---|
| 585 | } |
---|
| 586 | |
---|
[6b6c82] | 587 | if( @DEBUG ) |
---|
| 588 | { |
---|
| 589 | "SSinit::Input"; |
---|
| 590 | type(M); |
---|
[4b2e47] | 591 | // DetailedPrint(M); |
---|
[6b6c82] | 592 | attrib(M); |
---|
| 593 | } |
---|
| 594 | |
---|
| 595 | int @RANK = nrows(M); int @SIZE = ncols(M); |
---|
| 596 | |
---|
| 597 | int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?! |
---|
| 598 | |
---|
| 599 | if( !@IS_A_SB ) |
---|
| 600 | { |
---|
| 601 | def opts = option(get); |
---|
| 602 | option(redSB); option(redTail); |
---|
| 603 | M = std(M); |
---|
| 604 | option(set, opts); |
---|
| 605 | kill opts; |
---|
| 606 | } else |
---|
| 607 | { |
---|
| 608 | M = simplify(M, 2 + 4 + 32); |
---|
| 609 | } |
---|
| 610 | |
---|
[8b78ee] | 611 | def @N = MySort(M); // TODO: replace with inplace sorting!!! |
---|
| 612 | def LEAD = lead(@N); |
---|
| 613 | |
---|
[f6c459] | 614 | if( @KERCHECK ) |
---|
[8b78ee] | 615 | { |
---|
| 616 | def @LEAD = lead(M); |
---|
| 617 | |
---|
| 618 | // sort wrt neg.deg.rev.lex! |
---|
| 619 | intvec iv_ds = sort(@LEAD, "c,ds", 1)[2]; // ,1 => reversed! |
---|
| 620 | |
---|
| 621 | M = M[iv_ds]; // sort M wrt ds on current leading terms |
---|
| 622 | @LEAD = @LEAD[iv_ds]; |
---|
| 623 | |
---|
| 624 | if( size(module( matrix(@N) - matrix(M) )) > 0 ) |
---|
| 625 | { |
---|
| 626 | "M:"; M; |
---|
| 627 | "@N:"; @N; |
---|
| 628 | |
---|
| 629 | "module( matrix(@N) - matrix(M) ): "; |
---|
| 630 | module( matrix(@N) - matrix(M) ); |
---|
[6b6c82] | 631 | |
---|
[8b78ee] | 632 | "ERROR: wrong sorting (in SSnit): @N != M!!!"; |
---|
| 633 | $ |
---|
| 634 | } |
---|
| 635 | |
---|
| 636 | if( size(module( matrix(@LEAD) - matrix(LEAD) )) > 0 ) |
---|
| 637 | { |
---|
| 638 | "LEAD:"; LEAD; |
---|
| 639 | "@LEAD:"; @LEAD; |
---|
| 640 | |
---|
| 641 | "module( matrix(@LEAD) - matrix(LEAD) ): "; |
---|
| 642 | module( matrix(@LEAD) - matrix(LEAD) ); |
---|
| 643 | |
---|
| 644 | "ERROR: wrong sorting (in SSnit): @LEAD != LEAD!!!"; |
---|
| 645 | $ |
---|
| 646 | } |
---|
| 647 | |
---|
| 648 | } |
---|
[6b6c82] | 649 | |
---|
[8b78ee] | 650 | M = @N; |
---|
| 651 | |
---|
[6b6c82] | 652 | def TAIL = Tail(M); |
---|
| 653 | |
---|
| 654 | intvec @DEGS = deg(M[1..@SIZE]); // store actuall degrees of input elements |
---|
| 655 | |
---|
| 656 | // TODO: what about real modules? weighted ones? |
---|
| 657 | |
---|
| 658 | list @l = ringlist(@save); |
---|
| 659 | |
---|
| 660 | int @z = 0; ideal @m = maxideal(1); intvec @wdeg = deg(@m[1..ncols(@m)]); |
---|
| 661 | |
---|
| 662 | // NOTE: @wdeg will be ignored anyway :( |
---|
| 663 | @l[3] = list(list("C", @z), list("lp", @wdeg)); |
---|
| 664 | |
---|
| 665 | kill @z, @wdeg; // since these vars are ring independent! |
---|
| 666 | |
---|
| 667 | def S = ring(@l); // --MakeInducedSchreyerOrdering(1); |
---|
| 668 | |
---|
| 669 | module F = freemodule(@RANK); |
---|
| 670 | intvec @V = deg(F[1..@RANK]); |
---|
| 671 | |
---|
| 672 | setring S; // ring with an easy divisibility test ("C, lex") |
---|
| 673 | |
---|
| 674 | if( @DEBUG ) |
---|
| 675 | { |
---|
[fdde6ce] | 676 | "SSinit::NewRing(C, lex)"; |
---|
[6b6c82] | 677 | basering; |
---|
[7b7c2c] | 678 | DetailedPrint(basering); |
---|
[6b6c82] | 679 | } |
---|
| 680 | |
---|
| 681 | // Setup the leading syzygy^{-1} module to zero: |
---|
| 682 | module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0)); |
---|
| 683 | |
---|
| 684 | module MRES = Z; |
---|
| 685 | |
---|
| 686 | list RES; RES[1] = Z; |
---|
| 687 | list LRES; LRES[1] = Z; |
---|
| 688 | list TRES; TRES[1] = Z; |
---|
| 689 | |
---|
| 690 | def M = imap(@save, M); |
---|
[f37467] | 691 | |
---|
[6b6c82] | 692 | attrib(M, "isHomog", @V); |
---|
| 693 | attrib(M, "isSB", 1); |
---|
| 694 | attrib(M, "degrees", @DEGS); |
---|
| 695 | |
---|
| 696 | def LEAD = imap(@save, LEAD); |
---|
[f37467] | 697 | |
---|
[6b6c82] | 698 | attrib(LEAD, "isHomog", @V); |
---|
| 699 | attrib(LEAD, "isSB", 1); |
---|
| 700 | |
---|
| 701 | def TAIL = imap(@save, TAIL); |
---|
| 702 | |
---|
| 703 | if( @DEBUG ) |
---|
| 704 | { |
---|
| 705 | "SSinit::(sorted) SB_Input: "; |
---|
| 706 | type(M); |
---|
| 707 | attrib(M); |
---|
| 708 | attrib(M, "isHomog"); |
---|
[4b2e47] | 709 | // DetailedPrint(M); |
---|
[6b6c82] | 710 | } |
---|
| 711 | |
---|
[b0ca43c] | 712 | if( @SYZCHECK ) |
---|
[6b6c82] | 713 | { |
---|
[f37467] | 714 | // 0^th syz. property |
---|
| 715 | if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 ) |
---|
| 716 | { |
---|
| 717 | transpose( transpose(M) * transpose(MRES) ); |
---|
| 718 | "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!"; |
---|
| 719 | $ |
---|
| 720 | } |
---|
[6b6c82] | 721 | } |
---|
| 722 | |
---|
[7b7c2c] | 723 | RES [size(RES)+1] = M; // list of all syzygy modules |
---|
[6b6c82] | 724 | LRES[size(LRES)+1] = LEAD; // list of all syzygy modules |
---|
| 725 | TRES[size(TRES)+1] = TAIL; // list of all syzygy modules |
---|
| 726 | |
---|
| 727 | MRES = MRES, M; //? |
---|
| 728 | |
---|
[f37467] | 729 | attrib(MRES, "isHomog", @V); |
---|
| 730 | |
---|
[b0ca43c] | 731 | // attrib(S, "InducionStart", @RANK); |
---|
[8e650e] | 732 | |
---|
| 733 | |
---|
| 734 | if( typeof( attrib(SSinit, "LEAD2SYZ") ) == "int" ) |
---|
| 735 | { |
---|
| 736 | attrib(S, "LEAD2SYZ", attrib(SSinit, "LEAD2SYZ") ); |
---|
| 737 | } else |
---|
| 738 | { |
---|
| 739 | attrib(S, "LEAD2SYZ", 1); |
---|
| 740 | } |
---|
| 741 | |
---|
| 742 | if( typeof( attrib(SSinit, "TAILREDSYZ") ) == "int" ) |
---|
| 743 | { |
---|
| 744 | attrib(S, "TAILREDSYZ", attrib(SSinit, "TAILREDSYZ") ); |
---|
| 745 | } else |
---|
| 746 | { |
---|
| 747 | attrib(S, "TAILREDSYZ", 1); |
---|
| 748 | } |
---|
| 749 | |
---|
| 750 | |
---|
| 751 | if( typeof( attrib(SSinit, "HYBRIDNF") ) == "int" ) |
---|
| 752 | { |
---|
| 753 | attrib(S, "HYBRIDNF", attrib(SSinit, "HYBRIDNF") ); |
---|
| 754 | } else |
---|
| 755 | { |
---|
| 756 | attrib(S, "HYBRIDNF", 0); |
---|
| 757 | } |
---|
| 758 | |
---|
[fdde6ce] | 759 | attrib(S, "DEBUG", @DEBUG); |
---|
[b0ca43c] | 760 | attrib(S, "SYZCHECK", @SYZCHECK); |
---|
[8b368ff] | 761 | attrib(S, "KERCHECK", @KERCHECK); |
---|
[6b6c82] | 762 | |
---|
| 763 | if( @DEBUG ) |
---|
| 764 | { |
---|
| 765 | "SSinit::MRES"; |
---|
[4b2e47] | 766 | MRES; |
---|
| 767 | // DetailedPrint(MRES); |
---|
[6b6c82] | 768 | attrib(MRES, "isHomog"); |
---|
| 769 | attrib(S); |
---|
| 770 | } |
---|
| 771 | |
---|
| 772 | export RES; |
---|
| 773 | export MRES; |
---|
| 774 | export LRES; |
---|
| 775 | export TRES; |
---|
| 776 | return (S); |
---|
| 777 | } |
---|
| 778 | example |
---|
| 779 | { "EXAMPLE:"; echo = 2; |
---|
| 780 | ring R = 0, (w, x, y, z), dp; |
---|
| 781 | |
---|
| 782 | def M = maxideal(1); |
---|
| 783 | def S = SSinit(M); setring S; S; |
---|
| 784 | |
---|
| 785 | "Only the first initialization: "; |
---|
| 786 | RES; LRES; TRES; |
---|
| 787 | MRES; |
---|
| 788 | |
---|
| 789 | kill S; setring R; kill M; |
---|
| 790 | |
---|
| 791 | ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; |
---|
| 792 | def S = SSinit(M); setring S; S; |
---|
| 793 | |
---|
| 794 | "Only the first initialization: "; |
---|
| 795 | RES; LRES; TRES; |
---|
| 796 | MRES; |
---|
| 797 | |
---|
| 798 | kill S; setring R; kill M; |
---|
| 799 | } |
---|
| 800 | |
---|
[8f57c0] | 801 | |
---|
| 802 | LIB "poly.lib"; // for lcm |
---|
| 803 | |
---|
| 804 | |
---|
[f37467] | 805 | |
---|
| 806 | /// Compute L(Syz(L)) |
---|
| 807 | proc SSComputeLeadingSyzygyTerms(def L) |
---|
[8f57c0] | 808 | { |
---|
[fdde6ce] | 809 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 810 | { |
---|
| 811 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 812 | } else |
---|
| 813 | { |
---|
| 814 | int @DEBUG = !system("with", "ndebug"); |
---|
| 815 | } |
---|
[8f57c0] | 816 | |
---|
[7b7c2c] | 817 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 818 | { |
---|
| 819 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 820 | } else |
---|
| 821 | { |
---|
| 822 | int @SYZCHECK = @DEBUG; |
---|
| 823 | } |
---|
[8b368ff] | 824 | |
---|
| 825 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 826 | { |
---|
| 827 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 828 | } else |
---|
| 829 | { |
---|
[f6c459] | 830 | int @KERCHECK = @DEBUG; |
---|
[8b368ff] | 831 | } |
---|
| 832 | |
---|
[8f57c0] | 833 | if( @DEBUG ) |
---|
| 834 | { |
---|
| 835 | "SSComputeLeadingSyzygyTerms::Input: "; |
---|
| 836 | L; |
---|
| 837 | } |
---|
| 838 | |
---|
[7b7c2c] | 839 | module SS = ComputeLeadingSyzygyTerms(L); |
---|
[8f57c0] | 840 | |
---|
[8b368ff] | 841 | if( @KERCHECK ) |
---|
[7b7c2c] | 842 | { |
---|
[8b78ee] | 843 | int i, j, r; |
---|
[7b7c2c] | 844 | int N = ncols(L); |
---|
| 845 | def a, b; |
---|
| 846 | poly aa, bb; |
---|
[8f57c0] | 847 | |
---|
[7b7c2c] | 848 | bigint c; |
---|
[8f57c0] | 849 | |
---|
[7b7c2c] | 850 | ideal M; |
---|
[4b2e47] | 851 | |
---|
[7b7c2c] | 852 | module S = 0; |
---|
[8f57c0] | 853 | |
---|
[7b7c2c] | 854 | for(i = 1; i <= N; i++) |
---|
[8f57c0] | 855 | { |
---|
[7b7c2c] | 856 | a = L[i]; |
---|
| 857 | c = leadcomp(a); |
---|
| 858 | r = int(c); |
---|
[8f57c0] | 859 | |
---|
[7b7c2c] | 860 | aa = leadmonomial(a); |
---|
| 861 | |
---|
| 862 | M = 0; |
---|
| 863 | |
---|
| 864 | for(j = i-1; j > 0; j--) |
---|
[8f57c0] | 865 | { |
---|
[7b7c2c] | 866 | b = L[j]; |
---|
| 867 | |
---|
| 868 | if( leadcomp(b) == c ) |
---|
[4b2e47] | 869 | { |
---|
[7b7c2c] | 870 | bb = leadmonomial(b); |
---|
[8f57c0] | 871 | |
---|
[7b7c2c] | 872 | M[j] = (lcm(aa, bb) / aa); |
---|
| 873 | } |
---|
[8f57c0] | 874 | } |
---|
[7b7c2c] | 875 | |
---|
| 876 | // TODO: add quotient relations here... |
---|
| 877 | |
---|
| 878 | M = simplify(M, 1 + 2 + 32); |
---|
| 879 | |
---|
[8b78ee] | 880 | M = MySort(M); |
---|
[7b7c2c] | 881 | |
---|
| 882 | S = S, M * gen(i); |
---|
[8f57c0] | 883 | } |
---|
| 884 | |
---|
[8b78ee] | 885 | S = MySort(simplify(S, 2)); |
---|
[8f57c0] | 886 | |
---|
[210d1b] | 887 | if( (size(S) + size(SS)) > 0 ) |
---|
[8b368ff] | 888 | { |
---|
[7b7c2c] | 889 | if( size(module(matrix(S) - matrix(SS))) > 0 ) |
---|
| 890 | { |
---|
[8b368ff] | 891 | "ERROR: SSComputeLeadingSyzygyTerms: S != SS "; |
---|
[8f57c0] | 892 | |
---|
[f6c459] | 893 | "basering: "; basering; |
---|
| 894 | // DetailedPrint(basering); |
---|
[8f57c0] | 895 | |
---|
[7b7c2c] | 896 | "S: "; S; |
---|
[f6c459] | 897 | // DetailedPrint(_, 1); |
---|
[7b7c2c] | 898 | "SS: "; SS; |
---|
[f6c459] | 899 | // DetailedPrint(_, 1); |
---|
[7b7c2c] | 900 | |
---|
| 901 | "DIFF: "; |
---|
[f6c459] | 902 | module(matrix(S) - matrix(SS)); |
---|
| 903 | // DetailedPrint(_, 2); |
---|
[7b7c2c] | 904 | print(matrix(S) - matrix(SS)); |
---|
| 905 | $ |
---|
| 906 | } |
---|
[8b368ff] | 907 | } |
---|
[7b7c2c] | 908 | } |
---|
[8f57c0] | 909 | |
---|
| 910 | |
---|
| 911 | if( @DEBUG ) |
---|
| 912 | { |
---|
| 913 | "SSComputeLeadingSyzygyTerms::Output: "; |
---|
[2c16b8] | 914 | "SS: "; SS; |
---|
[7b7c2c] | 915 | } |
---|
| 916 | |
---|
[8b368ff] | 917 | if( size(SS) > 0 ) |
---|
| 918 | { |
---|
| 919 | attrib(SS, "isSB", 1); |
---|
| 920 | } |
---|
| 921 | |
---|
[7b7c2c] | 922 | return (SS); |
---|
[f37467] | 923 | } |
---|
| 924 | |
---|
| 925 | /// Compute Syz(L), where L is a monomial (leading) module |
---|
[74afe1f] | 926 | proc SSCompute2LeadingSyzygyTerms(def L) |
---|
[f37467] | 927 | { |
---|
[fdde6ce] | 928 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 929 | { |
---|
| 930 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 931 | } else |
---|
| 932 | { |
---|
| 933 | int @DEBUG = !system("with", "ndebug"); |
---|
| 934 | } |
---|
[f37467] | 935 | |
---|
[b0ca43c] | 936 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 937 | { |
---|
| 938 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 939 | } else |
---|
| 940 | { |
---|
| 941 | int @SYZCHECK = @DEBUG; |
---|
| 942 | } |
---|
[74afe1f] | 943 | |
---|
[8b368ff] | 944 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 945 | { |
---|
| 946 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 947 | } else |
---|
| 948 | { |
---|
[f6c459] | 949 | int @KERCHECK = @DEBUG; |
---|
[8b368ff] | 950 | } |
---|
| 951 | |
---|
[f37467] | 952 | if( @DEBUG ) |
---|
| 953 | { |
---|
| 954 | "SSCompute2LeadingSyzygyTerms::Input: "; |
---|
| 955 | L; |
---|
| 956 | } |
---|
| 957 | |
---|
[d058ea] | 958 | module SS = Compute2LeadingSyzygyTerms(L); |
---|
[f37467] | 959 | |
---|
[d058ea] | 960 | if( @DEBUG ) |
---|
| 961 | { |
---|
| 962 | "SSCompute2LeadingSyzygyTerms::Syz(SS): "; SS; |
---|
| 963 | } |
---|
| 964 | |
---|
| 965 | if( @SYZCHECK ) |
---|
| 966 | { |
---|
| 967 | if( size(SS) > 0 and size(L) > 0 ) |
---|
| 968 | { |
---|
| 969 | if( size(module(transpose( transpose(SS) * transpose(L) ))) > 0 ) |
---|
| 970 | { |
---|
| 971 | transpose( transpose(SS) * transpose(L) ); |
---|
| 972 | "ERROR: transpose( transpose(SS) * transpose(L) ) != 0!!!"; |
---|
| 973 | $ |
---|
| 974 | } |
---|
| 975 | } |
---|
[8b368ff] | 976 | } |
---|
| 977 | |
---|
| 978 | if( @KERCHECK ) |
---|
| 979 | { |
---|
[f6c459] | 980 | int @TAILREDSYZ = 1; |
---|
| 981 | if( typeof( attrib(basering, "TAILREDSYZ") ) == "int" ) |
---|
| 982 | { |
---|
| 983 | @TAILREDSYZ = attrib(basering, "TAILREDSYZ"); |
---|
| 984 | } |
---|
[f37467] | 985 | |
---|
[d058ea] | 986 | int i, j, r; |
---|
| 987 | int N = ncols(L); |
---|
| 988 | def a, b; |
---|
[f37467] | 989 | |
---|
[d058ea] | 990 | poly aa, bb, @lcm; |
---|
[f37467] | 991 | |
---|
[d058ea] | 992 | bigint c; |
---|
[f37467] | 993 | |
---|
[d058ea] | 994 | module M; |
---|
[f37467] | 995 | |
---|
[d058ea] | 996 | module S = 0; |
---|
[f37467] | 997 | |
---|
[d058ea] | 998 | for(i = 1; i <= N; i++) |
---|
[f37467] | 999 | { |
---|
[d058ea] | 1000 | a = L[i]; |
---|
| 1001 | // "a: ", a; |
---|
| 1002 | c = leadcomp(a); |
---|
| 1003 | r = int(c); |
---|
| 1004 | |
---|
| 1005 | aa = leadmonomial(a); |
---|
| 1006 | |
---|
| 1007 | M = 0; |
---|
[f37467] | 1008 | |
---|
[d058ea] | 1009 | for(j = i-1; j > 0; j--) |
---|
[f37467] | 1010 | { |
---|
[d058ea] | 1011 | b = L[j]; |
---|
| 1012 | // "b: ", b; |
---|
| 1013 | |
---|
| 1014 | if( leadcomp(b) == c ) |
---|
| 1015 | { |
---|
| 1016 | bb = leadmonomial(b); |
---|
| 1017 | @lcm = lcm(aa, bb); |
---|
[f37467] | 1018 | |
---|
[d058ea] | 1019 | M[j] = (@lcm / aa)* gen(i) - (@lcm / bb)* gen(j); |
---|
| 1020 | } |
---|
[f37467] | 1021 | } |
---|
| 1022 | |
---|
[d058ea] | 1023 | M = simplify(M, 2); |
---|
[f37467] | 1024 | |
---|
[d058ea] | 1025 | // TODO: add quotient relations here... |
---|
| 1026 | S = S, M; |
---|
| 1027 | } |
---|
[f37467] | 1028 | |
---|
[d058ea] | 1029 | if( @TAILREDSYZ ) |
---|
| 1030 | { |
---|
| 1031 | // Make sure that 2nd syzygy terms are not reducible by 1st |
---|
| 1032 | def opts = option(get); |
---|
| 1033 | option(redSB); option(redTail); |
---|
| 1034 | S = std(S); // binomial module |
---|
| 1035 | option(set, opts); |
---|
| 1036 | // kill opts; |
---|
| 1037 | } else |
---|
| 1038 | { |
---|
| 1039 | S = simplify(S, 2 + 32); |
---|
| 1040 | } |
---|
[f37467] | 1041 | |
---|
[d058ea] | 1042 | S = MySort(S); |
---|
[f37467] | 1043 | |
---|
[d058ea] | 1044 | if( @DEBUG ) |
---|
[f37467] | 1045 | { |
---|
[d058ea] | 1046 | "SSCompute2LeadingSyzygyTerms::Syz(S): "; S; |
---|
[f37467] | 1047 | } |
---|
[74afe1f] | 1048 | |
---|
[9e69e0] | 1049 | if( @SYZCHECK ) |
---|
| 1050 | { |
---|
| 1051 | if( size(S) > 0 and size(L) > 0 ) |
---|
| 1052 | { |
---|
| 1053 | if( size(module(transpose( transpose(S) * transpose(L) ))) > 0 ) |
---|
| 1054 | { |
---|
| 1055 | transpose( transpose(S) * transpose(L) ); |
---|
| 1056 | "ERROR: transpose( transpose(S) * transpose(L) ) != 0!!!"; |
---|
| 1057 | $ |
---|
| 1058 | } |
---|
| 1059 | } |
---|
| 1060 | } |
---|
| 1061 | |
---|
| 1062 | if(size(S) != size(SS)) |
---|
[74afe1f] | 1063 | { |
---|
[9e69e0] | 1064 | "ERROR: SSCompute2LeadingSyzygyTerms: size(S) != size(SS)"; |
---|
[74afe1f] | 1065 | |
---|
[9e69e0] | 1066 | "basering: "; basering; // DetailedPrint(basering); |
---|
[74afe1f] | 1067 | |
---|
| 1068 | "S: "; S; |
---|
[9e69e0] | 1069 | // DetailedPrint(S, 2); |
---|
[74afe1f] | 1070 | "SS: "; SS; |
---|
[9e69e0] | 1071 | // DetailedPrint(SS, 2); |
---|
[74afe1f] | 1072 | $ |
---|
[9e69e0] | 1073 | } |
---|
| 1074 | |
---|
| 1075 | if(size(S) > 0 && size(SS) > 0) |
---|
| 1076 | { |
---|
| 1077 | if( size(module(matrix(lead(S)) - matrix(lead(SS)))) > 0 ) |
---|
| 1078 | { |
---|
| 1079 | "ERROR: SSCompute2LeadingSyzygyTerms: lead(S) != lead(SS) "; |
---|
| 1080 | |
---|
| 1081 | "basering: "; basering; |
---|
| 1082 | // DetailedPrint(basering); |
---|
| 1083 | |
---|
| 1084 | "lead(S ): "; lead(S ); |
---|
| 1085 | // DetailedPrint(_, 2); |
---|
| 1086 | "lead(SS): "; lead(SS); |
---|
| 1087 | // DetailedPrint(_, 2); |
---|
| 1088 | |
---|
| 1089 | "DIFF: "; |
---|
| 1090 | print( matrix(lead(S)) - matrix(lead(SS)) ); |
---|
| 1091 | module(matrix(lead(S)) - matrix(lead(SS))); |
---|
| 1092 | // DetailedPrint(_ , 4); |
---|
| 1093 | $ |
---|
| 1094 | } |
---|
| 1095 | |
---|
| 1096 | |
---|
| 1097 | if( @TAILREDSYZ ) |
---|
| 1098 | { |
---|
| 1099 | if( size(module(matrix(Tail(S)) - matrix(Tail(SS)))) > 0 ) |
---|
| 1100 | { |
---|
| 1101 | "ERROR: SSCompute2LeadingSyzygyTerms: Tail(S) != Tail(SS) "; |
---|
| 1102 | |
---|
| 1103 | "basering: "; basering; |
---|
| 1104 | // DetailedPrint(basering); |
---|
| 1105 | |
---|
| 1106 | "Tail(S ): "; Tail(S ); |
---|
| 1107 | // DetailedPrint(_, 2); |
---|
| 1108 | "Tail(SS): "; Tail(SS); |
---|
| 1109 | // DetailedPrint(_, 2); |
---|
| 1110 | |
---|
| 1111 | "DIFF: "; |
---|
| 1112 | module( matrix(Tail(S)) - matrix(Tail(SS)) ); |
---|
| 1113 | // DetailedPrint(_, 4); |
---|
| 1114 | print( matrix(Tail(S)) - matrix(Tail(SS)) ); |
---|
| 1115 | $ |
---|
| 1116 | } |
---|
| 1117 | } |
---|
[74afe1f] | 1118 | } |
---|
[d058ea] | 1119 | } |
---|
| 1120 | |
---|
| 1121 | module S2 = Tail(SS); |
---|
| 1122 | SS = lead(SS); // (C,lp) on base ring! |
---|
[2c16b8] | 1123 | |
---|
| 1124 | if( @SYZCHECK ) |
---|
| 1125 | { |
---|
| 1126 | if( ncols(SS) != ncols(S2) ) // || size(SS) != ncols(SS) || size(S2) != ncols(S2) |
---|
| 1127 | { |
---|
| 1128 | "ERROR: SSCompute2LeadingSyzygyTerms: inappropriate S2 / SS: "; |
---|
| 1129 | type(SS); |
---|
| 1130 | type(S2); |
---|
| 1131 | L; |
---|
| 1132 | $ |
---|
| 1133 | } |
---|
| 1134 | } |
---|
[f37467] | 1135 | |
---|
| 1136 | if( @DEBUG ) |
---|
| 1137 | { |
---|
[d058ea] | 1138 | "SSCompute2LeadingSyzygyTerms::Output: "; SS; S2; |
---|
[f37467] | 1139 | } |
---|
| 1140 | |
---|
[d058ea] | 1141 | attrib(SS, "isSB", 1); |
---|
[f37467] | 1142 | |
---|
[d058ea] | 1143 | return (SS, S2); |
---|
[8f57c0] | 1144 | } |
---|
| 1145 | |
---|
[f37467] | 1146 | // -------------------------------------------------------- // |
---|
| 1147 | |
---|
[b2fb0c] | 1148 | /// TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz? |
---|
[f6c459] | 1149 | proc SSFindReducer(def product, def syzterm, def L, list #) |
---|
[8f57c0] | 1150 | { |
---|
[fdde6ce] | 1151 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1152 | { |
---|
| 1153 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1154 | } else |
---|
| 1155 | { |
---|
| 1156 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1157 | } |
---|
[4b2e47] | 1158 | |
---|
[f6c459] | 1159 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1160 | { |
---|
| 1161 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1162 | } else |
---|
| 1163 | { |
---|
| 1164 | int @SYZCHECK = @DEBUG; |
---|
| 1165 | } |
---|
| 1166 | |
---|
| 1167 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 1168 | { |
---|
| 1169 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 1170 | } else |
---|
| 1171 | { |
---|
| 1172 | int @KERCHECK = @DEBUG; |
---|
| 1173 | } |
---|
| 1174 | |
---|
[b2fb0c] | 1175 | |
---|
[4b2e47] | 1176 | if( @DEBUG ) |
---|
| 1177 | { |
---|
[b2fb0c] | 1178 | "SSFindReducer::Input: "; |
---|
[4b2e47] | 1179 | |
---|
[b2fb0c] | 1180 | "syzterm: ", syzterm; |
---|
| 1181 | "product: ", product; |
---|
[4b2e47] | 1182 | "L: ", L; |
---|
[33161fd] | 1183 | // "T: ", T; |
---|
[fdde6ce] | 1184 | if( size(#) > 0 ) |
---|
| 1185 | { |
---|
| 1186 | "LSyz: ", #; |
---|
| 1187 | } |
---|
[4b2e47] | 1188 | } |
---|
| 1189 | |
---|
[b2fb0c] | 1190 | |
---|
[f6c459] | 1191 | if( @DEBUG && (syzterm != 0) ) |
---|
[4b2e47] | 1192 | { |
---|
[b2fb0c] | 1193 | def @@c = leadcomp(syzterm); int @@r = int(@@c); |
---|
| 1194 | def @@product = leadmonomial(syzterm) * L[@@r]; |
---|
| 1195 | |
---|
| 1196 | if( @@product != product) |
---|
| 1197 | { |
---|
| 1198 | "product: ", product, ", @@product: ", @@product; |
---|
| 1199 | "ERROR: 'syzterm' results in wrong product !!!???"; |
---|
| 1200 | $ |
---|
| 1201 | } |
---|
[4b2e47] | 1202 | } |
---|
| 1203 | |
---|
[33161fd] | 1204 | if( typeof(#[1]) == "module" ) |
---|
| 1205 | { |
---|
| 1206 | vector my = FindReducer(product, syzterm, L/*, T*/, #[1]); |
---|
| 1207 | } else |
---|
| 1208 | { |
---|
| 1209 | vector my = FindReducer(product, syzterm, L/*, T*/); |
---|
| 1210 | } |
---|
| 1211 | |
---|
[8f57c0] | 1212 | |
---|
[f6c459] | 1213 | if( @KERCHECK ) |
---|
[33161fd] | 1214 | { |
---|
| 1215 | bigint c = leadcomp(product); int r = int(c); |
---|
[b2fb0c] | 1216 | |
---|
[33161fd] | 1217 | def a, b, bb; |
---|
[8f57c0] | 1218 | |
---|
[33161fd] | 1219 | vector nf = [0]; |
---|
[b2fb0c] | 1220 | |
---|
[33161fd] | 1221 | // looking for an appropriate diviser |
---|
| 1222 | for( int k = ncols(L); k > 0; k-- ) |
---|
[4b2e47] | 1223 | { |
---|
[33161fd] | 1224 | a = L[k]; |
---|
| 1225 | // with the same mod. component |
---|
| 1226 | if( leadcomp(a) == c ) |
---|
[4b2e47] | 1227 | { |
---|
[33161fd] | 1228 | b = - (leadmonomial(product) / leadmonomial(L[k])); |
---|
[4b2e47] | 1229 | |
---|
[33161fd] | 1230 | // which divides the product: looking for the 1st appropriate one! |
---|
| 1231 | if( b != 0 ) |
---|
[fdde6ce] | 1232 | { |
---|
[33161fd] | 1233 | bb = b * gen(k); |
---|
| 1234 | |
---|
| 1235 | if (size(bb + syzterm) == 0) // cannot allow something like: a*gen(i) - a*gen(i) |
---|
| 1236 | { |
---|
| 1237 | nf = [0]; |
---|
| 1238 | } else |
---|
[fdde6ce] | 1239 | { |
---|
[33161fd] | 1240 | nf = bb; |
---|
[fdde6ce] | 1241 | } |
---|
| 1242 | |
---|
[33161fd] | 1243 | // new syz. term should not be in <LS = #> |
---|
| 1244 | if( size(#) > 0 ) |
---|
| 1245 | { |
---|
| 1246 | if( typeof(#[1]) == "module" ) |
---|
| 1247 | { |
---|
| 1248 | nf = NF(bb, #[1]); |
---|
| 1249 | } |
---|
| 1250 | } |
---|
[fdde6ce] | 1251 | |
---|
[33161fd] | 1252 | // while the complement (the fraction) is not reducible by leading syzygies |
---|
| 1253 | if( nf != 0 ) // nf must be == bb!!! |
---|
| 1254 | { |
---|
| 1255 | /// TODO: save shortcut LM(m) * T[i] -> ? |
---|
| 1256 | |
---|
| 1257 | // choose ANY such reduction... (with the biggest index?) |
---|
| 1258 | break; |
---|
| 1259 | } |
---|
[4b2e47] | 1260 | } |
---|
| 1261 | } |
---|
| 1262 | } |
---|
[33161fd] | 1263 | |
---|
| 1264 | if( my != nf ) |
---|
| 1265 | { |
---|
| 1266 | "ERROR in FindReducer => ", my, " != nf: ", nf; |
---|
| 1267 | $; |
---|
| 1268 | } |
---|
| 1269 | } |
---|
| 1270 | |
---|
[b2fb0c] | 1271 | if( @DEBUG ) |
---|
| 1272 | { |
---|
[33161fd] | 1273 | "SSFindReducer::Output: ", my; |
---|
[b2fb0c] | 1274 | } |
---|
[33161fd] | 1275 | |
---|
| 1276 | return (my); |
---|
[b2fb0c] | 1277 | } |
---|
| 1278 | |
---|
| 1279 | /// TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? |
---|
| 1280 | proc SSReduceTerm(poly m, def t, def syzterm, def L, def T, list #) |
---|
| 1281 | { |
---|
| 1282 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1283 | { |
---|
| 1284 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1285 | } else |
---|
| 1286 | { |
---|
| 1287 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1288 | } |
---|
| 1289 | |
---|
| 1290 | |
---|
| 1291 | if( @DEBUG ) |
---|
| 1292 | { |
---|
| 1293 | "SSReduce::Input: "; |
---|
| 1294 | |
---|
| 1295 | "syzterm: ", syzterm; |
---|
| 1296 | "mult: ", m; |
---|
| 1297 | "term: ", t; |
---|
| 1298 | "L: ", L; |
---|
| 1299 | "T: ", T; |
---|
| 1300 | if( size(#) > 0 ) |
---|
| 1301 | { |
---|
| 1302 | "LSyz: ", #; |
---|
| 1303 | } |
---|
| 1304 | // "attrib(LS, 'isSB')", attrib(LS, "isSB"); |
---|
| 1305 | } |
---|
| 1306 | |
---|
[f6c459] | 1307 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 1308 | { |
---|
| 1309 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 1310 | } else |
---|
| 1311 | { |
---|
| 1312 | int @KERCHECK = @DEBUG; |
---|
| 1313 | } |
---|
| 1314 | |
---|
[b2fb0c] | 1315 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1316 | { |
---|
| 1317 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1318 | } else |
---|
| 1319 | { |
---|
| 1320 | int @SYZCHECK = @DEBUG; |
---|
| 1321 | } |
---|
| 1322 | |
---|
| 1323 | if( @SYZCHECK && (syzterm != 0) ) |
---|
| 1324 | { |
---|
| 1325 | def @@c = leadcomp(syzterm); int @@r = int(@@c); |
---|
| 1326 | poly @@m = leadmonomial(syzterm); def @@t = L[@@r]; |
---|
| 1327 | |
---|
| 1328 | if( (@@m != m) || (@@t != t)) |
---|
| 1329 | { |
---|
| 1330 | "m: ", m, ", t: ", t; |
---|
| 1331 | "@@m: ", @@m, ", @@t: ", @@t; |
---|
| 1332 | "ERROR: 'syzterm' results in wrong m * t !!!"; |
---|
| 1333 | $ |
---|
| 1334 | } |
---|
| 1335 | } |
---|
| 1336 | |
---|
[fe35f2] | 1337 | if( typeof(#[1]) == "module" ) |
---|
| 1338 | { |
---|
| 1339 | vector ss = ReduceTerm(m, t, syzterm, L, T, #[1]); |
---|
| 1340 | } else |
---|
[b2fb0c] | 1341 | { |
---|
[fe35f2] | 1342 | vector ss = ReduceTerm(m, t, syzterm, L, T); |
---|
| 1343 | } |
---|
[b2fb0c] | 1344 | |
---|
[fe35f2] | 1345 | if( @KERCHECK ) |
---|
| 1346 | { |
---|
| 1347 | vector s = 0; |
---|
[b2fb0c] | 1348 | |
---|
[fe35f2] | 1349 | if( size(t) > 0 ) |
---|
[b2fb0c] | 1350 | { |
---|
[fe35f2] | 1351 | def product = m * t; |
---|
[b2fb0c] | 1352 | |
---|
[fe35f2] | 1353 | s = SSFindReducer(product, syzterm, L, #); |
---|
[b2fb0c] | 1354 | |
---|
[fe35f2] | 1355 | if( size(s) != 0 ) |
---|
| 1356 | { |
---|
| 1357 | poly @b = leadmonomial(s); |
---|
| 1358 | |
---|
| 1359 | def @c = leadcomp(s); int k = int(@c); |
---|
| 1360 | |
---|
| 1361 | s = s + SSTraverseTail(@b, T[k], L, T, #); // !!! |
---|
| 1362 | } |
---|
[b2fb0c] | 1363 | } |
---|
| 1364 | |
---|
[fe35f2] | 1365 | if( s != ss ) |
---|
| 1366 | { |
---|
| 1367 | "ERROR in ReduceTerm => old: ", s, " != ker: ", ss; |
---|
| 1368 | "m: ", m; |
---|
| 1369 | "t: ", t; |
---|
| 1370 | "syzterm: ", syzterm; |
---|
| 1371 | L; T; #; |
---|
| 1372 | $; |
---|
| 1373 | } |
---|
| 1374 | } |
---|
| 1375 | |
---|
[4b2e47] | 1376 | if( @DEBUG ) |
---|
| 1377 | { |
---|
[fe35f2] | 1378 | "SSReduceTerm::Output: ", ss; |
---|
[4b2e47] | 1379 | } |
---|
[b2fb0c] | 1380 | |
---|
[fe35f2] | 1381 | return (ss); |
---|
[8f57c0] | 1382 | } |
---|
| 1383 | |
---|
[b2fb0c] | 1384 | |
---|
[fdde6ce] | 1385 | // TODO: store m * @tail -.-^-.-^-.--> ? |
---|
| 1386 | proc SSTraverseTail(poly m, def @tail, def L, def T, list #) |
---|
[4b2e47] | 1387 | { |
---|
[fdde6ce] | 1388 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1389 | { |
---|
| 1390 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1391 | } else |
---|
| 1392 | { |
---|
| 1393 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1394 | } |
---|
[4b2e47] | 1395 | |
---|
[f6c459] | 1396 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 1397 | { |
---|
| 1398 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 1399 | } else |
---|
| 1400 | { |
---|
| 1401 | int @KERCHECK = @DEBUG; |
---|
| 1402 | } |
---|
| 1403 | |
---|
| 1404 | |
---|
[4b2e47] | 1405 | if( @DEBUG ) |
---|
| 1406 | { |
---|
| 1407 | "SSTraverse::Input: "; |
---|
[8f57c0] | 1408 | |
---|
[4b2e47] | 1409 | "mult: ", m; |
---|
[fdde6ce] | 1410 | "tail: ", @tail; // T[i]; |
---|
[4b2e47] | 1411 | |
---|
[fdde6ce] | 1412 | if( size(#) > 0 ) |
---|
| 1413 | { |
---|
| 1414 | "LSyz: "; #[1]; |
---|
| 1415 | } |
---|
[4b2e47] | 1416 | } |
---|
| 1417 | |
---|
[fe35f2] | 1418 | if( typeof(#[1]) == "module" ) |
---|
| 1419 | { |
---|
| 1420 | vector ss = TraverseTail(m, @tail, L, T, #[1]); |
---|
| 1421 | } else |
---|
| 1422 | { |
---|
| 1423 | vector ss = TraverseTail(m, @tail, L, T); |
---|
| 1424 | } |
---|
| 1425 | |
---|
| 1426 | if( @KERCHECK ) |
---|
| 1427 | { |
---|
| 1428 | vector s = 0; |
---|
[4b2e47] | 1429 | |
---|
[fe35f2] | 1430 | def @l, @p; |
---|
| 1431 | @p = @tail; |
---|
[fdde6ce] | 1432 | |
---|
| 1433 | // iterate tail-terms in ANY order! |
---|
[fe35f2] | 1434 | while( size(@p) > 0 ) |
---|
| 1435 | { |
---|
| 1436 | @l = lead(@p); |
---|
| 1437 | s = s + SSReduceTerm(m, @l, [0], L, T, #); // :( |
---|
| 1438 | @p = @p - @l; |
---|
| 1439 | } |
---|
| 1440 | |
---|
| 1441 | if( s != ss ) |
---|
| 1442 | { |
---|
| 1443 | "ERROR in TraverseTail => old: ", s, " != ker: ", ss; |
---|
| 1444 | "m: ", m; |
---|
| 1445 | "@tail: ", @tail; |
---|
| 1446 | L; T; #; |
---|
| 1447 | $; |
---|
| 1448 | } |
---|
| 1449 | } |
---|
| 1450 | |
---|
| 1451 | if( @DEBUG ) |
---|
| 1452 | { |
---|
| 1453 | "SSTraverseTail::Output: ", ss; |
---|
| 1454 | } |
---|
| 1455 | |
---|
| 1456 | return (ss); |
---|
| 1457 | } |
---|
| 1458 | |
---|
| 1459 | // -------------------------------------------------------- // |
---|
| 1460 | |
---|
| 1461 | proc SSSchreyerSyzygyNF(vector syz_lead, vector syz_2, def L, def T, list #) |
---|
| 1462 | " |
---|
| 1463 | Hybrid Syzygy computation: 'reduce' spoly by eliminating _any_ terms |
---|
| 1464 | while discurding terms of lower order! |
---|
| 1465 | |
---|
| 1466 | Return the tail syzygy (without: syz_lead, starting with: syz_2) |
---|
| 1467 | " |
---|
| 1468 | { |
---|
| 1469 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1470 | { |
---|
| 1471 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1472 | } else |
---|
| 1473 | { |
---|
| 1474 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1475 | } |
---|
| 1476 | |
---|
| 1477 | if( @DEBUG ) |
---|
| 1478 | { |
---|
| 1479 | "SSSchreyerSyzygyNF::Input: "; |
---|
| 1480 | |
---|
| 1481 | "syzygy_lead: ", syz_lead; |
---|
| 1482 | "syzygy 2nd : ", syz_2; |
---|
| 1483 | L; T; |
---|
| 1484 | if( size(#) > 0 ) |
---|
| 1485 | { |
---|
| 1486 | "LSyz: "; #[1]; |
---|
| 1487 | } |
---|
| 1488 | } |
---|
| 1489 | |
---|
| 1490 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
| 1491 | { |
---|
| 1492 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
| 1493 | } else |
---|
| 1494 | { |
---|
| 1495 | int @KERCHECK = @DEBUG; |
---|
| 1496 | } |
---|
| 1497 | |
---|
| 1498 | if( typeof(#[1]) == "module" ) |
---|
| 1499 | { |
---|
| 1500 | def my = SchreyerSyzygyNF(syz_lead, syz_2, L, T, #[1]); |
---|
| 1501 | } else |
---|
| 1502 | { |
---|
| 1503 | def my = SchreyerSyzygyNF(syz_lead, syz_2, L, T); |
---|
| 1504 | } |
---|
| 1505 | |
---|
| 1506 | if( @KERCHECK ) |
---|
[4b2e47] | 1507 | { |
---|
[fe35f2] | 1508 | def spoly = leadmonomial(syz_lead) * T[int(leadcomp(syz_lead))] |
---|
| 1509 | + leadmonomial(syz_2) * T[int(leadcomp(syz_2))]; |
---|
| 1510 | |
---|
| 1511 | vector @tail = syz_2; |
---|
| 1512 | |
---|
| 1513 | while (size(spoly) > 0) |
---|
| 1514 | { |
---|
| 1515 | syz_2 = SSFindReducer(lead(spoly), 0, L, #); spoly = Tail(spoly); |
---|
| 1516 | |
---|
| 1517 | if( size(syz_2) != 0) |
---|
| 1518 | { |
---|
| 1519 | spoly = spoly + leadmonomial(syz_2) * T[int(leadcomp(syz_2))]; |
---|
| 1520 | @tail = @tail + syz_2; |
---|
| 1521 | } |
---|
| 1522 | } |
---|
| 1523 | |
---|
| 1524 | if( my != @tail ) |
---|
| 1525 | { |
---|
| 1526 | "ERROR in SchreyerSyzygyNF => old: ", @tail, " != ker: ", my; |
---|
| 1527 | |
---|
| 1528 | "syzygy_lead: ", syz_lead; |
---|
| 1529 | "syzygy 2nd : ", syz_2; |
---|
| 1530 | |
---|
| 1531 | L; T; #; |
---|
| 1532 | $; |
---|
| 1533 | } |
---|
[4b2e47] | 1534 | } |
---|
| 1535 | |
---|
| 1536 | if( @DEBUG ) |
---|
| 1537 | { |
---|
[fe35f2] | 1538 | "SSSchreyerSyzygyNF::Output: ", my; |
---|
[4b2e47] | 1539 | } |
---|
[fe35f2] | 1540 | |
---|
| 1541 | return (my); |
---|
[4b2e47] | 1542 | } |
---|
[8f57c0] | 1543 | |
---|
[fe35f2] | 1544 | |
---|
| 1545 | |
---|
[f37467] | 1546 | // -------------------------------------------------------- // |
---|
| 1547 | |
---|
| 1548 | // module (N, LL, TT) = SSComputeSyzygy(L, T); |
---|
| 1549 | // Compute Syz(L ++ T) = N = LL ++ TT |
---|
[fdde6ce] | 1550 | proc SSComputeSyzygy(def L, def T) |
---|
[6b6c82] | 1551 | { |
---|
[fdde6ce] | 1552 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1553 | { |
---|
| 1554 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1555 | } else |
---|
| 1556 | { |
---|
| 1557 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1558 | } |
---|
[8e650e] | 1559 | |
---|
[2c16b8] | 1560 | if( typeof( attrib(basering, "KERCHECK") ) == "int" ) |
---|
[8e650e] | 1561 | { |
---|
[2c16b8] | 1562 | int @KERCHECK = attrib(basering, "KERCHECK"); |
---|
[8e650e] | 1563 | } else |
---|
| 1564 | { |
---|
[2c16b8] | 1565 | int @KERCHECK = @DEBUG; |
---|
[8e650e] | 1566 | } |
---|
[fdde6ce] | 1567 | |
---|
[6b6c82] | 1568 | if( @DEBUG ) |
---|
| 1569 | { |
---|
| 1570 | "SSComputeSyzygy::Input"; |
---|
| 1571 | "basering: ", basering; attrib(basering); |
---|
| 1572 | // DetailedPrint(basering); |
---|
| 1573 | |
---|
[f37467] | 1574 | // "iCompShift: ", iCompShift; |
---|
[6b6c82] | 1575 | |
---|
| 1576 | "L: "; L; |
---|
| 1577 | "T: "; T; |
---|
| 1578 | } |
---|
| 1579 | |
---|
[14e93b] | 1580 | list @res = ComputeSyzygy(L, T); |
---|
[f37467] | 1581 | |
---|
[14e93b] | 1582 | module @LL = @res[1]; module @TT = @res[2]; |
---|
[7b7c2c] | 1583 | |
---|
[14e93b] | 1584 | if( @KERCHECK ) |
---|
[b2fb0c] | 1585 | { |
---|
[14e93b] | 1586 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1587 | { |
---|
| 1588 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1589 | } else |
---|
| 1590 | { |
---|
| 1591 | int @SYZCHECK = @DEBUG; |
---|
| 1592 | } |
---|
[b2fb0c] | 1593 | |
---|
[14e93b] | 1594 | int @LEAD2SYZ = 1; |
---|
| 1595 | if( typeof( attrib(basering, "LEAD2SYZ") ) == "int" ) |
---|
| 1596 | { |
---|
| 1597 | @LEAD2SYZ = attrib(basering, "LEAD2SYZ"); |
---|
| 1598 | } |
---|
[b2fb0c] | 1599 | |
---|
[14e93b] | 1600 | int @TAILREDSYZ = 1; |
---|
| 1601 | if( typeof( attrib(basering, "TAILREDSYZ") ) == "int" ) |
---|
| 1602 | { |
---|
| 1603 | @TAILREDSYZ = attrib(basering, "TAILREDSYZ"); |
---|
| 1604 | } |
---|
[4b2e47] | 1605 | |
---|
[14e93b] | 1606 | int @HYBRIDNF = 0; |
---|
| 1607 | if( typeof( attrib(basering, "HYBRIDNF") ) == "int" ) |
---|
| 1608 | { |
---|
| 1609 | @HYBRIDNF = attrib(basering, "HYBRIDNF"); |
---|
| 1610 | } |
---|
[4b2e47] | 1611 | |
---|
[14e93b] | 1612 | module LL; |
---|
[fdde6ce] | 1613 | |
---|
[14e93b] | 1614 | /// Get the critical leading syzygy terms |
---|
| 1615 | if( @LEAD2SYZ ) // & 2nd syz. term |
---|
| 1616 | { |
---|
| 1617 | module LL2; |
---|
| 1618 | (LL, LL2) = SSCompute2LeadingSyzygyTerms(L); |
---|
| 1619 | } else |
---|
[fdde6ce] | 1620 | { |
---|
[14e93b] | 1621 | LL = SSComputeLeadingSyzygyTerms(L); |
---|
[fdde6ce] | 1622 | } |
---|
[b2fb0c] | 1623 | |
---|
[14e93b] | 1624 | module TT, SYZ; |
---|
[8f57c0] | 1625 | |
---|
[14e93b] | 1626 | vector a, a2; bigint c; int r; poly aa; |
---|
| 1627 | |
---|
| 1628 | if( size(LL) > 0 ) |
---|
[4b2e47] | 1629 | { |
---|
[14e93b] | 1630 | list LS; |
---|
[4b2e47] | 1631 | |
---|
[14e93b] | 1632 | if( @TAILREDSYZ) |
---|
[b2fb0c] | 1633 | { |
---|
[14e93b] | 1634 | LS = list(LL); |
---|
| 1635 | } |
---|
[b2fb0c] | 1636 | |
---|
[14e93b] | 1637 | vector @tail; |
---|
[b2fb0c] | 1638 | |
---|
[14e93b] | 1639 | for(int k = ncols(LL); k > 0; k-- ) |
---|
[fdde6ce] | 1640 | { |
---|
[14e93b] | 1641 | // leading syz. term: |
---|
| 1642 | a = LL[k]; c = leadcomp(a); r = int(c); aa = leadmonomial(a); |
---|
| 1643 | |
---|
| 1644 | // NF reduction: |
---|
| 1645 | if( !@HYBRIDNF ) // Traverse approach: |
---|
| 1646 | { |
---|
| 1647 | @tail = SSTraverseTail(aa, T[r], L, T, LS); |
---|
[b2fb0c] | 1648 | |
---|
[14e93b] | 1649 | // get the 2nd syzygy term... |
---|
| 1650 | if( @LEAD2SYZ ) // with the 2nd syz. term: |
---|
| 1651 | { |
---|
| 1652 | a2 = LL2[k]; c = leadcomp(a2); r = int(c); aa = leadmonomial(a2); |
---|
| 1653 | |
---|
| 1654 | @tail = a2 + @tail + SSTraverseTail(aa, T[r], L, T, LS); |
---|
| 1655 | } else |
---|
| 1656 | { |
---|
| 1657 | @tail = @tail + SSReduceTerm(aa, L[r], a, L, T, LS); |
---|
| 1658 | } |
---|
| 1659 | |
---|
| 1660 | } else // Hybrid approach: |
---|
[b2fb0c] | 1661 | { |
---|
[14e93b] | 1662 | |
---|
| 1663 | // get the 2nd syzygy term... |
---|
| 1664 | if( @LEAD2SYZ ) |
---|
| 1665 | { |
---|
| 1666 | a2 = LL2[k]; |
---|
| 1667 | } else |
---|
| 1668 | { |
---|
| 1669 | a2 = SSFindReducer( aa * L[r], a, L, LS); |
---|
| 1670 | } |
---|
| 1671 | |
---|
| 1672 | if ( (@SYZCHECK || @DEBUG) ) |
---|
[b2fb0c] | 1673 | { |
---|
[14e93b] | 1674 | if( size(a2) == 0 ) // if syzterm == 0!!!! |
---|
| 1675 | { |
---|
| 1676 | "ERROR in SSComputeSyzygy: could not find the 2nd syzygy term during the hybrid NF!!!"; |
---|
| 1677 | $ |
---|
| 1678 | } |
---|
[b2fb0c] | 1679 | } |
---|
[14e93b] | 1680 | |
---|
| 1681 | @tail = SSSchreyerSyzygyNF(a, a2, L, T, LS); |
---|
[b2fb0c] | 1682 | } |
---|
| 1683 | |
---|
[14e93b] | 1684 | TT[k] = @tail; |
---|
| 1685 | SYZ[k] = a + @tail; |
---|
[b2fb0c] | 1686 | } |
---|
[4b2e47] | 1687 | } |
---|
[14e93b] | 1688 | |
---|
| 1689 | if( ncols(LL) != ncols(@LL) ) |
---|
| 1690 | { |
---|
| 1691 | "ERROR in SSComputeSyzygy: wrong leading syzygies!?"; |
---|
| 1692 | ""; |
---|
| 1693 | L; T; |
---|
| 1694 | ""; |
---|
| 1695 | type(LL); |
---|
| 1696 | type(@LL); |
---|
| 1697 | $ |
---|
| 1698 | } |
---|
| 1699 | |
---|
| 1700 | if( ncols(TT) != ncols(@TT) ) |
---|
| 1701 | { |
---|
| 1702 | "ERROR in SSComputeSyzygy: wrong tail syzygies!?"; |
---|
| 1703 | ""; |
---|
| 1704 | L; T; |
---|
| 1705 | ""; |
---|
| 1706 | type(LL); |
---|
| 1707 | type(@LL); |
---|
| 1708 | ""; |
---|
| 1709 | type(TT); |
---|
| 1710 | type(@TT); |
---|
| 1711 | $ |
---|
| 1712 | } |
---|
| 1713 | |
---|
| 1714 | if( size( module( matrix(LL) - matrix(@LL) ) ) != 0 ) |
---|
| 1715 | { |
---|
| 1716 | "ERROR in SSComputeSyzygy: wrong leading syzygies!?"; |
---|
| 1717 | ""; |
---|
| 1718 | L; T; |
---|
| 1719 | ""; |
---|
| 1720 | type(LL); |
---|
| 1721 | type(@LL); |
---|
| 1722 | $ |
---|
| 1723 | } |
---|
| 1724 | |
---|
| 1725 | |
---|
| 1726 | if( size( module( matrix(TT) - matrix(@TT) ) ) != 0 ) |
---|
| 1727 | { |
---|
| 1728 | "ERROR in SSComputeSyzygy: wrong tail syzygies!?"; |
---|
[c7d29b] | 1729 | ""; |
---|
[14e93b] | 1730 | TT; @TT; |
---|
[c7d29b] | 1731 | ""; |
---|
[14e93b] | 1732 | L; T; |
---|
[c7d29b] | 1733 | ""; |
---|
| 1734 | type(LL); |
---|
| 1735 | type(@LL); |
---|
[14e93b] | 1736 | $ |
---|
| 1737 | } |
---|
| 1738 | |
---|
[8f57c0] | 1739 | } |
---|
[6b6c82] | 1740 | |
---|
[14e93b] | 1741 | module @SYZ; |
---|
| 1742 | |
---|
| 1743 | for(int @k = ncols(@LL); @k > 0; @k-- ) |
---|
| 1744 | { |
---|
| 1745 | @SYZ[@k] = @LL[@k] + @TT[@k]; |
---|
| 1746 | } |
---|
| 1747 | |
---|
[6b6c82] | 1748 | if( @DEBUG ) |
---|
| 1749 | { |
---|
| 1750 | "SSComputeSyzygy::Output"; |
---|
| 1751 | |
---|
[14e93b] | 1752 | // "SYZ: "; @SYZ; |
---|
| 1753 | "LL: "; @LL; |
---|
| 1754 | "TT: "; @TT; |
---|
[6b6c82] | 1755 | } |
---|
| 1756 | |
---|
[14e93b] | 1757 | return (@SYZ, @LL, @TT); |
---|
[6b6c82] | 1758 | } |
---|
| 1759 | |
---|
| 1760 | // resolution/syzygy step: |
---|
| 1761 | static proc SSstep() |
---|
| 1762 | { |
---|
[b0ca43c] | 1763 | if( typeof( attrib(basering, "DEBUG") ) == "int" ) |
---|
| 1764 | { |
---|
| 1765 | int @DEBUG = attrib(basering, "DEBUG"); |
---|
| 1766 | } else |
---|
| 1767 | { |
---|
| 1768 | int @DEBUG = !system("with", "ndebug"); |
---|
| 1769 | } |
---|
| 1770 | |
---|
| 1771 | |
---|
| 1772 | if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) |
---|
| 1773 | { |
---|
| 1774 | int @SYZCHECK = attrib(basering, "SYZCHECK"); |
---|
| 1775 | } else |
---|
| 1776 | { |
---|
| 1777 | int @SYZCHECK = @DEBUG; |
---|
| 1778 | } |
---|
[6b6c82] | 1779 | |
---|
| 1780 | if( @DEBUG ) |
---|
| 1781 | { |
---|
| 1782 | "SSstep::NextInducedRing"; |
---|
| 1783 | "basering: ", basering; attrib(basering); |
---|
| 1784 | } |
---|
| 1785 | |
---|
| 1786 | /* |
---|
| 1787 | // is initial weights are all zeroes! |
---|
| 1788 | def L = lead(M); |
---|
| 1789 | intvec @V = deg(M[1..ncols(M)]); @W; @V; @W = @V; attrib(L, "isHomog", @W); |
---|
| 1790 | SetInducedReferrence(L, @RANK, 0); |
---|
| 1791 | */ |
---|
| 1792 | |
---|
| 1793 | // def L = lead(MRES); |
---|
| 1794 | // @W = @W, @V; |
---|
| 1795 | // attrib(L, "isHomog", @W); |
---|
| 1796 | |
---|
| 1797 | |
---|
| 1798 | // General setting: |
---|
| 1799 | // SetInducedReferrence(MRES, 0, 0); // limit: 0! |
---|
| 1800 | int @l = size(RES); |
---|
| 1801 | |
---|
| 1802 | def M = RES[@l]; |
---|
| 1803 | |
---|
| 1804 | def L = LRES[@l]; |
---|
| 1805 | def T = TRES[@l]; |
---|
| 1806 | |
---|
| 1807 | |
---|
| 1808 | //// TODO: wrong !!!!! |
---|
| 1809 | int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?! |
---|
| 1810 | |
---|
| 1811 | |
---|
| 1812 | |
---|
| 1813 | /* |
---|
| 1814 | if( @RANK != nrows(M) ) |
---|
| 1815 | { |
---|
| 1816 | type(MRES); |
---|
| 1817 | @RANK; |
---|
| 1818 | type(M); |
---|
| 1819 | pause(); |
---|
| 1820 | } |
---|
| 1821 | */ |
---|
| 1822 | |
---|
| 1823 | intvec @W = attrib(M, "isHomog"); intvec @V = attrib(M, "degrees"); @V = @W, @V; |
---|
| 1824 | |
---|
| 1825 | if( @DEBUG ) |
---|
| 1826 | { |
---|
| 1827 | "Sstep::NextInput: "; |
---|
| 1828 | M; |
---|
| 1829 | L; |
---|
| 1830 | @V; |
---|
| 1831 | @RANK; |
---|
[4b2e47] | 1832 | // DetailedPrint(MRES); |
---|
[6b6c82] | 1833 | attrib(MRES, "isHomog"); |
---|
| 1834 | } |
---|
| 1835 | |
---|
| 1836 | |
---|
| 1837 | // TODO: N = SYZ( M )!!! |
---|
[f37467] | 1838 | module N, LL, TT; |
---|
| 1839 | (N, LL, TT) = SSComputeSyzygy(/*M, */L, T/*, @RANK*/); |
---|
| 1840 | |
---|
| 1841 | // shift syz.comp by @RANK: |
---|
| 1842 | module Z; |
---|
| 1843 | Z = 0; Z[@RANK] = 0; Z = Z, transpose(LL); LL = transpose(Z); |
---|
| 1844 | Z = 0; Z[@RANK] = 0; Z = Z, transpose(TT); TT = transpose(Z); |
---|
| 1845 | Z = 0; Z[@RANK] = 0; Z = Z, transpose(N); N = transpose(Z); |
---|
[6b6c82] | 1846 | |
---|
| 1847 | |
---|
[b0ca43c] | 1848 | if( @SYZCHECK ) |
---|
[6b6c82] | 1849 | { |
---|
[b0ca43c] | 1850 | if( size(N) > 0 ) |
---|
[6b6c82] | 1851 | { |
---|
[f37467] | 1852 | // next syz. property |
---|
| 1853 | if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 ) |
---|
| 1854 | { |
---|
| 1855 | "MRES", MRES; |
---|
[6b6c82] | 1856 | |
---|
[f37467] | 1857 | "N: "; N; // DetailedPrint(N, 2); |
---|
[6b6c82] | 1858 | |
---|
[f37467] | 1859 | "LL:"; LL; // DetailedPrint(LL, 1); |
---|
| 1860 | "TT:"; TT; // DetailedPrint(TT, 10); |
---|
[6b6c82] | 1861 | |
---|
[f37467] | 1862 | "RANKS: ", @RANK; |
---|
[6b6c82] | 1863 | |
---|
[f37467] | 1864 | "transpose( transpose(N) * transpose(MRES) ) != 0!!!"; |
---|
| 1865 | transpose( transpose(N) * transpose(MRES) ); |
---|
[6b6c82] | 1866 | |
---|
[f37467] | 1867 | "transpose(N) * transpose(MRES): "; |
---|
| 1868 | transpose(N) * transpose(MRES); |
---|
| 1869 | // DetailedPrint(module(_), 2); |
---|
| 1870 | $ |
---|
| 1871 | } |
---|
[6b6c82] | 1872 | } |
---|
| 1873 | } |
---|
[f37467] | 1874 | |
---|
| 1875 | attrib(N, "isHomog", @V); |
---|
| 1876 | |
---|
| 1877 | // TODO: correct the following: |
---|
| 1878 | intvec @DEGS = deg(N[1..ncols(N)]); // no mod. comp. weights :( |
---|
| 1879 | |
---|
| 1880 | |
---|
| 1881 | attrib(N, "degrees", @DEGS); |
---|
[6b6c82] | 1882 | |
---|
| 1883 | RES[@l + 1] = N; // list of all syzygy modules |
---|
| 1884 | LRES[@l + 1] = LL; // list of all syzygy modules |
---|
| 1885 | TRES[@l + 1] = TT; // list of all syzygy modules |
---|
| 1886 | |
---|
| 1887 | MRES = MRES, N; |
---|
[f37467] | 1888 | |
---|
[6b6c82] | 1889 | attrib(MRES, "isHomog", @V); |
---|
| 1890 | |
---|
| 1891 | // L = L, lead(N); attrib(basering, "InducionLeads", L); |
---|
| 1892 | |
---|
| 1893 | if( @DEBUG ) |
---|
| 1894 | { |
---|
| 1895 | "SSstep::NextSyzOutput: "; |
---|
[f37467] | 1896 | N; |
---|
[4b2e47] | 1897 | // DetailedPrint(N); |
---|
[6b6c82] | 1898 | attrib(N); |
---|
| 1899 | } |
---|
| 1900 | |
---|
| 1901 | } |
---|
| 1902 | |
---|
| 1903 | proc SScontinue(int l) |
---|
| 1904 | "USAGE: SScontinue(l) |
---|
| 1905 | RETURN: nothing, instead it changes RES and MRES variables in the current ring |
---|
| 1906 | PURPOSE: computes further (at most l) syzygies |
---|
| 1907 | NOTE: must be used within a ring returned by Sres or Ssyz. RES and MRES are |
---|
| 1908 | explained in Sres |
---|
| 1909 | EXAMPLE: example Scontinue; shows an example |
---|
| 1910 | " |
---|
| 1911 | { |
---|
| 1912 | |
---|
| 1913 | /// TODO! |
---|
| 1914 | // def data = GetInducedData(); |
---|
| 1915 | |
---|
| 1916 | if( (!defined(RES)) || (!defined(MRES)) ) /* || (typeof(data) != "list") || (size(data) != 2) */ |
---|
| 1917 | { |
---|
| 1918 | ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz"); |
---|
| 1919 | } |
---|
| 1920 | for (; (l != 0) && (size(RES[size(RES)]) > 0); l-- ) |
---|
| 1921 | { |
---|
| 1922 | SSstep(); |
---|
| 1923 | } |
---|
| 1924 | } |
---|
| 1925 | example |
---|
| 1926 | { "EXAMPLE:"; echo = 2; |
---|
| 1927 | ring r; |
---|
| 1928 | module M = maxideal(1); M; |
---|
| 1929 | def S = SSsyz(M); setring S; S; |
---|
| 1930 | "Only the first syzygy: "; |
---|
| 1931 | RES; MRES; |
---|
| 1932 | "More syzygies: "; |
---|
| 1933 | SScontinue(10); |
---|
| 1934 | RES; MRES; |
---|
| 1935 | } |
---|
| 1936 | |
---|
| 1937 | proc SSsyz(def M) |
---|
| 1938 | "USAGE: SSsyz(M) |
---|
| 1939 | RETURN: ring, containing a list of modules RES and a module MRES |
---|
| 1940 | PURPOSE: computes the first syzygy module of M (wrt some Schreyer ordering)? |
---|
| 1941 | NOTE: The output is explained in Sres |
---|
| 1942 | EXAMPLE: example Ssyz; shows an example |
---|
| 1943 | " |
---|
| 1944 | { |
---|
| 1945 | if( (typeof(M) != "module") && (typeof(M) != "ideal") ) |
---|
| 1946 | { |
---|
| 1947 | ERROR("Sorry: need an ideal or a module for input"); |
---|
| 1948 | } |
---|
| 1949 | |
---|
| 1950 | def SS = SSinit(M); setring SS; |
---|
| 1951 | |
---|
| 1952 | SSstep(); // NOTE: what if M is zero? |
---|
| 1953 | |
---|
| 1954 | return (SS); |
---|
| 1955 | } |
---|
| 1956 | example |
---|
| 1957 | { "EXAMPLE:"; echo = 2; |
---|
| 1958 | ring r; |
---|
| 1959 | |
---|
| 1960 | /* ideal M = 0; |
---|
| 1961 | def S = SSsyz(M); setring S; S; |
---|
| 1962 | "Only the first syzygy: "; |
---|
| 1963 | RES; LRES; TRES; |
---|
| 1964 | MRES; |
---|
| 1965 | |
---|
| 1966 | kill S; setring r; kill M; |
---|
| 1967 | */ |
---|
| 1968 | |
---|
[7b7c2c] | 1969 | ideal M = maxideal(1); M; |
---|
[b2fb0c] | 1970 | |
---|
[4b2e47] | 1971 | def S = SSres(M, 0); setring S; S; |
---|
[6b6c82] | 1972 | MRES; |
---|
[8b368ff] | 1973 | print(_); |
---|
[f37467] | 1974 | RES; |
---|
[6b6c82] | 1975 | |
---|
| 1976 | kill S; setring r; kill M; |
---|
| 1977 | |
---|
| 1978 | kill r; |
---|
| 1979 | |
---|
| 1980 | ring R = 0, (w, x, y, z), dp; |
---|
| 1981 | ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; |
---|
| 1982 | |
---|
[4b2e47] | 1983 | def S = SSres(M, 0); setring S; S; |
---|
[f37467] | 1984 | ""; |
---|
| 1985 | LRES; |
---|
| 1986 | ""; |
---|
[8b368ff] | 1987 | TRES; |
---|
| 1988 | ""; |
---|
| 1989 | MRES; |
---|
| 1990 | print(_); |
---|
| 1991 | RES; |
---|
[6b6c82] | 1992 | } |
---|
| 1993 | |
---|
| 1994 | proc SSres(def M, int l) |
---|
| 1995 | "USAGE: SSres(I, l) |
---|
| 1996 | RETURN: ring, containing a list of modules RES and a module MRES |
---|
| 1997 | PURPOSE: computes (at most l) syzygy modules of M wrt the classical Schreyer |
---|
| 1998 | induced ordering with gen(i) > gen(j) if i > j, provided both gens |
---|
| 1999 | are from the same syzygy level.??? |
---|
| 2000 | NOTE: RES contains the images of maps subsituting the beginning of the |
---|
| 2001 | Schreyer free resolution of baseRing^r/M, while MRES is a sum of |
---|
| 2002 | these images in a big free sum, containing all the syzygy modules. |
---|
| 2003 | The syzygy modules are shifted so that gen(i) correspons to MRES[i]. |
---|
| 2004 | The leading zero module RES[0] indicates the fact that coker of the |
---|
| 2005 | first map is zero. The number of zeroes inducates the rank of input. |
---|
| 2006 | NOTE: If l == 0 then l is set to be nvars(basering) + 1 |
---|
| 2007 | EXAMPLE: example SSres; shows an example |
---|
| 2008 | " |
---|
| 2009 | { |
---|
| 2010 | if( (typeof(M) != "module") && (typeof(M) != "ideal") ) |
---|
| 2011 | { |
---|
| 2012 | ERROR("Sorry: need an ideal or a module for input"); |
---|
| 2013 | } |
---|
| 2014 | |
---|
| 2015 | def SS = SSinit(M); setring SS; |
---|
| 2016 | |
---|
| 2017 | if (l == 0) |
---|
| 2018 | { |
---|
| 2019 | l = nvars(basering) + 1; // not really an estimate...?! |
---|
| 2020 | } |
---|
| 2021 | |
---|
| 2022 | SSstep(); l = l - 1; |
---|
| 2023 | |
---|
| 2024 | SScontinue(l); |
---|
| 2025 | |
---|
| 2026 | return (SS); |
---|
| 2027 | } |
---|
| 2028 | example |
---|
| 2029 | { "EXAMPLE:"; echo = 2; |
---|
| 2030 | ring r; |
---|
| 2031 | module M = maxideal(1); M; |
---|
| 2032 | def S = SSres(M, 0); setring S; S; |
---|
| 2033 | RES; |
---|
| 2034 | MRES; |
---|
| 2035 | kill S; |
---|
| 2036 | setring r; kill M; |
---|
| 2037 | |
---|
| 2038 | def A = nc_algebra(-1,0); setring A; |
---|
| 2039 | ideal Q = var(1)^2, var(2)^2, var(3)^2; |
---|
| 2040 | qring SCA = twostd(Q); |
---|
| 2041 | basering; |
---|
| 2042 | |
---|
| 2043 | module M = maxideal(1); |
---|
| 2044 | def S = SSres(M, 2); setring S; S; |
---|
| 2045 | RES; |
---|
| 2046 | MRES; |
---|
| 2047 | } |
---|
| 2048 | |
---|
| 2049 | |
---|
[4c6c938] | 2050 | |
---|
| 2051 | static proc loadme() |
---|
| 2052 | { |
---|
| 2053 | int @DEBUG = !system("with", "ndebug"); |
---|
| 2054 | |
---|
| 2055 | if( @DEBUG ) |
---|
| 2056 | { |
---|
| 2057 | |
---|
| 2058 | "ndebug?: ", system("with", "ndebug"); |
---|
| 2059 | "om_ndebug?: ", system("with", "om_ndebug"); |
---|
| 2060 | |
---|
| 2061 | listvar(Top); |
---|
| 2062 | listvar(Schreyer); |
---|
| 2063 | } |
---|
| 2064 | // listvar(Syzextra); listvar(Syzextra_g); |
---|
| 2065 | |
---|
| 2066 | if( !defined(DetailedPrint) ) |
---|
| 2067 | { |
---|
[b5d6f0] | 2068 | if( 1 ) |
---|
[4c6c938] | 2069 | { |
---|
| 2070 | |
---|
| 2071 | if( @DEBUG ) |
---|
| 2072 | { |
---|
| 2073 | "Loading the Release version!"; |
---|
| 2074 | } |
---|
| 2075 | load("syzextra.so"); |
---|
| 2076 | |
---|
| 2077 | if( @DEBUG ) |
---|
| 2078 | { |
---|
| 2079 | listvar(Syzextra); |
---|
| 2080 | } |
---|
[ff12c6] | 2081 | |
---|
| 2082 | exportto(Top, Syzextra::ClearContent); |
---|
| 2083 | exportto(Top, Syzextra::ClearDenominators); |
---|
[7b7c2c] | 2084 | |
---|
| 2085 | exportto(Schreyer, Syzextra::m2_end); |
---|
[4c6c938] | 2086 | |
---|
| 2087 | // export Syzextra; |
---|
| 2088 | |
---|
| 2089 | // exportto(Schreyer, Syzextra::noop); |
---|
| 2090 | exportto(Schreyer, Syzextra::DetailedPrint); |
---|
[4b2e47] | 2091 | exportto(Schreyer, Syzextra::leadmonomial); |
---|
[4c6c938] | 2092 | exportto(Schreyer, Syzextra::leadcomp); |
---|
| 2093 | // exportto(Schreyer, Syzextra::leadrawexp); |
---|
| 2094 | // exportto(Schreyer, Syzextra::ISUpdateComponents); |
---|
| 2095 | exportto(Schreyer, Syzextra::SetInducedReferrence); |
---|
| 2096 | exportto(Schreyer, Syzextra::GetInducedData); |
---|
[71e402] | 2097 | // exportto(Schreyer, Syzextra::GetAMData); |
---|
[4c6c938] | 2098 | // exportto(Schreyer, Syzextra::SetSyzComp); |
---|
| 2099 | exportto(Schreyer, Syzextra::MakeInducedSchreyerOrdering); |
---|
| 2100 | // exportto(Schreyer, Syzextra::MakeSyzCompOrdering); |
---|
| 2101 | exportto(Schreyer, Syzextra::idPrepare); |
---|
| 2102 | // exportto(Schreyer, Syzextra::reduce_syz); |
---|
| 2103 | // exportto(Schreyer, Syzextra::p_Content); |
---|
| 2104 | |
---|
[f63b13] | 2105 | exportto(Schreyer, Syzextra::ProfilerStart); exportto(Schreyer, Syzextra::ProfilerStop); |
---|
| 2106 | |
---|
[e89ff5] | 2107 | exportto(Schreyer, Syzextra::Tail); |
---|
[7b7c2c] | 2108 | exportto(Schreyer, Syzextra::ComputeLeadingSyzygyTerms); |
---|
[74afe1f] | 2109 | exportto(Schreyer, Syzextra::Compute2LeadingSyzygyTerms); |
---|
[8b78ee] | 2110 | exportto(Schreyer, Syzextra::Sort_c_ds); |
---|
[33161fd] | 2111 | |
---|
| 2112 | exportto(Schreyer, Syzextra::FindReducer); |
---|
[fe35f2] | 2113 | |
---|
| 2114 | exportto(Schreyer, Syzextra::ReduceTerm); |
---|
| 2115 | exportto(Schreyer, Syzextra::TraverseTail); |
---|
| 2116 | |
---|
| 2117 | exportto(Schreyer, Syzextra::SchreyerSyzygyNF); |
---|
[14e93b] | 2118 | exportto(Schreyer, Syzextra::ComputeSyzygy); |
---|
[4c6c938] | 2119 | } |
---|
[b5d6f0] | 2120 | /* |
---|
[4c6c938] | 2121 | else |
---|
| 2122 | { |
---|
| 2123 | if( @DEBUG ) |
---|
| 2124 | { |
---|
| 2125 | "Loading the Debug version!"; |
---|
| 2126 | } |
---|
| 2127 | |
---|
[b5d6f0] | 2128 | load("syzextra.so"); |
---|
[4c6c938] | 2129 | |
---|
| 2130 | if( @DEBUG ) |
---|
| 2131 | { |
---|
| 2132 | listvar(Syzextra_g); |
---|
| 2133 | } |
---|
| 2134 | |
---|
[ff12c6] | 2135 | exportto(Top, Syzextra_g::ClearContent); |
---|
| 2136 | exportto(Top, Syzextra_g::ClearDenominators); |
---|
| 2137 | |
---|
[7b7c2c] | 2138 | exportto(Schreyer, Syzextra_g::m2_end); |
---|
| 2139 | |
---|
[4c6c938] | 2140 | // export Syzextra_g; |
---|
| 2141 | // exportto(Schreyer, Syzextra_g::noop); |
---|
| 2142 | exportto(Schreyer, Syzextra_g::DetailedPrint); |
---|
[4b2e47] | 2143 | exportto(Schreyer, Syzextra_g::leadmonomial); |
---|
[4c6c938] | 2144 | exportto(Schreyer, Syzextra_g::leadcomp); |
---|
| 2145 | // exportto(Schreyer, Syzextra_g::leadrawexp); |
---|
| 2146 | // exportto(Schreyer, Syzextra_g::ISUpdateComponents); |
---|
| 2147 | exportto(Schreyer, Syzextra_g::SetInducedReferrence); |
---|
| 2148 | exportto(Schreyer, Syzextra_g::GetInducedData); |
---|
[71e402] | 2149 | // exportto(Schreyer, Syzextra_g::GetAMData); |
---|
[4c6c938] | 2150 | // exportto(Schreyer, Syzextra_g::SetSyzComp); |
---|
| 2151 | exportto(Schreyer, Syzextra_g::MakeInducedSchreyerOrdering); |
---|
| 2152 | // exportto(Schreyer, Syzextra_g::MakeSyzCompOrdering); |
---|
| 2153 | exportto(Schreyer, Syzextra_g::idPrepare); |
---|
| 2154 | // exportto(Schreyer, Syzextra_g::reduce_syz); |
---|
| 2155 | // exportto(Schreyer, Syzextra_g::p_Content); |
---|
| 2156 | |
---|
[f63b13] | 2157 | exportto(Schreyer, Syzextra_g::ProfilerStart); exportto(Schreyer, Syzextra_g::ProfilerStop); |
---|
| 2158 | |
---|
[e89ff5] | 2159 | exportto(Schreyer, Syzextra_g::Tail); |
---|
[8b78ee] | 2160 | exportto(Schreyer, Syzextra_g::ComputeLeadingSyzygyTerms); |
---|
[74afe1f] | 2161 | exportto(Schreyer, Syzextra_g::Compute2LeadingSyzygyTerms); |
---|
[8b78ee] | 2162 | exportto(Schreyer, Syzextra_g::Sort_c_ds); |
---|
[33161fd] | 2163 | |
---|
| 2164 | exportto(Schreyer, Syzextra_g::FindReducer); |
---|
[8b78ee] | 2165 | |
---|
[fe35f2] | 2166 | exportto(Schreyer, Syzextra_g::ReduceTerm); |
---|
| 2167 | exportto(Schreyer, Syzextra_g::TraverseTail); |
---|
| 2168 | |
---|
| 2169 | exportto(Schreyer, Syzextra_g::SchreyerSyzygyNF); |
---|
[14e93b] | 2170 | exportto(Schreyer, Syzextra_g::ComputeSyzygy); |
---|
[4c6c938] | 2171 | } |
---|
[b5d6f0] | 2172 | */ |
---|
[4c6c938] | 2173 | |
---|
| 2174 | exportto(Top, DetailedPrint); |
---|
| 2175 | exportto(Top, GetInducedData); |
---|
| 2176 | |
---|
| 2177 | if( @DEBUG ) |
---|
| 2178 | { |
---|
| 2179 | listvar(Top); |
---|
| 2180 | listvar(Schreyer); |
---|
| 2181 | } |
---|
| 2182 | } |
---|
| 2183 | |
---|
| 2184 | if( !defined(GetInducedData) ) |
---|
| 2185 | { |
---|
[b5d6f0] | 2186 | ERROR("Sorry but we are missing the dynamic module (syzextra.so)..."); |
---|
[4c6c938] | 2187 | } |
---|
| 2188 | |
---|
| 2189 | } |
---|
| 2190 | |
---|
| 2191 | static proc mod_init() |
---|
| 2192 | { |
---|
| 2193 | loadme(); |
---|
| 2194 | } |
---|
| 2195 | |
---|
| 2196 | |
---|
| 2197 | proc testallSexamples() |
---|
| 2198 | { |
---|
| 2199 | example Ssyz; |
---|
| 2200 | example Scontinue; |
---|
| 2201 | example Sres; |
---|
| 2202 | } |
---|
[6b6c82] | 2203 | |
---|
| 2204 | proc testallSSexamples() |
---|
| 2205 | { |
---|
| 2206 | example SSsyz; |
---|
| 2207 | example SScontinue; |
---|
| 2208 | example SSres; |
---|
| 2209 | } |
---|
| 2210 | |
---|
[4c6c938] | 2211 | example |
---|
| 2212 | { "EXAMPLE:"; echo = 2; |
---|
| 2213 | testallSexamples(); |
---|
[6b6c82] | 2214 | testallSSexamples(); |
---|
[ff12c6] | 2215 | } |
---|
[c1931a4] | 2216 | |
---|
| 2217 | proc TestSSres(def M) |
---|
| 2218 | { |
---|
[f6c459] | 2219 | "/ ----------------------------------- : ", "options: ", attrib(SSinit, "LEAD2SYZ"), attrib(SSinit, "TAILREDSYZ"), attrib(SSinit, "HYBRIDNF"), "..."; |
---|
[c1931a4] | 2220 | int t = timer; |
---|
| 2221 | def S = SSres(M, 0); |
---|
| 2222 | int tt = timer; |
---|
| 2223 | /* |
---|
| 2224 | setring S; |
---|
| 2225 | |
---|
| 2226 | MRES; |
---|
| 2227 | RES; |
---|
| 2228 | ""; |
---|
| 2229 | LRES; |
---|
| 2230 | ""; |
---|
| 2231 | TRES; |
---|
| 2232 | */ |
---|
| 2233 | kill S; |
---|
[4eba3ad] | 2234 | "\\ ----------------------------------- / ", "options: ", attrib(SSinit, "LEAD2SYZ"), attrib(SSinit, "TAILREDSYZ"), attrib(SSinit, "HYBRIDNF"), ": ", "Time: ", tt - t; |
---|
[9cf220] | 2235 | } |
---|
| 2236 | |
---|
| 2237 | |
---|
| 2238 | proc TestSres(def M) |
---|
| 2239 | { |
---|
| 2240 | def opts = option(get); |
---|
| 2241 | option(redSB); option(redTail); |
---|
| 2242 | "/ ----------------------------------- : Sres ..."; |
---|
| 2243 | int t = timer; |
---|
| 2244 | def S = Sres(M, 0); |
---|
| 2245 | int tt = timer; |
---|
| 2246 | /* |
---|
| 2247 | setring S; |
---|
| 2248 | |
---|
| 2249 | MRES; |
---|
| 2250 | RES; |
---|
| 2251 | ""; |
---|
| 2252 | LRES; |
---|
| 2253 | ""; |
---|
| 2254 | TRES; |
---|
| 2255 | */ |
---|
| 2256 | kill S; |
---|
| 2257 | "\ ----------------------------------- / Sres ", "Time: ", tt - t; |
---|
| 2258 | option(set, opts); |
---|
| 2259 | kill opts; |
---|
| 2260 | } |
---|
| 2261 | |
---|
| 2262 | |
---|
| 2263 | proc Testsres(def M) |
---|
| 2264 | { |
---|
| 2265 | def opts = option(get); |
---|
| 2266 | option(redSB); option(redTail); |
---|
| 2267 | "/ ----------------------------------- : sres ..."; |
---|
| 2268 | int t = timer; |
---|
| 2269 | def S = list(sres(M, 0)); |
---|
| 2270 | int tt = timer; |
---|
| 2271 | /* |
---|
| 2272 | setring S; |
---|
| 2273 | |
---|
| 2274 | MRES; |
---|
| 2275 | RES; |
---|
| 2276 | ""; |
---|
| 2277 | LRES; |
---|
| 2278 | ""; |
---|
| 2279 | TRES; |
---|
| 2280 | */ |
---|
| 2281 | kill S; |
---|
| 2282 | "\ ----------------------------------- / sres ", "Time: ", tt - t; |
---|
| 2283 | option(set, opts); |
---|
| 2284 | kill opts; |
---|
| 2285 | } |
---|
| 2286 | |
---|
| 2287 | |
---|
| 2288 | proc Testlres(def M) |
---|
| 2289 | { |
---|
| 2290 | def opts = option(get); |
---|
| 2291 | option(redSB); option(redTail); |
---|
| 2292 | "/ ----------------------------------- : lres ..."; |
---|
| 2293 | int t = timer; |
---|
| 2294 | def S = list(lres(M, 0)); |
---|
| 2295 | int tt = timer; |
---|
| 2296 | kill S; |
---|
| 2297 | "\ ----------------------------------- / lres ", "Time: ", tt - t; |
---|
| 2298 | option(set, opts); |
---|
| 2299 | kill opts; |
---|
| 2300 | } |
---|
| 2301 | |
---|
| 2302 | |
---|
| 2303 | proc Testnres(def M) |
---|
| 2304 | { |
---|
| 2305 | def opts = option(get); |
---|
| 2306 | option(redSB); option(redTail); |
---|
| 2307 | "/ ----------------------------------- : nres ..."; |
---|
| 2308 | int t = timer; |
---|
| 2309 | def S = list(nres(M, 0)); |
---|
| 2310 | int tt = timer; |
---|
| 2311 | kill S; |
---|
| 2312 | "\ ----------------------------------- / nres ", "Time: ", tt - t; |
---|
| 2313 | option(set, opts); |
---|
| 2314 | kill opts; |
---|
[c1931a4] | 2315 | } |
---|
| 2316 | |
---|
| 2317 | |
---|
| 2318 | proc TestSSresAttribs(def M) |
---|
| 2319 | { |
---|
[f6c459] | 2320 | // M = groebner(M); "groebner: "; M; ""; |
---|
| 2321 | |
---|
[c1931a4] | 2322 | |
---|
| 2323 | // the following 2 setups are bad for AGR@101n3d002s004%1:((( |
---|
[f6c459] | 2324 | |
---|
| 2325 | ////////// attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
---|
| 2326 | ////////// attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
---|
[c1931a4] | 2327 | |
---|
| 2328 | attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
---|
| 2329 | attrib(SSinit, "LEAD2SYZ", 0); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
---|
| 2330 | |
---|
| 2331 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
---|
| 2332 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 0); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
---|
| 2333 | |
---|
| 2334 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
---|
| 2335 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
---|
| 2336 | } |
---|
| 2337 | |
---|
| 2338 | |
---|
[9cf220] | 2339 | proc TestSSresAttribs2tr(def M) |
---|
| 2340 | { |
---|
| 2341 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 0); TestSSres(M); |
---|
| 2342 | attrib(SSinit, "LEAD2SYZ", 1); attrib(SSinit, "TAILREDSYZ", 1); attrib(SSinit, "HYBRIDNF", 1); TestSSres(M); |
---|
| 2343 | |
---|
| 2344 | Testlres(M); |
---|
| 2345 | Testnres(M); |
---|
| 2346 | Testsres(M); |
---|
| 2347 | // TestSres(M); // too long for the last medium test :( |
---|
| 2348 | } |
---|
| 2349 | |
---|
| 2350 | |
---|
[c1931a4] | 2351 | proc testALLA() |
---|
| 2352 | { |
---|
[d353e4f] | 2353 | // TODO: only for now!! |
---|
| 2354 | attrib(SSinit, "DEBUG", 0); |
---|
| 2355 | attrib(SSinit, "SYZCHECK", 1); |
---|
[f6c459] | 2356 | attrib(SSinit, "KERCHECK", 1); |
---|
[c1931a4] | 2357 | |
---|
| 2358 | ring r; r; ideal M = maxideal(1); M; |
---|
| 2359 | TestSSresAttribs(M); |
---|
| 2360 | kill r; |
---|
| 2361 | |
---|
| 2362 | ring r = 0, (a, b, c, d), lp; r; ideal M = maxideal(1); M; |
---|
| 2363 | TestSSresAttribs(M); |
---|
| 2364 | kill r; |
---|
| 2365 | |
---|
| 2366 | ring R = 0, (w, x, y, z), dp; R; |
---|
| 2367 | ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; M; |
---|
| 2368 | TestSSresAttribs(M); |
---|
| 2369 | kill R; |
---|
| 2370 | |
---|
[d353e4f] | 2371 | |
---|
| 2372 | ring r = 0, (a, b, c, d, e, f), dp; r; ideal M = maxideal(1); M; |
---|
| 2373 | TestSSresAttribs(M); |
---|
| 2374 | kill r; |
---|
[c1931a4] | 2375 | |
---|
| 2376 | ring AGR = (101), (a, b, c, d), dp; AGR; |
---|
| 2377 | // simple: AGR@101n3d002s004%1: |
---|
| 2378 | 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; |
---|
| 2379 | M; |
---|
| 2380 | TestSSresAttribs(M); |
---|
| 2381 | |
---|
| 2382 | // medium: AGR@101n3d004s009%1; |
---|
[f6c459] | 2383 | 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; |
---|
[c1931a4] | 2384 | M; |
---|
| 2385 | TestSSresAttribs(M); |
---|
[9cf220] | 2386 | } |
---|
| 2387 | |
---|
| 2388 | proc testAGR() |
---|
| 2389 | { |
---|
| 2390 | attrib(SSinit, "DEBUG", 0); |
---|
| 2391 | attrib(SSinit, "SYZCHECK", 1); |
---|
| 2392 | attrib(SSinit, "KERCHECK", 0); |
---|
[c1931a4] | 2393 | |
---|
[9cf220] | 2394 | ring AGR = (101), (a, b, c, d), dp; AGR; |
---|
| 2395 | // lengthy: AGR@101n3d008s058%3, kernel only! |
---|
[c1931a4] | 2396 | ideal M = 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|
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| 2397 | M; |
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[9cf220] | 2398 | TestSSresAttribs2tr(M); |
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| 2399 | |
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| 2400 | // AGR@101n3d010s010%3, a bit slower... |
---|
| 2401 | M = 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b*d^7+42*c*d^7+d^8,a^2*b^3*c^3+10*c^2*d^6+31*a*d^7+45*b*d^7-44*c*d^7+37*d^8,a^3*b^2*c^3-41*c^2*d^6-15*a*d^7-34*b*d^7-22*c*d^7+28*d^8,a^4*b*c^3+19*c^2*d^6-23*a*d^7+18*b*d^7-13*c*d^7-48*d^8,a^5*c^3+16*c^2*d^6+22*a*d^7-31*b*d^7+33*c*d^7+15*d^8,b^6*c^2-42*c^2*d^6-10*a*d^7-16*b*d^7-46*c*d^7+42*d^8,a*b^5*c^2-23*c^2*d^6+34*a*d^7-37*b*d^7+2*c*d^7+10*d^8,a^2*b^4*c^2-45*c^2*d^6-5*a*d^7+43*b*d^7-18*c*d^7+7*d^8,a^3*b^3*c^2+36*c^2*d^6+19*a*d^7+21*b*d^7+46*c*d^7-24*d^8,a^4*b^2*c^2-17*c^2*d^6+30*a*d^7-39*b*d^7-39*c*d^7-24*d^8,a^5*b*c^2+10*c^2*d^6-24*a*d^7-36*b*d^7-14*c*d^7+26*d^8,a^6*c^2+47*c^2*d^6-41*a*d^7+32*b*d^7+6*c*d^7+42*d^8,b^7*c+44*c^2*d^6-6*a*d^7+5*b*d^7+20*c*d^7+50*d^8,a*b^6*c+29*c^2*d^6-16*a*d^7+45*b*d^7-3*c*d^7+14*d^8,b^8+48*c^2*d^6-40*a*d^7-44*b*d^7-10*c*d^7-23*d^8,a*b^7-32*c^2*d^6-41*a*d^7-11*b*d^7+50*c*d^7+13*d^8,d^9,c*d^8,b*d^8,a*d^8,c^2*d^7; |
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| 2402 | M; |
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| 2403 | TestSSresAttribs2tr(M); |
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| 2404 | |
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[c1931a4] | 2405 | kill AGR; |
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| 2406 | |
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[9cf220] | 2407 | ring AGR = (101), (a,b,c,d,e,f,g,h), dp; AGR; |
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| 2408 | // AGR@101n7d005s010%2) medium: <= 2 |
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| 2409 | ideal M = f*h-g*h,e*h-g*h,d*h-g*h,c*h-g*h,b*h-g*h,a*h-g*h,e*g+48*f*g-49*g*h,d*g+5*f*g-6*g*h,c*g+49*f*g-50*g*h,b*g-7*f*g+6*g*h,a*g-50*f*g+49*g*h,e*f-20*f*g+19*g*h,d*f+40*f*g-41*g*h,c*f-12*f*g+11*g*h,b*f+45*f*g-46*g*h,a*f+4*f*g-5*g*h,d*e-f*g,c*e-30*f*g+29*g*h,b*e-39*f*g+38*g*h,a*e+10*f*g-11*g*h,c*d-41*f*g+40*g*h,b*d-23*f*g+22*g*h,a*d-20*f*g+19*g*h,b*c+17*f*g-18*g*h,a*c+6*f*g-7*g*h,a*b+28*f*g-29*g*h,g^2*h-g*h^2,f^2*g-8*f*g^2+7*g*h^2,g*h^4+50*h^5,g^5+41*h^5,f*g^4-18*h^5,f^5+29*h^5,e^5+6*h^5,d^5-23*h^5,c^5-32*h^5,b^5+17*h^5,a^5+17*h^5,h^6; |
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| 2410 | M; |
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| 2411 | TestSSresAttribs2tr(M); |
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[c1931a4] | 2412 | } |
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| 2413 | |
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| 2414 | // TODO: betti!!! |
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