/////////////////////////////////////////////////////////////////////////// version="version schreyer.lib 4.0.0.0 Jun_2013 "; // $Id$ category="General purpose"; info=" LIBRARY: schreyer.lib Helpers for computing a Schreyer resolution in @code{derham.lib} AUTHOR: Oleksandr Motsak , where U={motsak}, D={mathematik.uni-kl.de} KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy OVERVIEW: @* The library contains helper procedures for computing a Schreyer resoltion (cf. [SFO]), originally meant to be used by @code{derham.lib} (which requires resolutions over the homogenized Weyl algebra). The library works both in the commutative and non-commutative setting (cf. [MO]). Here, we call a free resolution a Schreyer resolution if each syzygy module is given by a Groebner basis with respect to the corresponding Schreyer ordering. A Schreyer resolution can be much bigger than a minimal resolution of the same module, but may be easier to construct. @* The input for the resolution computations is a set of vectors @code{M} in form of a module over some basering @code{R}. The ring @code{R} may be non-commutative, in which case the ring ordering should be global. @* These procedures produce/work with partial Schreyer resolutions of @code{(R^rank(M))/M} in form of a ring (endowed with a special ring ordering that will be extended in the course of a resolution computation) containing a list of modules @code{RES} and a module @code{MRES}: @* The list of modules @code{RES} contains the images of maps (also called syzygy modules) substituting the computed beginning of a Schreyer resolution, that is, each syzygy module is given by a Groebner basis with respect to the corresponding Schreyer ordering. @* The list @code{RES} starts with a zero map given by @code{rank(M)} zero generators indicating that the image of the first differential map is zero. The second map @code{RES[2]} is given by @code{M}, which indicates that the resolution of @code{(R^rank(M))/M} is being computed. @* The module @code{MRES} is a direct sum of modules from @code{RES} and thus comprises all computed differentials. @* Syzygies are shifted so that @code{gen(i)} is mapped to @code{MRES[i]} under the differential map. @* The Schreyer ordering succesively extends the starting module ordering on @code{M} (defined in Singular by the basering @code{R}) and is extended to higher syzygies using the following definition: @* a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ), @* where @code{d(a)} is the image of a under the differential (given by @code{MRES}), and @code{comp(a)} is the module component, for any module terms @code{a} and @code{b} from the same higher syzygy module. REFERENCES: [SFO] Schreyer, F.O.: Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrassschen Divisionssatz, Master's thesis, Univ. Hamburg, 1980. [MO] Motsak, O.: Non-commutative Computer Algebra with applications: Graded commutative algebra and related structures in Singular with applications, Ph.D. thesis, TU Kaiserslautern, 2010 NOTE: requires the dynamic or built-in module @code{syzextra} PROCEDURES: Sres(M,len) compute Schreyer resolution of module M of maximal length len Ssyz(M) compute Schreyer resolution of module M of length 1 Scontinue(len) extend currently active resolution by (at most) len syszygies "; static proc prepareSyz( module I, list # ) { int i; int k = 0; int r = nrows(I); int c = ncols(I); if( size(#) > 0 ) { if( typeof(#[1]) == "int" || typeof(#[1]) == "bigint" ) { k = #[1]; } } if( k < r ) { "// *** Wrong k: ", k, " < nrows: ", r, " => setting k = r = ", r; k = r; } // "k: ", k; "c: ", c; "I: ", I; for( i = c; i > 0; i-- ) { I[i] = I[i] + gen(k + i); } // DetailedPrint(I); return(I); } static proc separateSyzGB( module J, int c ) { module II, G; vector v; int i; J = simplify(J, 2); for( i = ncols(J); i > 0; i-- ) { v = J[i]; if( leadcomp(v) > c ) { II[i] = v; } else { G[i] = v; // leave only gen(i): i <= c } } II = simplify(II, 2); G = simplify(G, 2); return (list(G, II)); } static proc splitSyzGB( module J, int c ) { module JJ; vector v, vv; int i; for( i = ncols(J); i > 0; i-- ) { v = J[i]; vv = 0; while( leadcomp(v) <= c ) { vv = vv + lead(v); v = v - lead(v); } J[i] = vv; JJ[i] = v; } J = simplify(J, 2); JJ = simplify(JJ, 2); return (list(J, JJ)); } static proc Sinit(module M) { def @save = basering; int @DEBUG = !system("with", "ndebug"); if( @DEBUG ) { "Sinit::Input"; type(M); // DetailedPrint(M); attrib(M); } int @RANK = nrows(M); int @SIZE = ncols(M); int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?! if( !@IS_A_SB ) { M = std(M); // this should be faster than computing std in S (later on) } def S = MakeInducedSchreyerOrdering(1); // 1 puts history terms to the back // TODO: NOTE: +1 causes trouble to Singular interpreter!!!??? setring S; // a new ring with a Schreyer ordering if( @DEBUG ) { "Sinit::StartingISRing"; basering; // DetailedPrint(basering); } // Setup the leading syzygy^{-1} module to zero: module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0)); module MRES = Z; list RES; RES[1] = Z; module F = freemodule(@RANK); intvec @V = deg(F[1..@RANK]); module M = imap(@save, M); attrib(M, "isHomog", @V); attrib(M, "isSB", 1); if( @DEBUG ) { "Sinit::SB_Input: "; type(M); attrib(M); attrib(M, "isHomog"); // DetailedPrint(M); } if( @DEBUG ) { // 0^th syz. property if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 ) { transpose( transpose(M) * transpose(MRES) ); "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!"; m2_end(666); } } RES[size(RES)+1] = M; // list of all syzygy modules MRES = MRES, M; attrib(MRES, "isHomog", @V); attrib(S, "InducionLeads", lead(M)); attrib(S, "InducionStart", @RANK); if( @DEBUG ) { "Sinit::MRES"; DetailedPrint(MRES); attrib(MRES, "isHomog"); attrib(S); } export RES; export MRES; return (S); } static proc Sstep() { int @DEBUG = !system("with", "ndebug"); if( @DEBUG ) { "Sstep::NextInducedRing"; DetailedPrint(basering); attrib(basering, "InducionLeads"); attrib(basering, "InducionStart"); GetInducedData(); } // syzygy step: /* // is initial weights are all zeroes! def L = lead(M); intvec @V = deg(M[1..ncols(M)]); @W; @V; @W = @V; attrib(L, "isHomog", @W); SetInducedReferrence(L, @RANK, 0); */ // def L = lead(MRES); // @W = @W, @V; // attrib(L, "isHomog", @W); // General setting: // SetInducedReferrence(MRES, 0, 0); // limit: 0! int @l = size(RES); module M = RES[@l]; module L = attrib(basering, "InducionLeads"); int limit = attrib(basering, "InducionStart"); // L; limit; int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?! /* if( @RANK != nrows(M) ) { type(MRES); @RANK; type(M); pause(); } */ intvec @W = attrib(M, "isHomog"); intvec @V = deg(M[1..ncols(M)]); @V = @W, @V; if( @DEBUG ) { "Sstep::NextInput: "; M; deg(M[1..ncols(M)]); // no use of @W :(? @RANK; DetailedPrint(MRES); attrib(MRES, "isHomog"); @W; deg(MRES[1..ncols(MRES)]); } SetInducedReferrence(L, limit, 0); def K = prepareSyz(M, @RANK); // K; // attrib(K, "isHomog", @V); DetailedPrint(K, 1000); // pause(); K = idPrepare(K, @RANK); // std(K); // ? K = simplify(K, 2); // K; module N = separateSyzGB(K, @RANK)[2]; // 1^st syz. module: vectors which start in lower part (comp >= @RANK) // "N_0: "; N; DetailedPrint(N, 10); // basering; print(@V); type(N); // attrib(N, "isHomog", @V); // TODO: fix "wrong weights"!!!? deg is wrong :((( N = std(N); attrib(N, "isHomog", @V); // N; if( @DEBUG ) { if( size(N) > 0 ) { // next syz. property if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 ) { MRES; "N: "; N; DetailedPrint(N, 10); "K:"; K; DetailedPrint(K, 10); "RANKS: ", @RANK; "ERROR: transpose( transpose(N) * transpose(MRES) ) != 0!!!"; transpose( transpose(N) * transpose(MRES) ); "transpose(N) * transpose(MRES): "; transpose(N) * transpose(MRES); DetailedPrint(module(_), 2); m2_end(666); } } } RES[@l + 1] = N; // list of all syzygy modules MRES = MRES, N; attrib(MRES, "isHomog", @V); L = L, lead(N); attrib(basering, "InducionLeads", L); if( @DEBUG ) { "Sstep::NextSyzOutput: "; DetailedPrint(N); attrib(N, "isHomog"); } } proc Scontinue(int l) "USAGE: Scontinue(int len) RETURN: nothing, instead it changes the currently active resolution PURPOSE: extends the currently active resolution by at most len syzygies ASSUME: must be used within a ring returned by Sres or Ssyz EXAMPLE: example Scontinue; shows an example " { def data = GetInducedData(); if( (!defined(RES)) || (!defined(MRES)) || (typeof(data) != "list") || (size(data) != 2) ) { ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz"); } for (; (l != 0) && (size(RES[size(RES)]) > 0); l-- ) { Sstep(); } } example { "EXAMPLE:"; echo = 2; ring r; module M = maxideal(1); M; def S = Ssyz(M); setring S; S; "Only the first syzygy: "; RES; MRES; "More syzygies: "; Scontinue(10); RES; MRES; } proc Ssyz(module M) "USAGE: Ssyz(module M) RETURN: ring, containing a Schreyer resolution PURPOSE: computes a Schreyer resolution of M of length 1 (see the library overview) SEE ALSO: Sres EXAMPLE: example Ssyz; shows an example " { def S = Sinit(M); setring S; Sstep(); // NOTE: what if M is zero? return (S); } example { "EXAMPLE:"; echo = 2; ring r; module M = maxideal(1); M; def S = Ssyz(M); setring S; S; "Only the first syzygy: "; RES; MRES; // Note gen(i) kill S; setring r; kill M; module M = 0; def S = Ssyz(M); setring S; S; "Only the first syzygy: "; RES; MRES; } proc Sres(module M, int l) "USAGE: Sres(module M, int len) RETURN: ring, containing a Schreyer resolution PURPOSE: computes a Schreyer resolution of M of length at most len (see the library overview) NOTE: If given len is zero then nvars(basering) + 1 is used instead. SEE ALSO: Ssyz EXAMPLE: example Sres; shows an example " { def S = Sinit(M); setring S; if (l == 0) { l = nvars(basering) + 1; // not really an estimate...?! } Sstep(); l = l - 1; Scontinue(l); return (S); } example { "EXAMPLE:"; echo = 2; ring r; module M = maxideal(1); M; def S = Sres(M, 0); setring S; S; RES; MRES; kill S; setring r; kill M; def A = nc_algebra(-1,0); setring A; ideal Q = var(1)^2, var(2)^2, var(3)^2; qring SCA = twostd(Q); basering; module M = maxideal(1); def S = Sres(M, 2); setring S; S; RES; MRES; } // ================================================================== // LIB "general.lib"; // for sort /* static proc Tail(def M) // DONE: in C++ (dyn. module: syzextra)! { int i = ncols(M); def m; while (i > 0) { m = M[i]; m = m - lead(m); // m = tail(m) M[i] = m; i--; } return (M); }*/ /* static */ proc MySort(def M) " Sorts the given ideal or module wrt >_{(c, ds)} (.<.<.<.<) NOTE: inplace?? " { if( typeof( attrib(basering, "DEBUG") ) == "int" ) { int @DEBUG = attrib(basering, "DEBUG"); } else { int @DEBUG = 0; // !system("with", "ndebug"); } if( typeof( attrib(basering, "KERCHECK") ) == "int" ) { int @KERCHECK = attrib(basering, "KERCHECK"); } else { int @KERCHECK = @DEBUG; } if( @DEBUG ) { "MySort:: Input: "; M; } def @N = M; if( size(M) > 0 ) { Sort_c_ds(@N); if( @KERCHECK ) { def iv = sort(lead(M), "c,ds", 1)[2]; // ,1 => reversed! // TODO: not needed? def @M = M; @M = M[iv]; // 0^th syz. property if( (size(@N) + size(@M)) > 0 ) { if( size(module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) )) > 0 ) { "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!"; "@M:"; @M; "@N:"; @N; "module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) ): "; module( matrix(module(matrix(@N))) - matrix(module(matrix(@M))) ); "ERROR: MySort: wrong sorting in 'MySort': @N != @M!!!"; m2_end(666); } } } } if( @DEBUG ) { "MySort:: Ouput: "; @N; } return (@N); } static proc SSinit(def M) { // rtimer, "***TIMESNAP0 for SSinit: on level: [",-1,"] :: t: ", timer, ", r: ", rtimer; if( (typeof(M) != "module") && (typeof(M) != "ideal") ) { ERROR("Sorry: need an ideal or a module for input"); } // TODO! DONE? def @save = basering; int @DEBUG = !system("with", "ndebug"); if( typeof( attrib(SSinit, "DEBUG") ) == "int" ) { @DEBUG = attrib(SSinit, "DEBUG"); } int @SYZCHECK = @DEBUG; if( typeof( attrib(SSinit, "SYZCHECK") ) == "int" ) { @SYZCHECK = attrib(SSinit, "SYZCHECK"); } int @KERCHECK = @DEBUG; if( typeof( attrib(SSinit, "KERCHECK") ) == "int" ) { @KERCHECK = attrib(SSinit, "KERCHECK"); } int @IGNORETAILS = 0; if( typeof( attrib(SSinit, "IGNORETAILS") ) == "int" ) { @IGNORETAILS = attrib(SSinit, "IGNORETAILS"); } if( @DEBUG ) { "SSinit::Input"; type(M); // DetailedPrint(M); attrib(M); } int @IS_A_SB = attrib(M, "isSB"); // ??? only if all weights were zero?! if( !@IS_A_SB ) { def opts = option(get); option(redSB); option(redTail); M = std(M); option(set, opts); kill opts; } else { M = simplify(M, 2 + 4 + 32); // interreduce? } if( @IGNORETAILS ) { M = lead(M); if( @DEBUG ) { "SSinit::Ignorring tails: M: "; type(M); } } def @N = MySort(M); // TODO: replace with inplace sorting!!! def LEAD = lead(@N); if( @KERCHECK ) { def @LEAD = lead(M); // sort wrt neg.deg.rev.lex! intvec iv_ds = sort(@LEAD, "c,ds", 1)[2]; // ,1 => reversed! M = M[iv_ds]; // sort M wrt ds on current leading terms @LEAD = @LEAD[iv_ds]; if( size(module( matrix(@N) - matrix(M) )) > 0 ) { "M:"; M; "@N:"; @N; "module( matrix(@N) - matrix(M) ): "; module( matrix(@N) - matrix(M) ); "ERROR: wrong sorting (in SSnit): @N != M!!!"; m2_end(666); } if( size(module( matrix(@LEAD) - matrix(LEAD) )) > 0 ) { "LEAD:"; LEAD; "@LEAD:"; @LEAD; "module( matrix(@LEAD) - matrix(LEAD) ): "; module( matrix(@LEAD) - matrix(LEAD) ); "ERROR: wrong sorting (in SSnit): @LEAD != LEAD!!!"; m2_end(666); } } M = @N; def TAIL = Tail(M); int @RANK = nrows(M); int @SIZE = ncols(M); intvec @DEGS = deg(M[1..@SIZE]); // store actuall degrees of input elements // TODO: what about real modules? weighted ones? list @l = ringlist(@save); int @z = 0; ideal @m = maxideal(1); intvec @wdeg = deg(@m[1..ncols(@m)]); // NOTE: @wdeg will be ignored anyway :( @l[3] = list(list("C", @z), list("lp", @wdeg)); kill @z, @wdeg; // since these vars are ring independent! def S = ring(@l); // --MakeInducedSchreyerOrdering(1); module F = freemodule(@RANK); intvec @V = deg(F[1..@RANK]); setring S; // ring with an easy divisibility test ("C, lex") if( @DEBUG ) { "SSinit::NewRing(C, lex)"; basering; DetailedPrint(basering); } // Setup the leading syzygy^{-1} module to zero: module Z = 0; Z[@RANK] = 0; attrib(Z, "isHomog", intvec(0)); module MRES = Z; list RES; RES[1] = Z; list LRES; LRES[1] = Z; list TRES; TRES[1] = Z; def M = imap(@save, M); attrib(M, "isHomog", @V); attrib(M, "isSB", 1); attrib(M, "degrees", @DEGS); def LEAD = imap(@save, LEAD); attrib(LEAD, "isHomog", @V); attrib(LEAD, "isSB", 1); def TAIL = imap(@save, TAIL); if( @DEBUG ) { "SSinit::(sorted) SB_Input: "; type(M); attrib(M); attrib(M, "isHomog"); // DetailedPrint(M); } if( @SYZCHECK ) { // 0^th syz. property if( size(module(transpose( transpose(M) * transpose(MRES) ))) > 0 ) { transpose( transpose(M) * transpose(MRES) ); "ERROR: transpose( transpose(M) * transpose(MRES) ) != 0!!!"; m2_end(666); } } RES [size(RES)+1] = M; // list of all syzygy modules LRES[size(LRES)+1] = LEAD; // list of all syzygy modules TRES[size(TRES)+1] = TAIL; // list of all syzygy modules MRES = MRES, M; //? attrib(MRES, "isHomog", @V); // attrib(S, "InducionStart", @RANK); if( typeof( attrib(SSinit, "LEAD2SYZ") ) == "int" ) { attrib(S, "LEAD2SYZ", attrib(SSinit, "LEAD2SYZ") ); } else { attrib(S, "LEAD2SYZ", 1); } if( typeof( attrib(SSinit, "TAILREDSYZ") ) == "int" ) { attrib(S, "TAILREDSYZ", attrib(SSinit, "TAILREDSYZ") ); } else { attrib(S, "TAILREDSYZ", 1); } if( typeof( attrib(SSinit, "HYBRIDNF") ) == "int" ) { attrib(S, "HYBRIDNF", attrib(SSinit, "HYBRIDNF") ); } else { attrib(S, "HYBRIDNF", 2); } attrib(S, "DEBUG", @DEBUG); attrib(S, "SYZCHECK", @SYZCHECK); attrib(S, "KERCHECK", @KERCHECK); attrib(S, "IGNORETAILS", @IGNORETAILS); attrib(S, "SYZNUMBER", 0); if( @DEBUG ) { "SSinit::MRES"; MRES; // DetailedPrint(MRES); attrib(MRES, "isHomog"); attrib(S); } export RES; export MRES; export LRES; export TRES; // rtimer, "***TIMESNAP1 for SSinit: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; return (S); } example { "EXAMPLE:"; echo = 2; ring R = 0, (w, x, y, z), dp; def M = maxideal(1); def S = SSinit(M); setring S; S; "Only the first initialization: "; RES; LRES; TRES; MRES; kill S; setring R; kill M; ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; def S = SSinit(M); setring S; S; "Only the first initialization: "; RES; LRES; TRES; MRES; kill S; setring R; kill M; } LIB "poly.lib"; // for lcm /// Compute L(Syz(L)) proc SSComputeLeadingSyzygyTerms(def L) { if( typeof( attrib(basering, "DEBUG") ) == "int" ) { int @DEBUG = attrib(basering, "DEBUG"); } else { int @DEBUG = !system("with", "ndebug"); } if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) { int @SYZCHECK = attrib(basering, "SYZCHECK"); } else { int @SYZCHECK = @DEBUG; } if( typeof( attrib(basering, "KERCHECK") ) == "int" ) { int @KERCHECK = attrib(basering, "KERCHECK"); } else { int @KERCHECK = @DEBUG; } if( @DEBUG ) { "SSComputeLeadingSyzygyTerms::Input: "; L; } module SS = ComputeLeadingSyzygyTerms(L); if( @KERCHECK ) { int i, j, r; int N = ncols(L); def a, b; poly aa, bb; bigint c; ideal M; module S = 0; for(i = 1; i <= N; i++) { a = L[i]; c = leadcomp(a); r = int(c); aa = leadmonomial(a); M = 0; for(j = i-1; j > 0; j--) { b = L[j]; if( leadcomp(b) == c ) { bb = leadmonomial(b); M[j] = (lcm(aa, bb) / aa); } } // TODO: add quotient relations here... M = simplify(M, 1 + 2 + 32); M = MySort(M); S = S, M * gen(i); } S = MySort(simplify(S, 2)); if( (size(S) + size(SS)) > 0 ) { if( size(module(matrix(S) - matrix(SS))) > 0 ) { "ERROR: SSComputeLeadingSyzygyTerms: S != SS "; "basering: "; basering; // DetailedPrint(basering); "S: "; S; // DetailedPrint(_, 1); "SS: "; SS; // DetailedPrint(_, 1); "DIFF: "; module(matrix(S) - matrix(SS)); // DetailedPrint(_, 2); print(matrix(S) - matrix(SS)); m2_end(666); } } } if( @DEBUG ) { "SSComputeLeadingSyzygyTerms::Output: "; "SS: "; SS; } if( size(SS) > 0 ) { attrib(SS, "isSB", 1); } return (SS); } /// Compute Syz(L), where L is a monomial (leading) module proc SSCompute2LeadingSyzygyTerms(def L) { if( typeof( attrib(basering, "DEBUG") ) == "int" ) { int @DEBUG = attrib(basering, "DEBUG"); } else { int @DEBUG = !system("with", "ndebug"); } if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) { int @SYZCHECK = attrib(basering, "SYZCHECK"); } else { int @SYZCHECK = @DEBUG; } if( typeof( attrib(basering, "KERCHECK") ) == "int" ) { int @KERCHECK = attrib(basering, "KERCHECK"); } else { int @KERCHECK = @DEBUG; } if( @DEBUG ) { "SSCompute2LeadingSyzygyTerms::Input: "; L; } module SS = Compute2LeadingSyzygyTerms(L); if( @DEBUG ) { "SSCompute2LeadingSyzygyTerms::Syz(SS): "; SS; } if( @SYZCHECK ) { if( size(SS) > 0 and size(L) > 0 ) { if( size(module(transpose( transpose(SS) * transpose(L) ))) > 0 ) { transpose( transpose(SS) * transpose(L) ); "ERROR: transpose( transpose(SS) * transpose(L) ) != 0!!!"; m2_end(666); } } } if( @KERCHECK ) { int @TAILREDSYZ = 1; if( typeof( attrib(basering, "TAILREDSYZ") ) == "int" ) { @TAILREDSYZ = attrib(basering, "TAILREDSYZ"); } int i, j, r; int N = ncols(L); def a, b; poly aa, bb, @lcm; bigint c; module M; module S = 0; for(i = 1; i <= N; i++) { a = L[i]; // "a: ", a; c = leadcomp(a); r = int(c); aa = leadmonomial(a); M = 0; for(j = i-1; j > 0; j--) { b = L[j]; // "b: ", b; if( leadcomp(b) == c ) { bb = leadmonomial(b); @lcm = lcm(aa, bb); M[j] = (@lcm / aa)* gen(i) - (@lcm / bb)* gen(j); } } M = simplify(M, 2); // TODO: add quotient relations here... S = S, M; } if( @TAILREDSYZ ) { // Make sure that 2nd syzygy terms are not reducible by 1st def opts = option(get); option(redSB); option(redTail); S = std(S); // binomial module option(set, opts); // kill opts; } else { S = simplify(S, 2 + 32); } S = MySort(S); if( @DEBUG ) { "SSCompute2LeadingSyzygyTerms::Syz(S): "; S; } if( @SYZCHECK ) { if( size(S) > 0 and size(L) > 0 ) { if( size(module(transpose( transpose(S) * transpose(L) ))) > 0 ) { transpose( transpose(S) * transpose(L) ); "ERROR: transpose( transpose(S) * transpose(L) ) != 0!!!"; m2_end(666); } } } if(size(S) != size(SS)) { "ERROR: SSCompute2LeadingSyzygyTerms: size(S) != size(SS)"; "basering: "; basering; // DetailedPrint(basering); "S: "; S; // DetailedPrint(S, 2); "SS: "; SS; // DetailedPrint(SS, 2); m2_end(666); } if(size(S) > 0 && size(SS) > 0) { if( size(module(matrix(lead(S)) - matrix(lead(SS)))) > 0 ) { "ERROR: SSCompute2LeadingSyzygyTerms: lead(S) != lead(SS) "; "basering: "; basering; // DetailedPrint(basering); "lead(S ): "; lead(S ); // DetailedPrint(_, 2); "lead(SS): "; lead(SS); // DetailedPrint(_, 2); "DIFF: "; print( matrix(lead(S)) - matrix(lead(SS)) ); module(matrix(lead(S)) - matrix(lead(SS))); // DetailedPrint(_ , 4); m2_end(666); } if( @TAILREDSYZ ) { if( size(module(matrix(Tail(S)) - matrix(Tail(SS)))) > 0 ) { "ERROR: SSCompute2LeadingSyzygyTerms: Tail(S) != Tail(SS) "; "basering: "; basering; // DetailedPrint(basering); "Tail(S ): "; Tail(S ); // DetailedPrint(_, 2); "Tail(SS): "; Tail(SS); // DetailedPrint(_, 2); "DIFF: "; module( matrix(Tail(S)) - matrix(Tail(SS)) ); // DetailedPrint(_, 4); print( matrix(Tail(S)) - matrix(Tail(SS)) ); m2_end(666); } } } } module S2 = Tail(SS); SS = lead(SS); // (C,lp) on base ring! if( @SYZCHECK ) { if( ncols(SS) != ncols(S2) ) // || size(SS) != ncols(SS) || size(S2) != ncols(S2) { "ERROR: SSCompute2LeadingSyzygyTerms: inappropriate S2 / SS: "; type(SS); type(S2); L; m2_end(666); } } if( @DEBUG ) { "SSCompute2LeadingSyzygyTerms::Output: "; SS; S2; } attrib(SS, "isSB", 1); return (SS, S2); } // -------------------------------------------------------- // /// TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz? proc SSFindReducer(def product, def syzterm, def L, list #) { if( typeof( attrib(basering, "DEBUG") ) == "int" ) { int @DEBUG = attrib(basering, "DEBUG"); } else { int @DEBUG = !system("with", "ndebug"); } if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) { int @SYZCHECK = attrib(basering, "SYZCHECK"); } else { int @SYZCHECK = @DEBUG; } if( typeof( attrib(basering, "KERCHECK") ) == "int" ) { int @KERCHECK = attrib(basering, "KERCHECK"); } else { int @KERCHECK = @DEBUG; } if( @DEBUG ) { "SSFindReducer::Input: "; "syzterm: ", syzterm; "product: ", product; "L: ", L; // "T: ", T; if( size(#) > 0 ) { "LSyz: ", #; } } if( @DEBUG && (syzterm != 0) ) { def @@c = leadcomp(syzterm); int @@r = int(@@c); def @@product = leadmonomial(syzterm) * L[@@r]; if( @@product != product) { "product: ", product, ", @@product: ", @@product; "ERROR: 'syzterm' results in wrong product !!!???"; m2_end(666); } } if( typeof(#[1]) == "module" ) { vector my = FindReducer(product, syzterm, L/*, T*/, #[1]); } else { vector my = FindReducer(product, syzterm, L/*, T*/); } if( @KERCHECK ) { bigint c = leadcomp(product); int r = int(c); def a, b, bb; vector nf = [0]; // looking for an appropriate diviser for( int k = ncols(L); k > 0; k-- ) { a = L[k]; // with the same mod. component if( leadcomp(a) == c ) { b = - (leadmonomial(product) / leadmonomial(L[k])); // which divides the product: looking for the 1st appropriate one! if( b != 0 ) { bb = b * gen(k); if (size(bb + syzterm) == 0) // cannot allow something like: a*gen(i) - a*gen(i) { nf = [0]; } else { nf = bb; } // new syz. term should not be in if( size(#) > 0 ) { if( typeof(#[1]) == "module" ) { nf = NF(bb, #[1]); } } // while the complement (the fraction) is not reducible by leading syzygies if( nf != 0 ) // nf must be == bb!!! { /// TODO: save shortcut LM(m) * T[i] -> ? // choose ANY such reduction... (with the biggest index?) break; } } } } if( my != nf ) { "ERROR in FindReducer => ", my, " != nf: ", nf; m2_end(666); } } if( @DEBUG ) { "SSFindReducer::Output: ", my; } return (my); } /// TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? proc SSReduceTerm(poly m, def t, def syzterm, def L, def T, list #) { if( typeof( attrib(basering, "DEBUG") ) == "int" ) { int @DEBUG = attrib(basering, "DEBUG"); } else { int @DEBUG = !system("with", "ndebug"); } if( @DEBUG ) { "SSReduce::Input: "; "syzterm: ", syzterm; "mult: ", m; "term: ", t; "L: ", L; "T: ", T; if( size(#) > 0 ) { "LSyz: ", #; } // "attrib(LS, 'isSB')", attrib(LS, "isSB"); } if( typeof( attrib(basering, "KERCHECK") ) == "int" ) { int @KERCHECK = attrib(basering, "KERCHECK"); } else { int @KERCHECK = @DEBUG; } if( typeof( attrib(basering, "SYZCHECK") ) == "int" ) { int @SYZCHECK = attrib(basering, "SYZCHECK"); } else { int @SYZCHECK = @DEBUG; } if( @SYZCHECK && (syzterm != 0) ) { def @@c = leadcomp(syzterm); int @@r = int(@@c); poly @@m = leadmonomial(syzterm); def @@t = L[@@r]; if( (@@m != m) || (@@t != t)) { "m: ", m, ", t: ", t; "@@m: ", @@m, ", @@t: ", @@t; "ERROR: 'syzterm' results in wrong m * t !!!"; m2_end(666); } } if( typeof(#[1]) == "module" ) { vector ss = ReduceTerm(m, t, syzterm, L, T, #[1]); } else { vector ss = ReduceTerm(m, t, syzterm, L, T); } if( @KERCHECK ) { vector s = 0; if( size(t) > 0 ) { def product = m * t; s = SSFindReducer(product, syzterm, L, #); if( size(s) != 0 ) { poly @b = leadmonomial(s); def @c = leadcomp(s); int k = int(@c); s = s + SSTraverseTail(@b, T[k], L, T, #); // !!! } } if( s != ss ) { "ERROR in ReduceTerm => old: ", s, " != ker: ", ss; "m: ", m; "t: ", t; "syzterm: ", syzterm; L; T; #; m2_end(666); } } if( @DEBUG ) { "SSReduceTerm::Output: ", ss; } return (ss); } // TODO: store m * @tail -.-^-.-^-.--> ? proc SSTraverseTail(poly m, def @tail, def L, def T, list #) { if( typeof( attrib(basering, "DEBUG") ) == "int" ) { int @DEBUG = attrib(basering, "DEBUG"); } else { int @DEBUG = !system("with", "ndebug"); } if( typeof( attrib(basering, "KERCHECK") ) == "int" ) { int @KERCHECK = attrib(basering, "KERCHECK"); } else { int @KERCHECK = @DEBUG; } if( @DEBUG ) { "SSTraverse::Input: "; "mult: ", m; "tail: ", @tail; // T[i]; if( size(#) > 0 ) { "LSyz: "; #[1]; } } if( typeof(#[1]) == "module" ) { vector ss = TraverseTail(m, @tail, L, T, #[1]); } else { vector ss = TraverseTail(m, @tail, L, T); } if( @KERCHECK ) { vector s = 0; def @l, @p; @p = @tail; // iterate tail-terms in ANY order! while( size(@p) > 0 ) { @l = lead(@p); s = s + SSReduceTerm(m, @l, [0], L, T, #); // :( @p = @p - @l; } if( s != ss ) { "ERROR in TraverseTail => old: ", s, " != ker: ", ss; "m: ", m; "@tail: ", @tail; L; T; #; m2_end(666); } } if( @DEBUG ) { "SSTraverseTail::Output: ", ss; } return (ss); } // -------------------------------------------------------- // proc SSSchreyerSyzygyNF(vector syz_lead, vector syz_2, def L, def T, list #) " Hybrid Syzygy computation: 'reduce' spoly by eliminating _any_ terms while discurding terms of lower order! Return the tail syzygy (without: syz_lead, starting with: syz_2) " { if( typeof( attrib(basering, "DEBUG") ) == "int" ) { int @DEBUG = attrib(basering, "DEBUG"); } else { int @DEBUG = !system("with", "ndebug"); } if( @DEBUG ) { "SSSchreyerSyzygyNF::Input: "; "syzygy_lead: ", syz_lead; "syzygy 2nd : ", syz_2; L; T; if( size(#) > 0 ) { "LSyz: "; #[1]; } } if( typeof( attrib(basering, "KERCHECK") ) == "int" ) { int @KERCHECK = attrib(basering, "KERCHECK"); } else { int @KERCHECK = @DEBUG; } if( typeof(#[1]) == "module" ) { def my = SchreyerSyzygyNF(syz_lead, syz_2, L, T, #[1]); } else { def my = SchreyerSyzygyNF(syz_lead, syz_2, L, T); } if( @KERCHECK ) { def spoly = leadmonomial(syz_lead) * T[int(leadcomp(syz_lead))] + leadmonomial(syz_2) * T[int(leadcomp(syz_2))]; vector @tail = syz_2; while (size(spoly) > 0) { syz_2 = SSFindReducer(lead(spoly), 0, L, #); spoly = Tail(spoly); if( size(syz_2) != 0) { spoly = spoly + leadmonomial(syz_2) * T[int(leadcomp(syz_2))]; @tail = @tail + syz_2; } } if( my != @tail ) { "ERROR in SchreyerSyzygyNF => old: ", @tail, " != ker: ", my; "syzygy_lead: ", syz_lead; "syzygy 2nd : ", syz_2; L; T; #; m2_end(666); } } if( @DEBUG ) { "SSSchreyerSyzygyNF::Output: ", my; } return (my); } // -------------------------------------------------------- // // module (N, LL, TT) = SSComputeSyzygy(L, T); // Compute Syz(L ++ T) = N = LL ++ TT proc SSComputeSyzygy(def L, def T) { // rtimer, "***TIMESNAP0 for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; int @DEBUG = attrib(basering, "DEBUG"); int @KERCHECK = attrib(basering, "KERCHECK"); if( @DEBUG ) { "SSComputeSyzygy::Input"; "basering: ", basering; attrib(basering); // DetailedPrint(basering); // "iCompShift: ", iCompShift; "L: "; L; "T: "; T; } // option(prot); // rtimer, "***TIME for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; list @res=ComputeSyzygy(L,T); // rtimer, "***TIME for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; // option(noprot); // TODO: restore! module @LL = @res[1]; module @TT = @res[2]; if( @KERCHECK ) { int @SYZCHECK = attrib(basering, "SYZCHECK"); int @LEAD2SYZ = attrib(basering, "LEAD2SYZ"); int @TAILREDSYZ = attrib(basering, "TAILREDSYZ"); int @HYBRIDNF = attrib(basering, "HYBRIDNF"); int @IGNORETAILS = attrib(basering, "IGNORETAILS"); int @SYZNUMBER = attrib(basering,"SYZNUMBER"); if( @HYBRIDNF == 2 ) { if( @SYZNUMBER < 3 ){ @HYBRIDNF = 1; } else { @HYBRIDNF = 0; } } module LL; /// Get the critical leading syzygy terms if( @LEAD2SYZ ) // & 2nd syz. term { module LL2; (LL, LL2) = SSCompute2LeadingSyzygyTerms(L); } else { LL = SSComputeLeadingSyzygyTerms(L); } module TT, SYZ; vector a, a2; bigint c; int r; poly aa; if( size(LL) > 0 ) { list LS; if( @TAILREDSYZ) { LS = list(LL); } vector @tail = 0; for(int k = ncols(LL); k > 0; k-- ) { // leading syz. term: a = LL[k]; if( !@IGNORETAILS ) { c = leadcomp(a); r = int(c); aa = leadmonomial(a); // NF reduction: if( @HYBRIDNF == 0 ) // Traverse approach: { @tail = SSTraverseTail(aa, T[r], L, T, LS); // get the 2nd syzygy term... if( @LEAD2SYZ ) // with the 2nd syz. term: { a2 = LL2[k]; c = leadcomp(a2); r = int(c); aa = leadmonomial(a2); @tail = a2 + @tail + SSTraverseTail(aa, T[r], L, T, LS); } else { @tail = @tail + SSReduceTerm(aa, L[r], a, L, T, LS); } } else // Hybrid approach: { // get the 2nd syzygy term... if( @LEAD2SYZ ) { a2 = LL2[k]; } else { a2 = SSFindReducer( aa * L[r], a, L, LS); } if ( (@SYZCHECK || @DEBUG) ) { if( size(a2) == 0 ) // if syzterm == 0!!!! { "ERROR in SSComputeSyzygy: could not find the 2nd syzygy term during the hybrid NF!!!"; m2_end(666); } } @tail = SSSchreyerSyzygyNF(a, a2, L, T, LS); } } // else @tail remains zero! TT[k] = @tail; SYZ[k] = a + @tail; } } if( ncols(LL) != ncols(@LL) ) { "ERROR in SSComputeSyzygy: wrong leading syzygies!?"; ""; L; T; ""; type(LL); type(@LL); m2_end(666); } if( ncols(TT) != ncols(@TT) ) { "ERROR in SSComputeSyzygy: wrong tail syzygies!?"; ""; L; T; ""; type(LL); type(@LL); ""; type(TT); type(@TT); m2_end(666); } if( size( module( matrix(LL) - matrix(@LL) ) ) != 0 ) { "ERROR in SSComputeSyzygy: wrong leading syzygies!?"; ""; L; T; ""; type(LL); type(@LL); m2_end(666); } if( size( module( matrix(TT) - matrix(@TT) ) ) != 0 ) { "ERROR in SSComputeSyzygy: wrong tail syzygies!?"; ""; TT; @TT; ""; L; T; ""; type(LL); type(@LL); m2_end(666); } } module @SYZ; for(int @k = ncols(@LL); @k > 0; @k-- ) { @SYZ[@k] = @LL[@k] + @TT[@k]; } if( @DEBUG ) { "SSComputeSyzygy::Output"; // "SYZ: "; @SYZ; "LL: "; @LL; "TT: "; @TT; } // rtimer, "***TIMESNAP1 for ComputeSyzygy(L,T): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; return (@SYZ, @LL, @TT); } // resolution/syzygy step: static proc SSstep() { // rtimer, "***TIMESNAP0 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; int @DEBUG = attrib(basering, "DEBUG"); int @SYZCHECK = attrib(basering, "SYZCHECK"); if( @DEBUG ) { "SSstep::NextInducedRing"; "basering: ", basering; attrib(basering); } /* // is initial weights are all zeroes! def L = lead(M); intvec @V = deg(M[1..ncols(M)]); @W; @V; @W = @V; attrib(L, "isHomog", @W); SetInducedReferrence(L, @RANK, 0); */ // def L = lead(MRES); // @W = @W, @V; // attrib(L, "isHomog", @W); // General setting: // SetInducedReferrence(MRES, 0, 0); // limit: 0! int @l = size(RES); def M = RES[@l]; def L = LRES[@l]; def T = TRES[@l]; //// TODO: wrong !!!!! int @RANK = ncols(MRES) - ncols(M); // nrows(M); // what if M is zero?! /* if( @RANK != nrows(M) ) { type(MRES); @RANK; type(M); pause(); } */ intvec @W = attrib(M, "isHomog"); intvec @V = attrib(M, "degrees"); @V = @W, @V; if( @DEBUG ) { "Sstep::NextInput: "; M; L; @V; @RANK; // DetailedPrint(MRES); attrib(MRES, "isHomog"); } // TODO: N = SYZ( M )!!! module N, LL, TT; (N, LL, TT) = SSComputeSyzygy(/*M, */L, T/*, @RANK*/); // shift syz.comp by @RANK: module Z; Z = 0; Z[@RANK] = 0; Z = Z, transpose(LL); LL = transpose(Z); Z = 0; Z[@RANK] = 0; Z = Z, transpose(TT); TT = transpose(Z); Z = 0; Z[@RANK] = 0; Z = Z, transpose(N); N = transpose(Z); if( @SYZCHECK ) { if( size(N) > 0 ) { // next syz. property if( size(module(transpose( transpose(N) * transpose(MRES) ))) > 0 ) { "MRES", MRES; "N: "; N; // DetailedPrint(N, 2); "LL:"; LL; // DetailedPrint(LL, 1); "TT:"; TT; // DetailedPrint(TT, 10); "RANKS: ", @RANK; "transpose( transpose(N) * transpose(MRES) ) != 0!!!"; transpose( transpose(N) * transpose(MRES) ); "transpose(N) * transpose(MRES): "; transpose(N) * transpose(MRES); // DetailedPrint(module(_), 2); m2_end(666); } } } attrib(N, "isHomog", @V); // TODO: correct the following: intvec @DEGS = deg(N[1..ncols(N)]); // no mod. comp. weights :( attrib(N, "degrees", @DEGS); RES[@l + 1] = N; // list of all syzygy modules LRES[@l + 1] = LL; // list of all syzygy modules TRES[@l + 1] = TT; // list of all syzygy modules MRES = MRES, N; attrib(MRES, "isHomog", @V); // L = L, lead(N); attrib(basering, "InducionLeads", L); if( @DEBUG ) { "SSstep::NextSyzOutput: "; N; // DetailedPrint(N); attrib(N); } int ss = attrib(basering, "SYZNUMBER"); attrib(basering, "SYZNUMBER", ss + 1 ); // rtimer, "***TIMESNAP1 for SSstep(): on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; } proc SScontinue(int l) "USAGE: SScontinue(l) RETURN: nothing, instead it changes RES and MRES variables in the current ring PURPOSE: computes further (at most l) syzygies NOTE: must be used within a ring returned by Sres or Ssyz. RES and MRES are explained in Sres EXAMPLE: example Scontinue; shows an example " { // rtimer, "***TIMESNAP0 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; /// TODO! // def data = GetInducedData(); if( (!defined(RES)) || (!defined(MRES)) ) /* || (typeof(data) != "list") || (size(data) != 2) */ { ERROR("Sorry, but basering does not seem to be returned by Sres or Ssyz"); } for (; (l != 0) && (size(RES[size(RES)]) > 0); l-- ) { SSstep(); } // rtimer, "***TIMESNAP1 for SScontinue: on level: [",attrib(basering,"SYZNUMBER"),"] :: t: ", timer, ", r: ", rtimer; } example { "EXAMPLE:"; echo = 2; ring r; module M = maxideal(1); M; def S = SSsyz(M); setring S; S; "Only the first syzygy: "; RES; MRES; "More syzygies: "; SScontinue(10); RES; MRES; } proc SSsyz(def M) "USAGE: SSsyz(M) RETURN: ring, containing a list of modules RES and a module MRES PURPOSE: computes the first syzygy module of M (wrt some Schreyer ordering)? NOTE: The output is explained in Sres EXAMPLE: example Ssyz; shows an example " { if( (typeof(M) != "module") && (typeof(M) != "ideal") ) { ERROR("Sorry: need an ideal or a module for input"); } def SS = SSinit(M); setring SS; SSstep(); // NOTE: what if M is zero? return (SS); } example { "EXAMPLE:"; echo = 2; ring r; /* ideal M = 0; def S = SSsyz(M); setring S; S; "Only the first syzygy: "; RES; LRES; TRES; MRES; kill S; setring r; kill M; */ ideal M = maxideal(1); M; def S = SSres(M, 0); setring S; S; MRES; print(_); RES; kill S; setring r; kill M; kill r; ring R = 0, (w, x, y, z), dp; ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; def S = SSres(M, 0); setring S; S; ""; LRES; ""; TRES; ""; MRES; print(_); RES; } proc SSres(def M, int l) "USAGE: SSres(I, l) RETURN: ring, containing a list of modules RES and a module MRES PURPOSE: computes (at most l) syzygy modules of M wrt the classical Schreyer induced ordering with gen(i) > gen(j) if i > j, provided both gens are from the same syzygy level.??? NOTE: RES contains the images of maps subsituting the beginning of the Schreyer free resolution of baseRing^r/M, while MRES is a sum of these images in a big free sum, containing all the syzygy modules. The syzygy modules are shifted so that gen(i) correspons to MRES[i]. The leading zero module RES[0] indicates the fact that coker of the first map is zero. The number of zeroes inducates the rank of input. NOTE: If l == 0 then l is set to be nvars(basering) + 1 EXAMPLE: example SSres; shows an example " { if( (typeof(M) != "module") && (typeof(M) != "ideal") ) { ERROR("Sorry: need an ideal or a module for input"); } /* "KERCHECK: ", attrib(SSinit, "KERCHECK"); "SYZCHECK: ", attrib(SSinit, "SYZCHECK"); "DEBUG: ", attrib(SSinit, "DEBUG"); "HYBRIDNF: ", attrib(SSinit, "HYBRIDNF"); "TAILREDSYZ: ", attrib(SSinit, "TAILREDSYZ"); "LEAD2SYZ: ", attrib(SSinit, "LEAD2SYZ"); */ def SS = SSinit(M); setring SS; /* "KERCHECK: ", attrib(SS, "KERCHECK"); "SYZCHECK: ", attrib(SS, "SYZCHECK"); "DEBUG: ", attrib(SS, "DEBUG"); "HYBRIDNF: ", attrib(SS, "HYBRIDNF"); "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ"); "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ"); ""; "IGNORETAILS: ", attrib(SS, "IGNORETAILS"); "SYZNUMBER: ", attrib(SS, "SYZNUMBER"); */ if (l == 0) { l = nvars(basering) + 2; // not really an estimate...?! } SSstep(); l = l - 1; SScontinue(l); /* "KERCHECK: ", attrib(SS, "KERCHECK"); "SYZCHECK: ", attrib(SS, "SYZCHECK"); "DEBUG: ", attrib(SS, "DEBUG"); "HYBRIDNF: ", attrib(SS, "HYBRIDNF"); "TAILREDSYZ: ", attrib(SS, "TAILREDSYZ"); "LEAD2SYZ: ", attrib(SS, "LEAD2SYZ"); ""; "IGNORETAILS: ", attrib(SS, "IGNORETAILS"); "SYZNUMBER: ", attrib(SS, "SYZNUMBER"); */ return (SS); } example { "EXAMPLE:"; echo = 2; ring r; module M = maxideal(1); M; def S = SSres(M, 0); setring S; S; RES; MRES; kill S; setring r; kill M; def A = nc_algebra(-1,0); setring A; ideal Q = var(1)^2, var(2)^2, var(3)^2; qring SCA = twostd(Q); basering; module M = maxideal(1); def S = SSres(M, 2); setring S; S; RES; MRES; } static proc loadme() { int @DEBUG = !system("with", "ndebug"); if( @DEBUG ) { "ndebug?: ", system("with", "ndebug"); "om_ndebug?: ", system("with", "om_ndebug"); listvar(Top); listvar(Schreyer); } // listvar(Syzextra); listvar(Syzextra_g); if( !defined(DetailedPrint) ) { if( 1 ) { if( @DEBUG ) { "Loading the Release version!"; } load("syzextra.so"); if( @DEBUG ) { listvar(Syzextra); } exportto(Top, Syzextra::ClearContent); exportto(Top, Syzextra::ClearDenominators); exportto(Schreyer, Syzextra::m2_end); // export Syzextra; // exportto(Schreyer, Syzextra::noop); exportto(Schreyer, Syzextra::DetailedPrint); exportto(Schreyer, Syzextra::leadmonomial); exportto(Schreyer, Syzextra::leadcomp); // exportto(Schreyer, Syzextra::leadrawexp); // exportto(Schreyer, Syzextra::ISUpdateComponents); exportto(Schreyer, Syzextra::SetInducedReferrence); exportto(Schreyer, Syzextra::GetInducedData); // exportto(Schreyer, Syzextra::GetAMData); // exportto(Schreyer, Syzextra::SetSyzComp); exportto(Schreyer, Syzextra::MakeInducedSchreyerOrdering); // exportto(Schreyer, Syzextra::MakeSyzCompOrdering); exportto(Schreyer, Syzextra::idPrepare); // exportto(Schreyer, Syzextra::reduce_syz); // exportto(Schreyer, Syzextra::p_Content); exportto(Schreyer, Syzextra::ProfilerStart); exportto(Schreyer, Syzextra::ProfilerStop); exportto(Schreyer, Syzextra::Tail); exportto(Schreyer, Syzextra::ComputeLeadingSyzygyTerms); exportto(Schreyer, Syzextra::Compute2LeadingSyzygyTerms); exportto(Schreyer, Syzextra::Sort_c_ds); exportto(Schreyer, Syzextra::FindReducer); exportto(Schreyer, Syzextra::ReduceTerm); exportto(Schreyer, Syzextra::TraverseTail); exportto(Schreyer, Syzextra::SchreyerSyzygyNF); exportto(Schreyer, Syzextra::ComputeSyzygy); } /* else { if( @DEBUG ) { "Loading the Debug version!"; } load("syzextra.so"); if( @DEBUG ) { listvar(Syzextra_g); } exportto(Top, Syzextra_g::ClearContent); exportto(Top, Syzextra_g::ClearDenominators); exportto(Schreyer, Syzextra_g::m2_end); // export Syzextra_g; // exportto(Schreyer, Syzextra_g::noop); exportto(Schreyer, Syzextra_g::DetailedPrint); exportto(Schreyer, Syzextra_g::leadmonomial); exportto(Schreyer, Syzextra_g::leadcomp); // exportto(Schreyer, Syzextra_g::leadrawexp); // exportto(Schreyer, Syzextra_g::ISUpdateComponents); exportto(Schreyer, Syzextra_g::SetInducedReferrence); exportto(Schreyer, Syzextra_g::GetInducedData); // exportto(Schreyer, Syzextra_g::GetAMData); // exportto(Schreyer, Syzextra_g::SetSyzComp); exportto(Schreyer, Syzextra_g::MakeInducedSchreyerOrdering); // exportto(Schreyer, Syzextra_g::MakeSyzCompOrdering); exportto(Schreyer, Syzextra_g::idPrepare); // exportto(Schreyer, Syzextra_g::reduce_syz); // exportto(Schreyer, Syzextra_g::p_Content); exportto(Schreyer, Syzextra_g::ProfilerStart); exportto(Schreyer, Syzextra_g::ProfilerStop); exportto(Schreyer, Syzextra_g::Tail); exportto(Schreyer, Syzextra_g::ComputeLeadingSyzygyTerms); exportto(Schreyer, Syzextra_g::Compute2LeadingSyzygyTerms); exportto(Schreyer, Syzextra_g::Sort_c_ds); exportto(Schreyer, Syzextra_g::FindReducer); exportto(Schreyer, Syzextra_g::ReduceTerm); exportto(Schreyer, Syzextra_g::TraverseTail); exportto(Schreyer, Syzextra_g::SchreyerSyzygyNF); exportto(Schreyer, Syzextra_g::ComputeSyzygy); } */ exportto(Top, DetailedPrint); exportto(Top, GetInducedData); if( @DEBUG ) { listvar(Top); listvar(Schreyer); } } if( !defined(GetInducedData) ) { ERROR("Sorry but we are missing the dynamic module (syzextra.so)..."); } } static proc mod_init() { loadme(); } proc testallSexamples() { example Ssyz; example Scontinue; example Sres; } proc testallSSexamples() { example SSsyz; example SScontinue; example SSres; } example { "EXAMPLE:"; echo = 2; testallSexamples(); testallSSexamples(); } /*static*/ proc StartResTesting(list #) { if( defined(@save_res_list) ) { ERROR("Sorry: existing global variable @save_res_list - run StopAddResTesting before another Start!!!"); } string @save_res_desc = string(#); ">>>>>>>>> {{{{{{{{{ STARTING TESTING ('" + @save_res_desc + "') :::::::::::: "; list @save_res_list = list(); export @save_res_list; export @save_res_desc; } /*static*/ proc StopResTesting() { if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) ) { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); } if( !defined(@save_res_list) || !defined(@save_res_desc) ) { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); } int i, j; int f = 0; def m; for (i = size(@save_res_list); i > 0; i--) { "Total Time: ", @save_res_list[i][5], ", Res: ", @save_res_list[i][6], ", Minimal Betti: ", @save_res_list[i][5] - @save_res_list[i][6], ", ", @save_res_list[i][1], " :with: ", @save_res_list[i][2]; } for (i = size(@save_res_list); i > 1; i--) { m = @save_res_list[i][4]; for (j = i-1; j > 0; j--) { if( m != @save_res_list[j][4] ) { "ERROR: Betti[j: ", j, "] != Betti[i: ", i, "]:"; "j: ", j; print( @save_res_list[j][4], "betti"); print(@save_res_list[j]); "i: ", i; print( @save_res_list[i][4], "betti"); print(@save_res_list[i]); f = 1; }; }; }; if( f ) { print(@save_res_list); "<<<<<<<<< }}}}}}}}} STOP TESTING (", @save_res_desc, ") !!!!!!!!!!!! "; "ERROR: There were some wrong betti numbers... "; m2_end(666); } else { "BETTI: "; print( @save_res_list[1][4], "betti"); } kill @save_res_list; "<<<<<<<<< }}}}}}}}} STOP TESTING (", @save_res_desc, ") !!!!!!!!!!!! "; kill @save_res_desc; } /*static*/ proc StartAddResTest(string method, string desc) { if( !defined(@save_res_list) ) { ERROR("Sorry: no global variable - run StartResTesting beforehand!!!"); } if( defined(@save_opts) || defined(@save_method) || defined(@save_desc) ) { ERROR("Sorry: existing global variables - run StopAddResTest before another Start!!!"); } def @save_opts = option(get); export @save_opts; def @save_method = method; export @save_method; def @save_desc = desc; export @save_desc; "< START RES TEST{{{ ", @save_method, ", with:", @save_desc, " ... "; } /*static*/ proc StopAddResTest(def RR, intmat S, int @t, int @m) { if( !(defined(@save_opts) && defined(@save_method) && defined(@save_desc)) ) { ERROR("Sorry: no global variables - run StartAddResTest beforehand!!!"); } list @l = list(@save_method, @save_desc, option(get), S, @t, @m); // RR, // print(S, "betti"); "> -STOP RES TEST}}} ", @save_method, ", with:", @save_desc, ", Timer:", @t; option(); option(set, @save_opts); kill @save_opts; kill @save_method; kill @save_desc; @save_res_list[1 + size(@save_res_list)] = @l; } /*static*/ proc SCheck(def S) { setring S; // for checking... module M = MRES; if( ncols(M) < nrows(M) ) { M[nrows(M)] = 0; } else { M = transpose(M); if( ncols(M) < nrows(M) ) { M[nrows(M)] = 0; } M = transpose(M); } if( nrows(M) != ncols(M) ) { "ERROR: non-square M!!!"; m2_end(666); } if( size(module( M*M )) > 0 ) { "ERROR: module( M*M ) != 0!!!"; module( M*M ); "MRES': "; M; print(M); m2_end(666); } // "MRES': "; M; print(M); if( size(RES[1]) != 0 ) { "ERROR: wrong starting zero module!!!"; m2_end(666); } // RES; /* MRES; RES; ""; LRES; ""; TRES; */ } //// TODO: SSres(0) fails..!!!?? proc TestSSres(def I) { def save = basering; int @t,@m,r,rr,i; string name = "LEAD2SYZ:" +string(attrib(SSinit,"LEAD2SYZ")) + ",TAILREDSYZ:"+string(attrib(SSinit,"TAILREDSYZ")) + ",HYBRIDNF:" +string(attrib(SSinit,"HYBRIDNF")); StartAddResTest( "SSres", "minres + betti(,1) + mods: {" + name + "}" ); option(redSB); option(redTail); timer=0;rtimer=0;def R=SSres(I,0);@m=rtimer; setring R;module M;list @l=list();@l[size(RES)-1]=list();r=nrows(RES[1]);for(i=2;i<=size(RES);i++){M=RES[i];rr=nrows(M);if((r>0)&&(size(M)>0)&&(r0)&&(size(M)>0)&&(r 0) { DEBUG = #[1]; } system("--min-time", "0.01"); system("--ticks-per-sec", 100); // option(prot); // TODO: only for now!! attrib(SSinit, "DEBUG", (DEBUG > 0)); attrib(SSinit, "SYZCHECK", (DEBUG > 0)); attrib(SSinit, "KERCHECK", 1); ring r; r; ideal M = maxideal(1); // M; TestSSresAttribs(M, "<" + string(M) + "> in " + string(basering)); kill r; ring r = 0, (a, b, c, d), lp; r; ideal M = maxideal(1); // M; TestSSresAttribs(M, "<" + string(M) + "> in " + string(basering)); kill r; ring R = 0, (w, x, y, z), dp; R; ideal M = w^2 - x*z, w*x - y*z, x^2 - w*y, x*y - z^2, y^2 - w*z; // M; TestSSresAttribs(M, "<" + string(M) + "> in " + string(basering)); kill R; ring r = 0, (a, b, c, d, e, f), dp; r; ideal M = maxideal(1); // M; TestSSresAttribs(M, "<" + string(M) + "> in " + string(basering)); kill r; ring AGR = (101), (a, b, c, d), dp; AGR; // simple: AGR@101n3d002s004%1: 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; // M; TestSSresAttribs(M, "simple: AGR@101n3d002s004%1"); // medium: AGR@101n3d004s009%1; 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; // M; TestSSresAttribs(M, "medium: AGR@101n3d004s009%1"); } proc testAGR(list #) { def DEBUG = 0; if(size(#) > 0) { DEBUG = #[1]; } system("--min-time", "0.01"); system("--ticks-per-sec", 100); attrib(SSinit, "DEBUG", 0); attrib(SSinit, "SYZCHECK", (DEBUG > 0)); attrib(SSinit, "KERCHECK", 0); // option(prot); ring AGR = (101), (a, b, c, d), dp; AGR; // lengthy: AGR@101n3d008s058%3, kernel only! ideal M = 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// M; TestSSresAttribs2tr(M, "AGR@101n3d008s058%3"); // AGR@101n3d010s010%3, a bit slower... 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; // M; TestSSresAttribs2tr(M, "AGR@101n3d010s010%3"); kill AGR; ring AGR = (101), (a,b,c,d,e,f,g,h), dp; AGR; // AGR@101n7d005s010%2, medium: <= 2 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; // M; TestSSresAttribs2tr(M, "AGR@101n7d005s010%2"); /* options: 1 1 0 : Time: 3/10 options: 1 1 1 : Time: 2/6 lres Time: 0 nres Time: 25 sres Time: 0 */ kill AGR; // from Andreas...tooo long!? ring AGR = (101), (a,b,c,d,e), dp; AGR; // AGR101n4d007s021%4 ideal M = 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a^3*b^2-40*a^2*c^2*d+50*a*b*c^2*d+25*b^2*c^2*d+46*a*c^3*d-45*b*c^3*d-6*c^4*d-24*a^3*d^2-9*a^2*b*d^2-15*a*b^2*d^2+5*b^3*d^2+36*a^2*c*d^2-19*a*b*c*d^2+19*b^2*c*d^2+17*a*c^2*d^2+12*b*c^2*d^2-25*c^3*d^2-33*a^2*d^3-27*a*b*d^3+42*b^2*d^3-4*a*c*d^3+33*b*c*d^3+32*c^2*d^3+10*a*d^4+47*c*d^4-3*d^5-23*a^4*e-45*a^3*b*e+41*a^2*b^2*e+47*a*b^3*e+15*b^4*e-2*a^3*c*e+12*a^2*b*c*e+13*a*b^2*c*e-45*b^3*c*e-28*a^2*c^2*e-3*a*b*c^2*e-37*b^2*c^2*e+39*a*c^3*e+37*c^4*e-12*a^3*d*e-48*a^2*b*d*e-5*a*b^2*d*e+47*b^3*d*e-41*a^2*c*d*e-36*a*b*c*d*e-37*b^2*c*d*e-a*c^2*d*e-38*b*c^2*d*e+17*c^3*d*e-29*a^2*d^2*e-3*a*b*d^2*e-23*b^2*d^2*e-19*a*c*d^2*e+43*b*c*d^2*e-48*c^2*d^2*e-46*a*d^3*e+48*b*d^3*e+40*c*d^3*e-15*d^4*e-23*a^3*e^2-22*a^2*b*e^2-50*a*b^2*e^2-33*b^3*e^2+27*a^2*c*e^2-46*a*b*c*e^2+29*b^2*c*e^2-14*a*c^2*e^2+9*b*c^2*e^2-43*c^3*e^2-19*a^2*d*e^2-38*a*b*d*e^2+12*b^2*d*e^2+18*a*c*d*e^2+20*b*c*d*e^2+3*c^2*d*e^2-9*a*d^2*e^2-27*b*d^2*e^2-6*c*d^2*e^2+38*d^3*e^2+43*a^2*e^3+43*a*b*e^3+3*b^2*e^3+10*a*c*e^3+8*b*c*e^3+13*c^2*e^3+37*a*d*e^3+b*d*e^3-21*c*d*e^3+27*d^2*e^3+26*a*e^4-29*b*e^4-39*c*e^4+29*d*e^4+21*e^5, a^4*b-45*a^2*c^2*d-6*a*b*c^2*d-42*b^2*c^2*d-4*a*c^3*d-49*b*c^3*d+14*c^4*d+35*a^3*d^2-3*a^2*b*d^2+23*a*b^2*d^2+21*b^3*d^2-24*a^2*c*d^2-14*a*b*c*d^2+20*b^2*c*d^2-20*a*c^2*d^2+41*b*c^2*d^2-34*c^3*d^2-13*a^2*d^3-48*a*b*d^3-13*b^2*d^3+38*a*c*d^3+21*b*c*d^3+40*c^2*d^3-28*a*d^4-34*b*d^4+38*c*d^4-24*d^5-48*a^4*e-2*a^3*b*e-35*a^2*b^2*e+2*a*b^3*e-25*b^4*e+47*a^3*c*e-14*a^2*b*c*e+25*a*b^2*c*e-12*b^3*c*e-11*a^2*c^2*e+22*a*b*c^2*e+15*b^2*c^2*e+17*a*c^3*e+47*b*c^3*e-43*c^4*e+28*a^3*d*e+9*a^2*b*d*e+6*a*b^2*d*e+30*a^2*c*d*e+31*a*b*c*d*e-2*b^2*c*d*e-6*a*c^2*d*e-45*b*c^2*d*e-24*c^3*d*e-39*a^2*d^2*e-7*a*b*d^2*e-11*b^2*d^2*e+8*a*c*d^2*e-47*b*c*d^2*e+c^2*d^2*e+30*a*d^3*e-30*b*d^3*e-38*c*d^3*e-14*d^4*e-25*a^3*e^2-14*a^2*b*e^2+24*a*b^2*e^2-37*b^3*e^2-14*a^2*c*e^2+40*a*b*c*e^2+27*b^2*c*e^2+22*a*c^2*e^2-38*b*c^2*e^2+43*c^3*e^2-44*a^2*d*e^2+28*a*b*d*e^2-4*b^2*d*e^2-26*a*c*d*e^2+18*b*c*d*e^2+24*c^2*d*e^2-35*a*d^2*e^2+6*b*d^2*e^2+5*c*d^2*e^2-38*d^3*e^2-37*a^2*e^3+34*a*b*e^3-27*b^2*e^3-4*a*c*e^3-3*b*c*e^3-16*c^2*e^3+22*a*d*e^3-4*b*d*e^3-41*c*d*e^3+25*d^2*e^3-38*a*e^4+49*b*e^4+c*e^4+14*d*e^4+47*e^5, a^5-45*a^2*c^2*d-14*a*b*c^2*d-47*b^2*c^2*d-8*a*c^3*d+13*b*c^3*d+50*c^4*d-34*a^3*d^2-5*a^2*b*d^2+36*a*b^2*d^2+11*b^3*d^2+41*a^2*c*d^2-32*a*b*c*d^2+41*b^2*c*d^2-40*a*c^2*d^2+14*b*c^2*d^2+5*c^3*d^2+25*a^2*d^3+10*a*b*d^3-24*b^2*d^3-33*b*c*d^3-21*c^2*d^3+a*d^4+44*b*d^4-46*c*d^4-23*d^5-13*a^4*e+13*a^3*b*e-49*a*b^3*e+18*b^4*e+2*a^3*c*e+15*a^2*b*c*e-14*a*b^2*c*e-38*b^3*c*e+34*a^2*c^2*e+42*a*b*c^2*e-42*b^2*c^2*e-36*a*c^3*e+35*b*c^3*e-11*c^4*e+20*a^3*d*e+41*a*b^2*d*e+40*b^3*d*e-39*a^2*c*d*e-35*a*b*c*d*e-7*b^2*c*d*e-34*a*c^2*d*e-35*b*c^2*d*e+45*c^3*d*e+17*a^2*d^2*e+39*a*b*d^2*e+5*b^2*d^2*e-35*a*c*d^2*e-26*b*c*d^2*e-47*c^2*d^2*e+5*a*d^3*e-2*b*d^3*e+44*c*d^3*e+9*d^4*e-12*a^3*e^2+49*a^2*b*e^2-2*a*b^2*e^2-11*b^3*e^2-49*a^2*c*e^2-16*a*b*c*e^2-34*b^2*c*e^2+19*a*c^2*e^2-24*b*c^2*e^2-33*c^3*e^2-39*a^2*d*e^2+2*a*b*d*e^2+46*b^2*d*e^2-17*a*c*d*e^2+47*b*c*d*e^2+39*c^2*d*e^2+13*a*d^2*e^2+50*b*d^2*e^2-11*c*d^2*e^2+3*d^3*e^2+22*a^2*e^3-50*a*b*e^3+30*b^2*e^3-22*a*c*e^3-29*b*c*e^3-40*c^2*e^3+34*a*d*e^3+15*b*d*e^3-17*c*d*e^3+43*d^2*e^3+46*a*e^4-19*b*e^4-46*c*e^4-39*d*e^4-e^5, e^6, d*e^5, c*e^5, b*e^5, a*e^5, d^2*e^4, c*d*e^4, b*d*e^4, a*d*e^4, c^2*e^4, b*c*e^4, a*c*e^4, b^2*e^4, a*b*e^4, a^2*e^4, d^3*e^3, c*d^2*e^3, b*d^2*e^3, a*d^2*e^3, c^2*d*e^3, b*c*d*e^3, a*c*d*e^3, b^2*d*e^3, a*b*d*e^3, a^2*d*e^3, c^3*e^3, b*c^2*e^3, a*c^2*e^3, b^2*c*e^3, a*b*c*e^3, a^2*c*e^3, b^3*e^3, a*b^2*e^3, a^2*b*e^3, a^3*e^3, d^4*e^2, c*d^3*e^2, b*d^3*e^2, a*d^3*e^2, c^2*d^2*e^2, b*c*d^2*e^2, a*c*d^2*e^2, b^2*d^2*e^2, a*b*d^2*e^2, a^2*d^2*e^2, c^3*d*e^2, b*c^2*d*e^2, a*c^2*d*e^2, b^2*c*d*e^2, a*b*c*d*e^2, a^2*c*d*e^2, b^3*d*e^2, a*b^2*d*e^2, a^2*b*d*e^2, a^3*d*e^2, c^4*e^2, b*c^3*e^2, a*c^3*e^2, b^2*c^2*e^2, a*b*c^2*e^2; // M; TestSSresAttribs2tr(M, "AGR101n4d007s021%4"); /* options: 1 1 0 : Time: 5/9/10 (35 without LCM) options: 1 1 1 : Time: 6/8/25 lres Time: 5 nres Time: 5 sres Time: 693 */ kill M; // AGR101n4d008s020%1, too big? ideal M = c^5*d-49*a^4*d^2-36*a^3*b*d^2-a^2*b^2*d^2-26*a*b^3*d^2+2*b^4*d^2+8*a^3*c*d^2-46*a^2*b*c*d^2-43*a*b^2*c*d^2-46*b^3*c*d^2-3*a^2*c^2*d^2-43*a*b*c^2*d^2+49*b^2*c^2*d^2-10*a*c^3*d^2+35*b*c^3*d^2+20*c^4*d^2-42*a^3*d^3+45*a^2*b*d^3+32*a*b^2*d^3-45*b^3*d^3-27*a^2*c*d^3+13*a*b*c*d^3+25*b^2*c*d^3+8*a*c^2*d^3+9*b*c^2*d^3+9*c^3*d^3+45*a^2*d^4+30*a*b*d^4+39*b^2*d^4-23*a*c*d^4+2*b*c*d^4-16*c^2*d^4+32*a*d^5-34*b*d^5+39*c*d^5+12*d^6-29*a^5*e-23*a^4*b*e-29*a^3*b^2*e-a^2*b^3*e-20*a*b^4*e+42*b^5*e+20*a^4*c*e-27*a^3*b*c*e-5*a^2*b^2*c*e-14*b^4*c*e-27*a^3*c^2*e-7*a^2*b*c^2*e-25*a*b^2*c^2*e+14*b^3*c^2*e+19*a^2*c^3*e+43*a*b*c^3*e-31*b^2*c^3*e+37*a*c^4*e-34*b*c^4*e+44*c^5*e+21*a^4*d*e+22*a^3*b*d*e+14*a^2*b^2*d*e-35*a*b^3*d*e-29*b^4*d*e-9*a^3*c*d*e-41*a^2*b*c*d*e+28*a*b^2*c*d*e+35*b^3*c*d*e+48*a^2*c^2*d*e+26*a*b*c^2*d*e-47*b^2*c^2*d*e+18*a*c^3*d*e+8*b*c^3*d*e-46*c^4*d*e+50*a^3*d^2*e-46*a^2*b*d^2*e-41*a*b^2*d^2*e-44*b^3*d^2*e+7*a^2*c*d^2*e-a*b*c*d^2*e+38*b^2*c*d^2*e+33*a*c^2*d^2*e-24*b*c^2*d^2*e-7*c^3*d^2*e+27*a^2*d^3*e+19*a*b*d^3*e-14*b^2*d^3*e+9*a*c*d^3*e+3*b*c*d^3*e+34*c^2*d^3*e-49*a*d^4*e-2*b*d^4*e+9*c*d^4*e+17*d^5*e+12*a^4*e^2-17*a^3*b*e^2+16*a^2*b^2*e^2+2*a*b^3*e^2+25*b^4*e^2+49*a^3*c*e^2+10*a^2*b*c*e^2-43*a*b^2*c*e^2+5*b^3*c*e^2+4*a^2*c^2*e^2-44*a*b*c^2*e^2-25*b^2*c^2*e^2+15*a*c^3*e^2-44*b*c^3*e^2-17*c^4*e^2+17*a^3*d*e^2+40*a^2*b*d*e^2+3*a*b^2*d*e^2-25*b^3*d*e^2-47*a^2*c*d*e^2-45*a*b*c*d*e^2+9*b^2*c*d*e^2-41*a*c^2*d*e^2-36*b*c^2*d*e^2-17*c^3*d*e^2-15*a^2*d^2*e^2+49*a*b*d^2*e^2+13*b^2*d^2*e^2-39*a*c*d^2*e^2+36*b*c*d^2*e^2-32*c^2*d^2*e^2+23*a*d^3*e^2+14*b*d^3*e^2+10*c*d^3*e^2-d^4*e^2+24*a^3*e^3+27*a^2*b*e^3+31*a*b^2*e^3-45*b^3*e^3-50*a^2*c*e^3-a*b*c*e^3+43*b^2*c*e^3+46*a*c^2*e^3-25*b*c^2*e^3+2*c^3*e^3+44*a^2*d*e^3+43*a*b*d*e^3-30*b^2*d*e^3-18*a*c*d*e^3+44*b*c*d*e^3-34*c^2*d*e^3-49*a*d^2*e^3-18*b*d^2*e^3-21*c*d^2*e^3-43*d^3*e^3-26*a^2*e^4-18*a*b*e^4+6*b^2*e^4-48*a*c*e^4+6*b*c*e^4-16*c^2*e^4-2*a*d*e^4-21*b*d*e^4+5*c*d*e^4-18*d^2*e^4+33*a*e^5-23*b*e^5-48*c*e^5+37*d*e^5-44*e^6, 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e^7, d*e^6, c*e^6, b*e^6, a*e^6, d^2*e^5, c*d*e^5, b*d*e^5, a*d*e^5, c^2*e^5, b*c*e^5, a*c*e^5, b^2*e^5, a*b*e^5, a^2*e^5, d^3*e^4, c*d^2*e^4, b*d^2*e^4, a*d^2*e^4, c^2*d*e^4, b*c*d*e^4, a*c*d*e^4, b^2*d*e^4, a*b*d*e^4, a^2*d*e^4, c^3*e^4, b*c^2*e^4, a*c^2*e^4, b^2*c*e^4, a*b*c*e^4, a^2*c*e^4, b^3*e^4, a*b^2*e^4, a^2*b*e^4, a^3*e^4, d^4*e^3, c*d^3*e^3, b*d^3*e^3, a*d^3*e^3, c^2*d^2*e^3, b*c*d^2*e^3, a*c*d^2*e^3, b^2*d^2*e^3, a*b*d^2*e^3, a^2*d^2*e^3, c^3*d*e^3, b*c^2*d*e^3, a*c^2*d*e^3, b^2*c*d*e^3, a*b*c*d*e^3, a^2*c*d*e^3, b^3*d*e^3, a*b^2*d*e^3, a^2*b*d*e^3, a^3*d*e^3, c^4*e^3, b*c^3*e^3, a*c^3*e^3, b^2*c^2*e^3, a*b*c^2*e^3, a^2*c^2*e^3, b^3*c*e^3, a*b^2*c*e^3, a^2*b*c*e^3, a^3*c*e^3, b^4*e^3, a*b^3*e^3, a^2*b^2*e^3, a^3*b*e^3, a^4*e^3, d^5*e^2, c*d^4*e^2, b*d^4*e^2, a*d^4*e^2, c^2*d^3*e^2, b*c*d^3*e^2, a*c*d^3*e^2, b^2*d^3*e^2, a*b*d^3*e^2, a^2*d^3*e^2, c^3*d^2*e^2, b*c^2*d^2*e^2, a*c^2*d^2*e^2, b^2*c*d^2*e^2, a*b*c*d^2*e^2; // M; TestSSresAttribs2tr(M, "AGR101n4d008s020%1_big"); /* options: 1 1 0 : Time: 29/32/73/92 (316 without LCM) options: 1 1 1 : Time: 32/34/43/202 lres Time: 24 nres Time: 19 sres Time: 71 */ kill M; kill AGR; ring AGR = (101), (a,b,c,d,e,f), dp; AGR; // AGR@101n5d005s016%1, new, medium difficulty? ideal M = b*d-13*c*d+7*a*e-32*b*e+31*c*e+3*d*e+46*a*f-13*b*f+22*c*f-19*d*f-33*e*f, a*d+2*c*d-42*a*e+46*b*e+7*c*e-38*d*e+31*a*f+9*b*f+27*c*f-19*d*f-24*e*f, b*c-35*c*d-34*a*e+4*b*e+33*c*e+23*d*e+4*a*f-43*b*f+43*c*f+17*d*f-13*e*f, a*c+49*c*d-28*a*e+18*b*e-23*c*e+3*d*e-5*a*f-23*b*f+2*c*f+46*d*f-40*e*f, a*b-38*c*d+a*e-49*b*e-20*c*e+32*d*e+13*a*f+25*b*f+37*c*f-27*d*f+25*e*f, f^4, e*f^3, d*f^3, c*f^3, b*f^3, a*f^3, e^2*f^2, d*e*f^2, c*e*f^2, b*e*f^2, a*e*f^2, d^2*f^2, c*d*f^2, c^2*f^2, b^2*f^2, a^2*f^2, e^3*f, d*e^2*f, c*e^2*f, b*e^2*f, a*e^2*f, d^2*e*f, d^3*f, c^3*f, b^3*f, a^3*f, e^4, d^4, c^4, b^4, a^4; // M; TestSSresAttribs(M, "AGR@101n5d005s016%1"); /* * ? */ kill M; } proc testAGRhard(list #) { def DEBUG = 0; if(size(#) > 0) { DEBUG = #[1]; } system("--min-time", "0.01"); system("--ticks-per-sec", 100); attrib(SSinit, "DEBUG", 0); attrib(SSinit, "SYZCHECK", (DEBUG > 0)); attrib(SSinit, "KERCHECK", 0); // option(prot); ring AGR = (101), (a,b,c,d,e,f), dp; AGR; // AGR@101n5d006s016%1, new, hard!? ideal M = b*d+47*c*d-27*a*e+37*b*e+21*c*e+31*d*e-31*a*f+23*b*f+47*c*f+42*d*f+11*e*f, a*d+7*c*d+19*a*e+28*b*e-33*c*e-28*d*e+15*a*f+28*b*f+47*c*f+3*d*f+14*e*f, b*c+29*c*d-25*a*e+12*b*e+23*c*e-50*d*e-17*a*f+30*b*f-37*c*f+35*d*f-e*f, a*c+46*c*d+12*a*e+27*b*e+39*c*e+23*d*e-45*a*f+39*b*f-35*c*f+4*d*f-10*e*f, a*b+38*c*d-18*a*e-34*b*e-30*c*e+38*d*e+22*a*f+34*b*f+39*c*f+30*d*f-19*e*f, f^5, e*f^4, d*f^4, c*f^4, b*f^4, a*f^4, e^2*f^3, d*e*f^3, c*e*f^3, b*e*f^3, a*e*f^3, d^2*f^3, c*d*f^3, c^2*f^3, b^2*f^3, a^2*f^3, e^3*f^2, d*e^2*f^2, c*e^2*f^2, b*e^2*f^2, a*e^2*f^2, d^2*e*f^2, d^3*f^2, c^3*f^2, b^3*f^2, a^3*f^2, e^4*f, e^5, d^5, c^5, b^5, a^5; TestSSresAttribs(M, "AGR@101n5d006s016%1_hard"); /* * ? */ kill M; } /* proc testAGRFrame() { system("--min-time", "0.01"); system("--ticks-per-sec", 100); attrib(SSinit, "DEBUG", 0); attrib(SSinit, "SYZCHECK", 0); // no such tests anymore with IGNORETAILS == 1! attrib(SSinit, "KERCHECK", 1); attrib(SSinit, "IGNORETAILS", 1); // option(prot); ring AGR = (101), (a, b, c, d), dp; AGR; "lengthy: AGR@101n3d008s058%3, kernel only!"; ideal M = 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// M; TestSSresAttribs(M); "AGR@101n3d010s010%3, a bit slower..."; M = 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3*d^3+19*c^2*d^6-50*a*d^7-33*b*d^7+16*c*d^7-45*d^8,a*b*c^3*d^3-6*c^2*d^6-38*a*d^7+35*b*d^7+32*c*d^7-12*d^8,a^2*c^3*d^3+44*c^2*d^6+35*a*d^7+42*b*d^7-10*c*d^7-48*d^8,b^3*c^2*d^3+33*c^2*d^6-7*a*d^7-41*b*d^7-3*c*d^7-33*d^8,a*b^2*c^2*d^3-21*c^2*d^6-22*a*d^7-23*b*d^7+24*c*d^7+47*d^8,a^2*b*c^2*d^3+c^2*d^6-32*a*d^7-34*b*d^7-42*c*d^7+7*d^8,a^3*c^2*d^3+6*c^2*d^6-31*a*d^7-26*b*d^7+19*c*d^7-49*d^8,b^4*c*d^3+6*c^2*d^6-24*a*d^7+10*b*d^7-18*c*d^7-4*d^8,a*b^3*c*d^3+46*c^2*d^6+41*a*d^7+7*b*d^7+8*c*d^7-28*d^8,a^2*b^2*c*d^3+33*c^2*d^6-15*a*d^7-11*b*d^7+38*c*d^7+14*d^8,a^3*b*c*d^3-29*c^2*d^6-4*a*d^7-32*b*d^7+13*c*d^7-3*d^8,a^4*c*d^3-34*c^2*d^6+5*a*d^7+29*b*d^7-15*c*d^7-48*d^8,b^5*d^3-42*c^2*d^6+33*a*d^7-49*b*d^7+33*c*d^7-43*d^8,a*b^4*d^3+25*c^2*d^6-11*a*d^7-16*b*d^7+32*c*d^7-2*d^8,a^2*b^3*d^3-36*c^2*d^6-47*a*d^7-16*b*d^7+19*c*d^7+9*d^8,a^3*b^2*d^3-30*c^2*d^6-21*a*d^7-6*b*d^7+16*c*d^7-14*d^8,a^4*b*d^3+47*c^2*d^6-16*a*d^7-13*b*d^7+21*c*d^7+30*d^8,a^5*d^3-2*c^2*d^6+40*a*d^7+34*b*d^7+14*c*d^7-50*d^8,c^6*d^2-4*c^2*d^6-41*a*d^7+46*b*d^7+17*c*d^7+19*d^8,b*c^5*d^2-49*c^2*d^6+5*a*d^7-31*b*d^7+30*c*d^7+28*d^8,a*c^5*d^2-12*c^2*d^6-23*a*d^7-39*b*d^7+6*c*d^7-27*d^8,b^2*c^4*d^2-12*c^2*d^6-30*a*d^7+13*b*d^7-42*c*d^7+38*d^8,a*b*c^4*d^2-31*c^2*d^6+5*a*d^7-41*b*d^7-24*c*d^7,a^2*c^4*d^2-c^2*d^6+4*a*d^7+21*b*d^7+19*c*d^7-34*d^8,b^3*c^3*d^2-50*c^2*d^6-11*a*d^7+24*b*d^7+24*c*d^7-44*d^8,a*b^2*c^3*d^2+2*c^2*d^6-42*a*d^7-17*b*d^7-33*c*d^7-10*d^8,a^2*b*c^3*d^2+20*c^2*d^6+29*a*d^7+35*b*d^7-31*c*d^7-35*d^8,a^3*c^3*d^2+35*c^2*d^6-13*a*d^7+20*b*d^7-15*c*d^7-45*d^8,b^4*c^2*d^2+c^2*d^6+36*a*d^7-42*b*d^7+32*c*d^7+16*d^8,a*b^3*c^2*d^2-9*c^2*d^6-43*a*d^7-5*b*d^7-17*c*d^7+50*d^8,a^2*b^2*c^2*d^2-36*c^2*d^6+31*a*d^7+4*b*d^7-26*c*d^7-11*d^8,a^3*b*c^2*d^2+15*c^2*d^6+40*a*d^7-18*b*d^7-31*c*d^7+43*d^8,a^4*c^2*d^2+41*c^2*d^6-49*a*d^7+37*b*d^7+47*c*d^7-48*d^8,b^5*c*d^2-49*c^2*d^6+15*a*d^7+48*b*d^7+22*c*d^7+38*d^8,a*b^4*c*d^2+12*c^2*d^6+16*a*d^7-22*b*d^7-c*d^7+29*d^8,a^2*b^3*c*d^2+31*c^2*d^6+19*a*d^7+45*b*d^7-6*c*d^7+42*d^8,a^3*b^2*c*d^2+29*c^2*d^6-39*a*d^7+25*b*d^7-48*c*d^7-d^8,a^4*b*c*d^2-31*c^2*d^6+24*a*d^7-2*b*d^7+36*c*d^7+37*d^8,a^5*c*d^2+33*c^2*d^6-46*a*d^7-41*b*d^7-29*c*d^7-12*d^8,b^6*d^2-39*c^2*d^6+35*a*d^7-8*b*d^7+35*c*d^7+47*d^8,a*b^5*d^2-38*c^2*d^6-11*a*d^7-37*b*d^7-7*c*d^7-5*d^8,a^2*b^4*d^2+29*c^2*d^6+36*a*d^7-29*b*d^7+20*c*d^7+39*d^8,a^3*b^3*d^2-44*c^2*d^6+43*a*d^7-50*b*d^7-24*c*d^7-16*d^8,a^4*b^2*d^2+20*c^2*d^6+33*a*d^7+6*b*d^7+47*c*d^7+40*d^8,a^5*b*d^2-10*c^2*d^6+25*a*d^7-8*b*d^7-14*c*d^7+16*d^8,a^6*d^2+48*c^2*d^6+14*a*d^7+32*b*d^7+17*c*d^7+13*d^8,c^7*d+38*c^2*d^6-39*a*d^7+22*b*d^7+15*c*d^7-d^8,b*c^6*d+9*c^2*d^6+37*a*d^7+12*b*d^7+27*c*d^7+3*d^8,a*c^6*d-5*c^2*d^6+34*a*d^7+15*b*d^7+2*c*d^7-21*d^8,b^2*c^5*d+35*c^2*d^6+27*a*d^7+13*b*d^7-39*c*d^7+8*d^8,a*b*c^5*d-34*c^2*d^6-18*a*d^7-21*b*d^7-31*c*d^7+46*d^8,a^2*c^5*d-16*c^2*d^6-6*a*d^7-18*b*d^7+3*c*d^7+47*d^8,b^3*c^4*d-46*c^2*d^6+4*a*d^7-38*b*d^7-29*c*d^7-4*d^8,a*b^2*c^4*d-35*c^2*d^6-14*a*d^7-32*b*d^7-40*c*d^7-35*d^8,a^2*b*c^4*d+23*c^2*d^6-44*a*d^7-3*b*d^7+4*c*d^7-4*d^8,a^3*c^4*d+24*c^2*d^6-7*a*d^7-44*b*d^7-16*c*d^7+10*d^8,b^4*c^3*d+43*c^2*d^6+12*a*d^7+43*b*d^7-49*c*d^7-23*d^8,a*b^3*c^3*d+22*c^2*d^6+6*a*d^7+2*b*d^7-9*c*d^7,a^2*b^2*c^3*d+4*c^2*d^6+21*a*d^7-24*b*d^7-26*c*d^7+33*d^8,a^3*b*c^3*d+13*c^2*d^6-18*a*d^7+31*b*d^7-28*c*d^7+2*d^8,a^4*c^3*d+10*c^2*d^6-14*a*d^7+30*b*d^7-40*c*d^7+33*d^8,b^5*c^2*d-35*c^2*d^6-33*a*d^7+7*b*d^7+13*c*d^7+26*d^8,a*b^4*c^2*d-49*c^2*d^6+9*a*d^7+20*b*d^7+11*c*d^7-32*d^8,a^2*b^3*c^2*d+33*c^2*d^6-43*a*d^7-27*b*d^7-31*c*d^7-41*d^8,a^3*b^2*c^2*d-6*c^2*d^6+23*a*d^7+20*b*d^7-8*c*d^7-6*d^8,a^4*b*c^2*d+10*c^2*d^6-24*a*d^7+30*b*d^7+42*c*d^7-23*d^8,a^5*c^2*d+12*c^2*d^6+20*a*d^7+24*b*d^7-9*c*d^7-9*d^8,b^6*c*d-12*c^2*d^6+36*a*d^7+4*b*d^7-12*c*d^7+26*d^8,a*b^5*c*d-19*c^2*d^6-39*a*d^7-26*b*d^7-4*c*d^7+10*d^8,a^2*b^4*c*d+38*c^2*d^6-6*a*d^7+6*b*d^7+41*c*d^7+49*d^8,a^3*b^3*c*d-34*c^2*d^6-42*a*d^7+22*b*d^7-26*c*d^7-13*d^8,a^4*b^2*c*d+14*c^2*d^6+40*a*d^7+39*b*d^7-34*d^8,a^5*b*c*d-8*c^2*d^6+45*a*d^7-35*b*d^7+48*c*d^7+47*d^8,a^6*c*d-6*c^2*d^6-24*a*d^7-2*b*d^7-9*c*d^7+7*d^8,b^7*d+34*c^2*d^6-14*a*d^7+46*b*d^7-50*c*d^7+26*d^8,a*b^6*d+6*c^2*d^6+23*a*d^7-27*b*d^7-25*c*d^7-2*d^8,c^8+43*c^2*d^6+11*b*d^7-39*c*d^7-30*d^8,b*c^7-44*c^2*d^6-4*a*d^7-10*b*d^7+31*c*d^7+42*d^8,a*c^7-6*a*d^7+31*b*d^7+37*c*d^7-41*d^8,b^2*c^6-11*c^2*d^6-35*a*d^7+32*b*d^7-25*c*d^7-21*d^8,a*b*c^6+2*c^2*d^6+43*a*d^7-48*b*d^7-49*c*d^7-19*d^8,a^2*c^6-20*c^2*d^6-11*a*d^7-35*b*d^7-33*c*d^7+28*d^8,b^3*c^5+4*c^2*d^6-7*a*d^7-21*b*d^7-14*c*d^7+48*d^8,a*b^2*c^5+17*c^2*d^6+45*a*d^7-32*b*d^7+29*c*d^7+38*d^8,a^2*b*c^5-13*c^2*d^6+46*a*d^7+4*b*d^7-18*c*d^7+19*d^8,a^3*c^5-23*c^2*d^6-a*d^7-3*b*d^7-15*c*d^7+19*d^8,b^4*c^4-50*c^2*d^6+39*a*d^7+49*b*d^7+47*c*d^7+7*d^8,a*b^3*c^4-33*c^2*d^6+10*a*d^7+32*b*d^7+21*c*d^7-39*d^8,a^2*b^2*c^4+23*c^2*d^6+27*a*d^7-17*b*d^7+29*c*d^7+9*d^8,a^3*b*c^4-47*c^2*d^6-43*a*d^7-47*b*d^7-34*c*d^7-23*d^8,a^4*c^4-6*c^2*d^6+7*a*d^7+38*b*d^7-27*c*d^7-9*d^8,b^5*c^3-47*c^2*d^6+18*a*d^7-44*b*d^7-4*c*d^7-18*d^8,a*b^4*c^3+30*c^2*d^6+36*a*d^7+25*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; // M; TestSSresAttribs(M); kill AGR; ring AGR = (101), (a,b,c,d,e,f,g,h), dp; AGR; "AGR@101n7d005s010%2_medium"; 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; // M; TestSSresAttribs(M); // with tails: // options: 1 1 0 : Time: 3/10 // options: 1 1 1 : Time: 2/6 kill AGR; // from Andreas...tooo long!? ring AGR = (101), (a,b,c,d,e), dp; AGR; "AGR101n4d007s021%4... too hard?"; ideal M = 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e^6, d*e^5, c*e^5, b*e^5, a*e^5, d^2*e^4, c*d*e^4, b*d*e^4, a*d*e^4, c^2*e^4, b*c*e^4, a*c*e^4, b^2*e^4, a*b*e^4, a^2*e^4, d^3*e^3, c*d^2*e^3, b*d^2*e^3, a*d^2*e^3, c^2*d*e^3, b*c*d*e^3, a*c*d*e^3, b^2*d*e^3, a*b*d*e^3, a^2*d*e^3, c^3*e^3, b*c^2*e^3, a*c^2*e^3, b^2*c*e^3, a*b*c*e^3, a^2*c*e^3, b^3*e^3, a*b^2*e^3, a^2*b*e^3, a^3*e^3, d^4*e^2, c*d^3*e^2, b*d^3*e^2, a*d^3*e^2, c^2*d^2*e^2, b*c*d^2*e^2, a*c*d^2*e^2, b^2*d^2*e^2, a*b*d^2*e^2, a^2*d^2*e^2, c^3*d*e^2, b*c^2*d*e^2, a*c^2*d*e^2, b^2*c*d*e^2, a*b*c*d*e^2, a^2*c*d*e^2, b^3*d*e^2, a*b^2*d*e^2, a^2*b*d*e^2, a^3*d*e^2, c^4*e^2, b*c^3*e^2, a*c^3*e^2, b^2*c^2*e^2, a*b*c^2*e^2; // M; TestSSresAttribs(M); // with tails: // options: 1 1 0 : Time: 5/9/10 (35 without LCM) // options: 1 1 1 : Time: 6/8/25 kill M; // too big? // AGR101n4d008s020%1 ideal M = 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e^7, d*e^6, c*e^6, b*e^6, a*e^6, d^2*e^5, c*d*e^5, b*d*e^5, a*d*e^5, c^2*e^5, b*c*e^5, a*c*e^5, b^2*e^5, a*b*e^5, a^2*e^5, d^3*e^4, c*d^2*e^4, b*d^2*e^4, a*d^2*e^4, c^2*d*e^4, b*c*d*e^4, a*c*d*e^4, b^2*d*e^4, a*b*d*e^4, a^2*d*e^4, c^3*e^4, b*c^2*e^4, a*c^2*e^4, b^2*c*e^4, a*b*c*e^4, a^2*c*e^4, b^3*e^4, a*b^2*e^4, a^2*b*e^4, a^3*e^4, d^4*e^3, c*d^3*e^3, b*d^3*e^3, a*d^3*e^3, c^2*d^2*e^3, b*c*d^2*e^3, a*c*d^2*e^3, b^2*d^2*e^3, a*b*d^2*e^3, a^2*d^2*e^3, c^3*d*e^3, b*c^2*d*e^3, a*c^2*d*e^3, b^2*c*d*e^3, a*b*c*d*e^3, a^2*c*d*e^3, b^3*d*e^3, a*b^2*d*e^3, a^2*b*d*e^3, a^3*d*e^3, c^4*e^3, b*c^3*e^3, a*c^3*e^3, b^2*c^2*e^3, a*b*c^2*e^3, a^2*c^2*e^3, b^3*c*e^3, a*b^2*c*e^3, a^2*b*c*e^3, a^3*c*e^3, b^4*e^3, a*b^3*e^3, a^2*b^2*e^3, a^3*b*e^3, a^4*e^3, d^5*e^2, c*d^4*e^2, b*d^4*e^2, a*d^4*e^2, c^2*d^3*e^2, b*c*d^3*e^2, a*c*d^3*e^2, b^2*d^3*e^2, a*b*d^3*e^2, a^2*d^3*e^2, c^3*d^2*e^2, b*c^2*d^2*e^2, a*c^2*d^2*e^2, b^2*c*d^2*e^2, a*b*c*d^2*e^2; M; TestSSresAttribs(M); // with tails // options: 1 1 0 : Time: 34/73/92 (316 without LCM) // options: 1 1 1 : Time: 35/43/202 kill M; kill AGR; ring AGR = (101), (a,b,c,d,e,f), dp; AGR; ideal M = b*f+7*c*f+30*d*f-38*e*f, a*f+10*c*f-25*d*f+14*e*f, d*e-10*c*f-17*d*f+26*e*f, c*e-43*c*f+12*d*f+30*e*f, b*e+37*c*f+15*d*f+48*e*f, a*e+21*c*f+37*d*f+42*e*f, c*d+21*c*f+20*d*f-42*e*f, b*d-39*c*f+27*d*f+11*e*f, a*d-39*c*f+17*d*f+21*e*f, b*c+36*c*f+6*d*f-43*e*f, a*c+12*c*f-2*d*f-11*e*f, a*b-35*c*f+d*f+33*e*f, e*f^6+46*f^7, d*f^6-37*f^7, c*f^6+9*f^7, e^7+19*f^7, d^7+40*f^7, c^7+34*f^7, b^7+17*f^7, a^7+40*f^7; TestSSresAttribs(M); kill M; } */ // TODO: faster betties!!!