///////////////////////////./bfct.lib////////////////////////////// Checking library './bfct.lib' Reporting most possible annomalies. Library function line,start-eod line,body-eob line,example-eoe Version:(1.5,2008/10/06); Procedure testbfctlib (line 43) has OLD-STYLE-HELP! g ./libparse testbfctlib line 43, 2142-2161 44, 2163-2484 0, 0-2484 *** Procedure 'testbfctlib' is global and has no help-section. *** Procedure 'testbfctlib' is global and has no example-section. l ./libparse gradedWeyl line 64, 2597-2633 72, 2985-3703 116, 3706-3917 g ./libparse ispositive line 129, 3924-3950 135, 4169-4300 147, 4303-4419 g ./libparse isin line 156, 4424-4445 162, 4665-4796 174, 4799-4903 g ./libparse scalarprod line 183, 4908-4944 190, 5191-5392 205, 5395-5494 g ./libparse linreduce line 217, 5595-5634 225, 6044-6872 275, 6875-7059 g ./libparse ncsolve line 287, 7064-7094 298, 7699-9729 378, 9732-9857 g ./libparse minpol line 388, 9862-9891 398,10394-12314 479,12317-12514 g ./libparse minpolsyz line 492,12519-12560 510,13674-16586 644,16589-16841 Procedure listofroots (line 659) has OLD-STYLE-HELP! l ./libparse listofroots line 659,16852-16878 660,16880-17837 0, 0-17837 Procedure bfctengine (line 707) has OLD-STYLE-HELP! l ./libparse bfctengine line 707,17848-17965 708,17967-19002 0, 0-19002 g ./libparse bfct line 756,19007-19033 771,20013-20875 806,20878-21015 g ./libparse bfctsyz line 816,21020-21049 835,22370-23771 889,23774-23921 g ./libparse bfctideal line 899,23926-23968 913,24856-25505 944,25508-25781 g ./libparse bfctonestep line 960,25788-25820 972,26560-27493 1008,27496-27626 Procedure hardexamples (line 1017) has OLD-STYLE-HELP! l ./libparse hardexamples line 1017,27637-27658 1018,27660-28164 0, 0-28164 ///////////////////////////./bfct.lib////////////////////////////// [10, L:81]: @* one is interested in the global Bernstein-Sato polynomial b(s) in K[s], [13, L:94]: @* Here, D stands for an n-th Weyl algebra K [16, L:96]: @* the list of all roots of b(s), which are known to be rational, with their multiplicities. [20, L:89]: bfct(f[,s,t,v]); compute the global Bernstein-Sato polynomial of a given poly [21, L:89]: bfctsyz(f[,r,s,t,u,v]); compute the global Bernstein-Sato polynomial of a given poly [22, L:89]: bfctonestep(f[,s,t]); compute the global Bernstein-Sato polynomial of a given poly [23, L:97]: bfctideal(I,w[,s,t]); compute the global b-function of a given ideal w.r.t. a given weight [24, L:121]: minpol(f,I); compute the minimal polynomial of the endormorphism in basering modulo ideal given by a poly [25, L:121]: minpolsyz(f,I[,p,s,t]); compute the minimal polynomial of the endormorphism in basering modulo ideal given by a poly [26, L:83]: linreduce(f,I[,s]); reduce a poly by linear reductions of its leading term [27, L:93]: ncsolve(I[,s]); find and compute a linear dependency of the elements of an ideal [219, L:99]: RETURN: a poly obtained by linear reductions of the leading term of the given poly with an ideal [221, L:85]: NOTE: If s<>0, a list consisting of the reduced poly and the vector of the used [290, L:90]: PURPOSE: compute a linear dependency between the elements of an ideal if such one exists [293, L:81]: @* By default, @code{slimgb} is used in char 0 and @code{std} in char >0. [348, L:93]: dbprint(ppl, "ncsolve: starting Groebner basis computation with engine:", whichengine); [390, L:109]: RETURN: coefficient vector of the minimal polynomial of the endomorphism of basering modulo I defined by f [493, L:94]: "USAGE: minpolsyz(f, I [,p,s,t]); f a poly, I an ideal, p, t optial ints, p a prime number [494, L:109]: RETURN: coefficient vector of the minimal polynomial of the endomorphism of basering modulo I defined by f [498, L:88]: @* If p>0 is given, the proc computes the minimal polynomial in char p first and [499, L:94]: @* then only searches for a minimal polynomial of the obtained degree in the basering. [502, L:81]: @* If s<>0, @code{std} is used for Groebner basis computations in char 0, [504, L:97]: @* If t<>0 and by default, @code{std} is used for Groebner basis computations in char >0, [692, L:100]: ideal bs; intvec m; //the Bernstein polynomial is monic, so we are not interested in constants [707, L:125]: static proc bfctengine (poly f, int whichengine, int methodord, int methodminpol, int minpolchar, int modengine, intvec u0) [758, L:86]: RETURN: list of roots of the Bernstein-Sato polynomial bs(f) and their multiplicies [759, L:133]: PURPOSE: compute the global Bernstein-Sato polynomial for a hypersurface, defined by f, according to the algorithm by Masayuki Noro [760, L:85]: NOTE: In this proc, a system of linear equations is solved by linear reductions. [765, L:87]: @* If v is a positive weight vector, v is used for homogenization computations, [817, L:90]: "USAGE: bfctsyz(f [,r,s,t,u,v]); f a poly, r,s,t,u optional ints, v an optional intvec [818, L:84]: RETURN: list of roots of the Bernstein-Sato polynomial bs(f) and its multiplicies [819, L:133]: PURPOSE: compute the global Bernstein-Sato polynomial for a hypersurface, defined by f, according to the algorithm by Masayuki Noro [820, L:86]: NOTE: In this proc, a system of linear equations is solved by computing syzygies. [821, L:91]: @* If r<>0, @code{std} is used for Groebner basis computations in characteristic 0, [825, L:97]: @* If t<>0, the minimal polynomial computation is solely performed over charasteristic 0, [827, L:107]: @* If u<>0 and by default, @code{std} is used for Groebner basis computations in characteristic >0, [829, L:87]: @* If v is a positive weight vector, v is used for homogenization computations, [901, L:109]: RETURN: list of roots and their multiplicies of the global b-function of I w.r.t. the weight vector (-w,w) [902, L:90]: PURPOSE: compute the global b-function of an ideal according to the algorithm by M. Noro [903, L:83]: NOTE: Assume, I is an ideal in the n-th Weyl algebra where the sequence of the [905, L:91]: @* If s<>0, @code{std} is used for Groebner basis computations in characteristic 0, [962, L:84]: RETURN: list of roots of the Bernstein-Sato polynomial bs(f) and its multiplicies [963, L:131]: PURPOSE: compute the global Bernstein-Sato polynomial for a hypersurface, defined by f, using only one Groebner basis computation [964, L:85]: NOTE: If s<>0, @code{std} is used for the Groebner basis computation, otherwise, ///////////////////////////./discretize.lib////////////////////////////// Checking library './discretize.lib' Reporting most possible annomalies. Library function line,start-eod line,body-eob line,example-eoe Version:(1.3,2008/08/07); g ./libparse xchange line 35, 1628-1674 41, 1856-2065 51, 2068-2237 g ./libparse par2tex line 62, 2242-2264 68, 2573-3202 94, 3205-3417 g ./libparse replace line 106, 3422-3470 112, 3667-4514 157, 4517-4760 g ./libparse exp2pt line 169, 4765-4792 177, 5146-5656 207, 5659-5811 g ./libparse mon2pt line 216, 5816-5845 221, 6012-7263 277, 7266-7560 g ./libparse npar line 290, 7565-7584 295, 7742-8097 316, 8100-8231 g ./libparse decoef line 326, 8236-8265 333, 8526-9656 378, 9659-9816 g ./libparse texcoef line 387, 9821-9843 394,10084-10807 435,10810-10992 Procedure rmDol (line 445) has OLD-STYLE-HELP! g ./libparse rmDol line 445,10997-11017 446,11019-11262 0, 0-11262 *** Procedure 'rmDol' is global and has no help-section. *** Procedure 'rmDol' is global and has no example-section. g ./libparse difpoly2tex line 456,11267-11308 467,11762-13949 586,13952-14190 g ./libparse magnitude line 599,14197-14219 606,14428-14580 613,14583-14705 Procedure clTex (line 622) has OLD-STYLE-HELP! g ./libparse clTex line 622,14712-14732 624,14771-14874 0, 0-14874 *** Procedure 'clTex' is global and has no example-section. Procedure ElimModComp (line 634) has OLD-STYLE-HELP! g ./libparse ElimModComp line 634,14879-14914 635,14916-15152 0, 0-15152 *** Procedure 'ElimModComp' is global and has no help-section. *** Procedure 'ElimModComp' is global and has no example-section. Procedure simfrac (line 651) has OLD-STYLE-HELP! g ./libparse simfrac line 651,15159-15191 652,15193-15417 0, 0-15417 *** Procedure 'simfrac' is global and has no help-section. *** Procedure 'simfrac' is global and has no example-section. Procedure discr_example (line 662) has OLD-STYLE-HELP! g ./libparse discr_example line 662,15422-15442 663,15444-17852 727,17855-17909 *** Procedure 'discr_example' is global and has no help-section. ///////////////////////////./discretize.lib////////////////////////////// [8, L:245]: THEORY: We provide the presentation of difference operators in a polynomial, semi-factorized and a nodal form. Running @code{example discr_example;} will show how we generate finite difference schemes of linear PDE's from given approximations. [66, L:163]: NOTE: the convention is the following: Tx goes to T_x, dx to tri x (the same for t,y,z). Moreover, some parameters (theta,ro,A,V) are converted to greek letters. ///////////////////////////./dmodapp.lib////////////////////////////// Checking library './dmodapp.lib' Reporting most possible annomalies. Library function line,start-eod line,body-eob line,example-eoe Version:(1.10,2008/10/09); Procedure testdmodapp (line 49) has OLD-STYLE-HELP! g ./libparse testdmodapp line 49, 2146-2164 50, 2166-2435 0, 0-2435 *** Procedure 'testdmodapp' is global and has no help-section. *** Procedure 'testdmodapp' is global and has no example-section. g ./libparse initialideal line 67, 2442-2497 84, 3561-4101 108, 4104-4299 g ./libparse initialmalgrange line 119, 4304-4341 138, 5580-6564 182, 6567-6806 Procedure initialidealengine (line 197) has OLD-STYLE-HELP! g ./libparse initialidealengine line 197, 6811-6892 198, 6894-12540 0, 0-12540 *** Procedure 'initialidealengine' is global and has no help-section. *** Procedure 'initialidealengine' is global and has no example-section. g ./libparse InForm line 439,12545-12565 446,12924-13990 503,13993-14316 l ./libparse charVariety line 521,14327-14353 534,14943-16081 591,16084-16318 l ./libparse charInfo line 607,16338-16361 622,17056-17161 0, 0-17161 Procedure AppelF1 (line 631) has OLD-STYLE-HELP! g ./libparse AppelF1 line 631,17168-17182 633,17231-17620 648,17623-17741 Procedure AppelF2 (line 657) has OLD-STYLE-HELP! g ./libparse AppelF2 line 657,17746-17760 659,17807-18134 673,18137-18255 Procedure AppelF4 (line 682) has OLD-STYLE-HELP! g ./libparse AppelF4 line 682,18260-18274 684,18325-18676 698,18679-18797 g ./libparse poly2list line 707,18802-18825 713,19042-19273 728,19276-19429 g ./libparse isFsat line 740,19436-19464 748,19760-20145 764,20148-20338 g ./libparse DLoc line 777,20343-20369 789,21033-21522 811,21525-21757 g ./libparse DLoc0 line 823,21762-21789 835,22517-27982 1043,27985-28294 g ./libparse SDLoc line 1057,28301-28328 1068,28884-33304 1250,33307-33496 g ./libparse annRat line 1263,33501-33528 1274,34050-36056 1352,36059-36585 Procedure ex_annRat (line 1369) has OLD-STYLE-HELP! l ./libparse ex_annRat line 1369,36596-36613 1370,36615-36766 0, 0-36766 g ./libparse annPoly line 1379,36771-36791 1391,37309-37856 1419,37859-38103 Procedure exCusp (line 1431) has OLD-STYLE-HELP! l ./libparse exCusp line 1431,38114-38128 1432,38130-38472 0, 0-38472 Procedure exWalther1 (line 1450) has OLD-STYLE-HELP! l ./libparse exWalther1 line 1450,38483-38501 1451,38503-38829 0, 0-38829 Procedure exWalther2 (line 1470) has OLD-STYLE-HELP! l ./libparse exWalther2 line 1470,38840-38858 1471,38860-39278 0, 0-39278 Procedure exWalther3 (line 1494) has OLD-STYLE-HELP! l ./libparse exWalther3 line 1494,39289-39307 1495,39309-39944 0, 0-39944 Procedure engine (line 1526) has OLD-STYLE-HELP! g ./libparse engine line 1526,39949-39976 1527,40005-40228 1543,40231-40435 ///////////////////////////./dmodapp.lib////////////////////////////// [10, L:92]: @* - Ann F^s = I = I(F^s) = LD in D(R)[s] can be computed by SannfsBM, SannfsOT, SannfsLOT [11, L:85]: @* - global Bernstein polynomial bs resp. BS in K[s] can be computed by bernsteinBM [16, L:91]: annRat(f,g); compute the annihilator of a rational function f/g in the corr. Weyl algebra [17, L:82]: annPoly(f); compute the annihilator of a polynomial f in the corr. Weyl algebra [18, L:105]: initialmalgrange(f[,s,t,u,v]); compute a Groebner basis of the initial Malgrange ideal for a given poly [19, L:92]: initialideal(I,u,v[,s,t]); compute the initial ideal of a given ideal w.r.t. given weights [23, L:105]: SDLoc(I, F); compute a generic presentation of the localization of D/I w.r.t. f^s, for D a Weyl algebra [24, L:87]: DLoc0(I, F); compute the localization of D/I w.r.t. f^s, based on the procedure SDLoc [25, L:81]: InForm(f,w); compute the initial form of a poly/ideal w.r.t. a given weight [68, L:82]: "USAGE: initialideal(I,u,v [,s,t]); I an ideal, u,v intvecs, s,t optional ints [69, L:104]: RETURN: an ideal, a Broebner basis of the initial ideal of the input ideal w.r.t. the weights u and v [71, L:83]: NOTE: Assume, I is an ideal in the n-th Weyl algebra where the sequence of the [73, L:90]: @* Further assume that u is the weight for the x(i) and v the weight for the D(i). [74, L:87]: @* Note that the returned ideal is not a D-ideal but an ideal in the associated [76, L:82]: @* If s<>0, @code{std} is used for Groebner basis computations, otherwise, [120, L:96]: "USAGE: initialmalgrange(f, [,s,t,u,v]); f a poly, s,t,u optional ints, v an optional intvec [121, L:100]: RETURN: a ring, the Weyl algebra induced by the basering, extended in the indeterminates t and Dt [122, L:87]: PURPOSE: compute the initial Malgrange ideal of a given poly w.r.t. the weight vector [123, L:91]: @* (-1,0...,0,1,0,...,0) such that the weight of t is -1 and the weight of Dt is 1. [127, L:82]: @* If s<>0, @code{std} is used for Groebner basis computations, otherwise, [132, L:87]: @* If v is a positive weight vector, v is used for homogenization computations, [178, L:100]: def D = initialidealengine("initialmalgrange",whichengine, methodord, f, 0, 0, u0, reversevars); [197, L:83]: proc initialidealengine(string calledfrom, int whichengine, int blockord, list #) [278, L:91]: ring Dh = 0,(t,s,x(n..1),Dt,D(n..1),h),(a(@a),a(@a2),a(uv),dp(noofvars-1),lp(1)); [364, L:82]: dbprint(ppl, "starting Groebner basis computation with engine:", whichengine); [429, L:93]: dbprint(ppl, "starting cosmetic Groebner basis computation with engine:", whichengine); [443, L:97]: NOTE: the size of the weight vector must be equal to the number of variables of the basering [783, L:94]: @* - the ideal LD0 (which is a Groebner basis) is the presentation of the localization [784, L:106]: @* - the ideal BS contains the roots with multiplicities of a Bernstein polynomial of D/I w.r.t f. [826, L:140]: PURPOSE: compute the presentation of the localization of D/I w.r.t. f^s, where D is a Weyl Algebra, based on the output of procedure SDLoc [829, L:94]: @* - the ideal LD0 (which is a Groebner basis) is the presentation of the localization [830, L:106]: @* - the ideal BS contains the roots with multiplicities of a Bernstein polynomial of D/I w.r.t f. [865, L:110]: ideal bs; intvec m; //the Bernstein polynomial is monic, so we are not interested in constants [1060, L:106]: PURPOSE: compute a generic presentation of the localization of D/I w.r.t. f^s, where D is a Weyl Algebra [1063, L:93]: @* - the ideal LD (which is a Groebner basis) is the presentation of the localization [1266, L:89]: PURPOSE: compute the ideal in Weyl algebra, annihilating the rational function g*f^{-1} [1269, L:83]: @* - the ideal RLD (which is given in a Groebner basis) is the annihilator. [1283, L:89]: int isr = 0; // checkRoot1(LD,f,1); // roots are negative, have to enter positive int [1361, L:189]: ideal tst = 3*x*Dx + 2*y*Dy + 1, y^3*Dy^2 - x^2*Dy^2 + 6*y^2*Dy + 6*y, 9*y^2*Dx^2*Dy - 4*y*Dy^3 + 27*y*Dx^2 + 2*Dy^2, 9*y^3*Dx^2 - 4*y^2*Dy^2 + 10*y*Dy -10; //todo: maybe a bit too long [1385, L:83]: @* - the ideal RLD (which is given in a Groebner basis) is the annihilator. ///////////////////////////./freegb.lib////////////////////////////// Checking library './freegb.lib' Reporting most possible annomalies. Library function line,start-eod line,body-eob line,example-eoe Version:(1.12,2008/10/06); g ./libparse lshift line 33, 1144-1199 34, 1200-2197 0, 0-2197 *** Procedure 'lshift' is global and has no help-section. *** Procedure 'lshift' is global and has no example-section. g ./libparse skip0 line 78, 2200-2220 79, 2221-2504 0, 0-2504 *** Procedure 'skip0' is global and has no help-section. *** Procedure 'skip0' is global and has no example-section. g ./libparse lst2str line 101, 2507-2535 108, 2823-3317 137, 3319-3545 g ./libparse mod2str line 149, 3549-3579 156, 3837-4330 190, 4332-4476 g ./libparse vct2str line 199, 4479-4509 206, 4761-6090 278, 6092-6300 g ./libparse IsVar line 290, 6303-6321 291, 6322-6792 314, 6794-6961 *** Procedure 'IsVar' is global and has no help-section. g ./libparse id2words line 330, 6992-7021 331, 7022-7602 365, 7604-7738 *** Procedure 'id2words' is global and has no help-section. g ./libparse mono2word line 373, 7741-7770 374, 7771-7773 0, 0-7773 *** Procedure 'mono2word' is global and has no help-section. *** Procedure 'mono2word' is global and has no example-section. g ./libparse freegbasis line 393, 8348-8379 400, 8622-13596 635,13598-13828 g ./libparse crs line 647,13831-13855 653,14007-16759 783,16761-16991 g ./libparse polylen line 796,16994-17015 797,17016-17238 0, 0-17238 *** Procedure 'polylen' is global and has no help-section. *** Procedure 'polylen' is global and has no example-section. g ./libparse freegbRing line 812,17241-17263 818,17429-18705 881,18707-18820 g ./libparse ex_shift line 890,18823-18838 891,18839-19313 0, 0-19313 *** Procedure 'ex_shift' is global and has no help-section. *** Procedure 'ex_shift' is global and has no example-section. g ./libparse test_shrink line 911,19316-19334 912,19335-20010 0, 0-20010 *** Procedure 'test_shrink' is global and has no help-section. *** Procedure 'test_shrink' is global and has no example-section. g ./libparse ex2 line 938,20013-20023 939,20024-20166 0, 0-20166 *** Procedure 'ex2' is global and has no help-section. *** Procedure 'ex2' is global and has no example-section. g ./libparse ex_nonhomog line 948,20169-20187 949,20188-20485 0, 0-20485 *** Procedure 'ex_nonhomog' is global and has no help-section. *** Procedure 'ex_nonhomog' is global and has no example-section. g ./libparse ex_nonhomog_comm line 966,20488-20511 967,20512-20643 0, 0-20643 *** Procedure 'ex_nonhomog_comm' is global and has no help-section. *** Procedure 'ex_nonhomog_comm' is global and has no example-section. g ./libparse ex_nonhomog_h line 976,20646-20666 977,20667-20823 0, 0-20823 *** Procedure 'ex_nonhomog_h' is global and has no help-section. *** Procedure 'ex_nonhomog_h' is global and has no example-section. g ./libparse ex_nonhomog_h2 line 986,20826-20847 987,20848-21148 0, 0-21148 *** Procedure 'ex_nonhomog_h2' is global and has no help-section. *** Procedure 'ex_nonhomog_h2' is global and has no example-section. g ./libparse ex_nonhomog_3 line 1005,21152-21172 1006,21173-21472 0, 0-21472 *** Procedure 'ex_nonhomog_3' is global and has no help-section. *** Procedure 'ex_nonhomog_3' is global and has no example-section. g ./libparse ex_densep_2 line 1024,21475-21493 1025,21494-21818 0, 0-21818 *** Procedure 'ex_densep_2' is global and has no help-section. *** Procedure 'ex_densep_2' is global and has no example-section. g ./libparse freegbold line 1048,21995-22025 1055,22266-27363 1294,27365-27594 g ./libparse sgb line 1306,27597-27621 1307,27622-28041 0, 0-28041 *** Procedure 'sgb' is global and has no help-section. *** Procedure 'sgb' is global and has no example-section. l ./libparse checkCeq line 1331,28052-28068 1332,28069-28338 0, 0-28338 g ./libparse exHom1 line 1345,28342-28355 1346,28356-29116 0, 0-29116 *** Procedure 'exHom1' is global and has no help-section. *** Procedure 'exHom1' is global and has no example-section. l ./libparse test1 line 1381,29125-29138 1382,29139-29355 0, 0-29355 l ./libparse test2 line 1395,29364-29377 1396,29378-29594 0, 0-29594 l ./libparse test3 line 1409,29603-29616 1410,29617-29837 0, 0-29837 Procedure schur2 (line 1422) has OLD-STYLE-HELP! g ./libparse schur2 line 1422,29840-29852 1423,29856-30057 0, 0-30057 *** Procedure 'schur2' is global and has no example-section. g ./libparse adem line 1431,30060-30083 1432,30084-30655 1460,30657-30736 *** Procedure 'adem' is global and has no help-section. g ./libparse adem2mod line 1498,31378-31398 1499,31399-31425 0, 0-31425 *** Procedure 'adem2mod' is global and has no help-section. *** Procedure 'adem2mod' is global and has no example-section. g ./libparse stringpoly2lplace line 1503,31428-31460 1504,31461-34031 1638,34033-34269 *** Procedure 'stringpoly2lplace' is global and has no help-section. g ./libparse addplaces line 1649,34272-34294 1650,34295-34624 1669,34626-34732 *** Procedure 'addplaces' is global and has no help-section. g ./libparse sent2lplace line 1677,34735-34761 1678,34762-34937 1688,34939-35064 *** Procedure 'sent2lplace' is global and has no help-section. g ./libparse testnumber line 1696,35067-35092 1697,35093-35910 1736,35912-36042 *** Procedure 'testnumber' is global and has no help-section. g ./libparse str2lplace line 1746,36045-36070 1747,36071-37392 1814,37394-37547 *** Procedure 'str2lplace' is global and has no help-section. g ./libparse strpower2rep line 1823,37550-37577 1824,37578-39547 1924,39549-39702 *** Procedure 'strpower2rep' is global and has no help-section. g ./libparse Liebr line 1933,39705-39739 1934,39740-40139 1962,40141-40363 *** Procedure 'Liebr' is global and has no help-section. g ./libparse pmLiebr line 1973,40366-40394 1974,40395-40523 0, 0-40523 *** Procedure 'pmLiebr' is global and has no help-section. *** Procedure 'pmLiebr' is global and has no example-section. g ./libparse pshift line 1986,40576-40602 1987,40603-40720 0, 0-40720 *** Procedure 'pshift' is global and has no help-section. *** Procedure 'pshift' is global and has no example-section. g ./libparse mmLiebr line 1993,40723-40751 1994,40752-40899 0, 0-40899 *** Procedure 'mmLiebr' is global and has no help-section. *** Procedure 'mmLiebr' is global and has no example-section. l ./libparse test_shift line 2004,40908-40926 2005,40927-41142 0, 0-41142 g ./libparse Serre line 2017,41145-41173 2018,41174-42253 2058,42255-42509 *** Procedure 'Serre' is global and has no help-section. g ./libparse lp2lstr line 2072,42512-42543 2078,42740-44683 2175,44685-44991 g ./libparse strList2poly line 2191,44994-45019 2192,45020-45513 2218,45515-45738 *** Procedure 'strList2poly' is global and has no help-section. g ./libparse file2lplace line 2231,45741-45771 2232,45772-46579 2273,46581-47016 *** Procedure 'file2lplace' is global and has no help-section. l ./libparse get_ls3nilp line 2289,47025-47044 2290,47045-47315 0, 0-47315 l ./libparse doc_example line 2303,47324-47342 2304,47342-47775 0, 0-47775 ///////////////////////////./freegb.lib////////////////////////////// [9, L:81]: freegbRing(int d); creates a ring with d blocks of shifted original variables [10, L:102]: freegbasis(list L, int n); compute two-sided Groebner basis of ideal, encoded via L, up to degree n [15, L:97]: lst2str(list L[,int n]); convert a list (of modules) into polynomials in free algebra [1338, L:81]: ideal I = x(1)*x(2) - x(1)*y(2), x(2)*x(3) - x(2)*y(3), x(3)*x(4) - x(3)*y(4); [1494, L:84]: s1*s1 =0, s2*s2 = s1*s2*s1, s(1)*s(3)== s(1)*s(1)*s(3) == 0 = 2*s(4) ->def for s(4) [2310, L:82]: ideal I = x(1)*y(2) + y(1)*z(2), x(1)*x(2) + x(1)*y(2) - y(1)*x(2) - y(1)*y(2); ///////////////////////////./jacobson.lib////////////////////////////// Checking library './jacobson.lib' Reporting most possible annomalies. Library function line,start-eod line,body-eob line,example-eoe Version:(1.3,2008/10/10); g ./libparse smith line 25, 1170-1202 40, 2057-3247 99, 3250-3430 Procedure diagonal_with_trafo (line 107) has OLD-STYLE-HELP! g ./libparse diagonal_with_trafo line 107, 3433-3479 108, 3481-8371 0, 0-8371 *** Procedure 'diagonal_with_trafo' is global and has no help-section. *** Procedure 'diagonal_with_trafo' is global and has no example-section. Procedure divisibility (line 331) has OLD-STYLE-HELP! g ./libparse divisibility line 331, 8378-8405 332, 8410-10005 0, 0-10005 *** Procedure 'divisibility' is global and has no example-section. Procedure diagonal_without_trafo (line 399) has OLD-STYLE-HELP! g ./libparse diagonal_without_trafo line 399,10010-10059 400,10061-13060 0, 0-13060 *** Procedure 'diagonal_without_trafo' is global and has no help-section. *** Procedure 'diagonal_without_trafo' is global and has no example-section. Procedure engine (line 536) has OLD-STYLE-HELP! l ./libparse engine line 536,13075-13104 537,13106-13264 0, 0-13264 g ./libparse jacobson line 554,13269-13304 567,14002-14834 613,14837-15134 Procedure triangle (line 626) has OLD-STYLE-HELP! g ./libparse triangle line 626,15143-15175 627,15177-19895 0, 0-19895 *** Procedure 'triangle' is global and has no help-section. *** Procedure 'triangle' is global and has no example-section. Procedure divideByContent (line 825) has OLD-STYLE-HELP! l ./libparse divideByContent line 825,19906-19937 826,19939-20192 0, 0-20192 Procedure Ex_One_wheeled_bicycle (line 843) has OLD-STYLE-HELP! l ./libparse Ex_One_wheeled_bicycle line 843,20260-20290 844,20292-20453 0, 0-20453 Procedure Ex_RLC (line 853) has OLD-STYLE-HELP! l ./libparse Ex_RLC line 853,20466-20479 854,20491-20671 0, 0-20671 Procedure Ex_two_pendula (line 863) has OLD-STYLE-HELP! l ./libparse Ex_two_pendula line 863,20684-20706 864,20708-20960 0, 0-20960 Procedure Ex_linerized_satellite_in_a_circular_equatorial_orbit (line 876) has OLD-STYLE-HELP! l ./libparse Ex_linerized_satellite_in_a_circular_equatorial_orbit line 876,20975-21036 877,21038-21281 0, 0-21281 Procedure Ex_flexible_one_link_robot (line 891) has OLD-STYLE-HELP! l ./libparse Ex_flexible_one_link_robot line 891,21292-21326 892,21328-21556 0, 0-21556 Procedure Ex_compare_output_with_maple_package_JanetOre (line 905) has OLD-STYLE-HELP! l ./libparse Ex_compare_output_with_maple_package_JanetOre line 905,21629-21682 906,21686-21962 0, 0-21962 Procedure Ex_cyclic (line 919) has OLD-STYLE-HELP! l ./libparse Ex_cyclic line 919,21975-21992 920,21994-22248 0, 0-22248 ///////////////////////////./jacobson.lib////////////////////////////// [10, L:89]: @* If R is non-commutative, we suppose R to be in two variables, say x and d. We treat [11, L:91]: @* then the Ore localization of R with respect to the mult.closed set S = K[x] without 0. [12, L:84]: @* Given a rectangular matrix M over R, one can compute unimodular matrices U, V [17, L:83]: smith(R,M[,eng1,eng2]); compute the Smith Normal Form of M over commutative ring [18, L:117]: jacobson(R,M[,eng]); compute a weak Jacobson Normal Form of M over non-commutative ring, i.e. a diagonal matrix [26, L:87]: "USAGE: smith(R, M[, eng1, eng2]); R ring, M matrix, eng1 and eng2 are optional int [30, L:90]: @* a list of matrices L such that L[1]*M*L[3]=L[2] with L[2]_11|L[2]_22|...|L[2]_nn and [32, L:95]: @* eng2 determines the engine, that computes the Groebner basis. By default eng2 equals zero. [33, L:82]: @* If optional integer eng2 = 0 than std is used to caculate a Groebner basis , [87, L:86]: list rueckL=CON*rueckLII[1]*rueckLI[1], CON*rueckLII[2], rueckLI[3]*rueckLII[3]; [151, L:108]: int flag=1; ///////////////counts if the underlying ring is r (flag mod 2 == 1) or ro (flag mod 2 == 0) [423, L:107]: int flag=1; ///////////////counts if the underlying ring is r (flag mod 2 == 1) or ro (flag mod 2 == 0) [557, L:96]: NOTE: A list of matrices L such that L[1]*M*L[3]=L[2] such that L[2] is a diagonal matrix and [559, L:93]: @* eng determines the engine, that computes the Groebner basis. By default eng equals zero. [660, L:110]: int flag=1; ///////////////counts if the underlying ring is r (flag mod 2 == 1) or ro (flag mod 2 == 0) [684, L:107]: if(flag mod 2==1){STD_EX=EXL,transpose(STD); ex=2*COL;} else {STD_EX=EXR,transpose(STD); ex=2*ROW;} [694, L:81]: dbprint(ppl,"Computing Groebner basis for transformation matrix: start"); [697, L:84]: dbprint(ppl,"Computing Groebner basis for transformation matrix: finished"); [720, L:102]: {if( leadcoef(STD[i-nz])!=leadcoef(STD_EX[i]) ) {STD[i-nz]=leadcoef(STD_EX[i])*STD[i-nz];} [819, L:83]: if (flag mod 2 ==0){ STD = involution(STD,inv);} else { STD = transpose(STD); } [867, L:96]: matrix pendula[3][4]=m1*L1*D^2,m2*L2*D^2,(M+m1+m2)*D^2,-1,m1*L1^2*D^2-m1*L1*g,0,m1*L1*D^2,0,0, [895, L:94]: matrix robot[3][4]=M11*D^2,M12*D^2,M13*D^2,-1,M21*D^2,M22*D^2+K1,0,0,M31*D^2,0,M33*D^2+K2,0; ///////////////////////////./matrix.lib////////////////////////////// Checking library './matrix.lib' Reporting most possible annomalies. Library function line,start-eod line,body-eob line,example-eoe Version:(1.43,2008/10/01); g ./libparse symmetricBasis line 23, 824-857 34, 1425-1681 47, 1683-1994 g ./libparse exteriorBasis line 65, 2077-2109 77, 2678-2972 91, 2974-3315 g ./libparse symmetricPower line 126, 3415-3451 134, 3777-5550 231, 5552-6230 g ./libparse exteriorPower line 267, 6313-6348 276, 6689-8393 373, 8395-9101 ///////////////////////////./matrix.lib////////////////////////////// ///////////////////////////./nchomolog.lib////////////////////////////// Checking library './nchomolog.lib' Reporting most possible annomalies. Library function line,start-eod line,body-eob line,example-eoe Version:(1.8,2008/08/07); g ./libparse contraHom line 26, 1057-1088 27, 1089-1343 43, 1345-1511 *** Procedure 'contraHom' is global and has no help-section. g ./libparse coHom line 53, 1514-1541 54, 1542-1796 70, 1798-1964 *** Procedure 'coHom' is global and has no help-section. g ./libparse ncHom line 80, 1967-1997 88, 2280-2830 109, 2832-3040 g ./libparse ncHom_alt line 121, 3043-3077 122, 3078-3349 131, 3351-3563 *** Procedure 'ncHom_alt' is global and has no help-section. g ./libparse ncHom_R line 143, 3566-3588 150, 3829-4255 166, 4257-4485 g ./libparse ncExt line 181, 4489-4528 188, 4770-5490 211, 5492-5662 g ./libparse ncExt_R line 221, 5665-5695 226, 5898-6817 259, 6819-7268 g ./libparse nctors line 278, 7271-7292 279, 7293-7895 0, 0-7895 *** Procedure 'nctors' is global and has no help-section. *** Procedure 'nctors' is global and has no example-section. Procedure altExt_R (line 301) has OLD-STYLE-HELP! g ./libparse altExt_R line 301, 7898-7939 305, 8001-9054 340, 9056-9226 g ./libparse tensorMaps line 350, 9229-9264 351, 9265-9635 0, 0-9635 *** Procedure 'tensorMaps' is global and has no help-section. *** Procedure 'tensorMaps' is global and has no example-section. g ./libparse ncTensorMod line 374, 9638-9678 375, 9679-9911 0, 0-9911 *** Procedure 'ncTensorMod' is global and has no help-section. *** Procedure 'ncTensorMod' is global and has no example-section. g ./libparse ncTor line 385, 9915-9954 386, 9955-10461 0, 0-10461 *** Procedure 'ncTor' is global and has no help-section. *** Procedure 'ncTor' is global and has no example-section. l ./libparse Hochschild line 401,10471-10489 402,10490-11292 0, 0-11292 l ./libparse Lie line 427,11301-11312 428,11313-12091 0, 0-12091 Procedure AllExts (line 466) has OLD-STYLE-HELP! g ./libparse AllExts line 466,12095-12125 471,12277-12758 0, 0-12758 *** Procedure 'AllExts' is global and has no example-section. l ./libparse dmod_exts line 503,12767-12792 504,12793-12834 0, 0-12834 g ./libparse dmodualtest line 508,12837-12870 509,12871-13689 535,13691-13826 *** Procedure 'dmodualtest' is global and has no help-section. g ./libparse dmodoublext line 545,13830-13864 553,14229-15300 600,15302-15584 l ./libparse part_Ext_R line 616,15593-15619 617,15620-16195 0, 0-16195 ///////////////////////////./nchomolog.lib////////////////////////////// [147, L:82]: NOTE: ncHom_R(M) is a right module, hence a right presentation matrix is returned [549, L:87]: NOTE: by default, i is set to the integer part of the half of number of variables of D [550, L:84]: @* for holonomic modules over Weyl algebra, the double ext is known to be holonomic