Annotation of OpenXM/src/k097/lib/minimal/debug-note.txt, Revision 1.1
1.1 ! takayama 1: $OpenXM$
! 2: a=Sannfs2("x*y*(x-y)*(x+y)");
! 3:
! 4: Correct answer by check.sm1 foo3;
! 5: es^2*x^2*Dx*Dy+es^3*y*Dx^2-es*y^3*Dy^2+4*x^2*y*Dy^4-es^3*y*Dy^2+8*x*y*Dx*Dy^2*h^2+2*es*y^2*Dy*h^2+4*x^2*Dy^3*h^2-24*y^2*Dy^3*h^2-2*es*y*h^4-8*y*Dy^2*h^4
! 6: by g=[ es^2*x^2*Dy+es^3*y*Dx-es^2*y^2*Dy+es^3*x*Dy+8*x*y*Dy^2*h^2+2*es^2*y*h^2 , es*y*Dy-es^2*Dx-4*y*Dy^3-es*h^2 , -4*y^2*Dy^2-es^2*x-es^3 , -es*x^2*Dy^2-es^3*Dx^2+es*y^2*Dy^2+es^3*Dy^2-8*x*Dx*Dy^2*h^2-2*es*y*Dy*h^2+24*y*Dy^3*h^2+2*es*h^4+8*Dy^2*h^4 , 4*y*Dx*Dy+es*x+es^2 , 4*x*y*Dy^3-es^3*Dx+es^2*y*Dy-2*es^2*h^2 ]
! 7:
! 8: Two bases are wrong.
! 9: In(15)=g2[4]:
! 10: -4*y*Dx*Dy-es*x+es^2
! 11: In(16)=g3[4]:
! 12: 4*y*Dx*Dy+es*x+es^2
! 13: In(17)=g2[5]:
! 14: 4*x*y*Dy^3-es^3*Dx-es^2*y*Dy+2*es^2*h^2
! 15: In(18)=g3[5]:
! 16: 4*x*y*Dy^3-es^3*Dx+es^2*y*Dy-2*es^2*h^2
! 17: In(19)=
! 18:
! 19:
! 20: -------- successful construction x^3-y^2-x
! 21: def Sannfs2_laScala(f) {
! 22: local p,pp;
! 23: p = Sannfs(f,"x,y");
! 24: /* Do not make laplace transform. */
! 25: sm1(" p 0 get { [(x) (y) (Dx) (Dy)] laplace0 } map /p set ");
! 26:
! 27: #define TOTAL_STRATEGY
! 28:
! 29: % k0
! 30: sm1>macro package : dr.sm1, 9/26,1995 --- Version 2/2, 2000.
! 31: sm1>macro package : module1.sm1, 1994 -- Nov 8, 1998
! 32: This is kan/k0 Version 1998,12/15
! 33: WARNING: This is an EXPERIMENTAL version
! 34: sm1>var.sm1 : Version 3/7, 1997
! 35:
! 36:
! 37: In(1)=Loading startup files (startup.k) 1997, 3/11.
! 38: sm1 version = 3.000320
! 39: Default ring is Z[x,h].
! 40: WARNING(sm): You rewrited the protected symbol pushVariables.
! 41: WARNING(sm): You rewrited the protected symbol popVariables.
! 42: In(2)=a=Sannfs2_laScala("x^3-y^2-x");
! 43:
! 44: %Warning: The identifier <<Sannfs2_laScala>> is not in the system dictionary
! 45: % nor in the user dictionaries. Push NullObject.
! 46: ERROR(sm): Warning: identifier is not in the dictionaries
! 47: --- Engine error or interrupt : The error occured on the top level.
! 48: Type in Cleards() to exit the debug mode and Where() to see the stack trace.
! 49: In(3)=load["minimal.k"];;
! 50: cpp: -lang-c++: linker input file unused since linking not done
! 51: --- Engine error or interrupt : The error occured on the top level.
! 52: Type in Cleards() to exit the debug mode and Where() to see the stack trace.
! 53: --- Engine error or interrupt : The error occured on the top level.
! 54: Type in Cleards() to exit the debug mode and Where() to see the stack trace.
! 55: cohom.sm1 is the top of an experimental package to compute restrictions
! 56: of all degrees based on restall.sm1 and restall_s.sm1
! 57: See, http://www.math.kobe-u.ac.jp to get these files of the latest version.
! 58: Note that the package b-function.sm1 cannot be used with this package.
! 59: r-interface.sm1 (C) N.Takayama, restriction, deRham
! 60:
! 61: oxasir.sm1, --- open asir protocol module 3/1 1998, 6/5 1999
! 62: asirconnect, asir, fctr, primadec, (C) M.Noro, N.Takayama
! 63: ox.sm1, --- open sm1 protocol module 11/11,1999 (C) N.Takayama. oxhelp for help
! 64: hol.sm1, basic package for holonomic systems (C) N.Takayama, 1999, 12/07
! 65: rank characteristic ch rrank gb pgb syz genericAnn annfs
! 66: sm1>gkz.sm1 generates gkz systems (C) N.Takayama, 1998, 11/8, cf. rrank in hol.sm1
! 67: gkz
! 68: sm1>appell.sm1 generates Appell hypergeometric differential equations (C) N.Takayama, 1998, 11/8, cf. rank in hol.sm1
! 69: appell1 appell4
! 70: sm1>resol0.sm1, package to construct schreyer resolutions -- not minimal
! 71: (C) N.Takayama, 1999, 5/18. resol0, resol1
! 72: complex.sm1 : 1999, 9/28, res-div, res-solv, res-kernel-image, res-dual
! 73: In this package, complex is expressed in terms of matrices.
! 74: restall.sm1 ... compute all the cohomology groups of the restriction
! 75: of a D-module to tt = (t_1,...,t_d) = (0,...,0).
! 76: non-Schreyer Version: 19980415 by T.Oaku
! 77: usage: [(P1)...] [(t1)...] bfm --> the b-function
! 78: [(P1)...] [(t1)...] k0 k1 deg restall --> cohomologies of restriction
! 79: [(P1)...] [(t1)...] intbfm --> the b-function for integration
! 80: [(P1)...] [(t1)...] k0 k1 deg intall --> cohomologies of integration
! 81: restall_s.sm1...compute all the cohomology groups of the restriction
! 82: of a D-module to tt = (t_1,...,t_d) = (0,...,0).
! 83: Schreyer Version: 19990521 by N.Takayama & T.Oaku
! 84: usage: [(P1)...] [(t1)...] k0 k1 deg restall_s -> cohomologies of restriction
! 85: [(P1)...] [(t1)...] k0 k1 deg intall_s --> cohomologies of integration
! 86: No truncation from below in restall
! 87: The variable Schreyer is set to 2.
! 88: Loading tower.sm1 in the standard context. You cannot use Schyrer 1. It is controlled from cohom.sm1
! 89:
! 90: /e_ $e_$. def /x $x$. def /y $y$. def /H $H$. def /E $E$. def /Dx $Dx$. def /Dy $Dy$. def /h $h$. def
! 91: /e_ $e_$. def /es $es$. def /x $x$. def /y $y$. def /z $z$. def /H $H$. def /E $E$. def /ES $ES$. def /Dx $Dx$. def /Dy $Dy$. def /Dz $Dz$. def /h $h$. def
! 92: In(4)=a=Sannfs2_laScala("x^3-y^2-x");
! 93: Starting ox_asir server.
! 94: Hello from open. serverName is localhost and portnumber is 0
! 95: Done the initialization. port =1146
! 96: Hello from open. serverName is localhost and portnumber is 0
! 97: Done the initialization. port =1147
! 98: [ 7 , 1147 , 6 , 1146 ]
! 99: [1] 6699
! 100: Trying to accept from localhost... len= 16
! 101: 4 7c 7f 0 0 1 0 0 0 0 0 0 0 0 8 0
! 102: Authentification: localhost is allowed to be accepted.
! 103: Accepted.
! 104: Trying to accept from localhost... len= 16
! 105: 4 7d 7f 0 0 1 0 0 0 0 0 0 0 0 6 0
! 106: Authentification: localhost is allowed to be accepted.
! 107: Accepted.
! 108:
! 109: Control port 1146 : Connected.
! 110:
! 111: Stream port 1147 : Connected.
! 112: Byte order for control process is network byte order.
! 113: Byte order for engine process is network byte order.
! 114: /e_ $e_$. def /es $es$. def /x $x$. def /y $y$. def /H $H$. def /E $E$. def /ES $ES$. def /Dx $Dx$. def /Dy $Dy$. def /h $h$. def
! 115: WeightOfSweyl=[ x , -1 , y , -1 , Dx , 1 , Dy , 1 ]
! 116: [ 3*y*Dx^2 , -2*x*Dx*Dy , -6*x*Dx^3 , 9*y^2*Dx*Dy^2 , 27*y^3*Dy^3 ]
! 117: Warning: Homogenization and ReduceLowerTerms options are automatically turned off.
! 118: .......Done. betti=7
! 119: Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.
! 120: Warning: Homogenization and ReduceLowerTerms options are automatically turned off.
! 121: ....Done. betti=4
! 122: Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.
! 123: Warning: Homogenization and ReduceLowerTerms options are automatically turned off.
! 124: .Done. betti=1
! 125: Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.
! 126: Warning: Homogenization and ReduceLowerTerms options are automatically turned off.
! 127: Done. betti=0
! 128: Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.
! 129: [ 0 , 0 ]
! 130: Processing [ 0 , 0 ] Strategy = 2
! 131: [ 0 , 1 ]
! 132: Processing [ 0 , 1 ] Strategy = 2
! 133: [ 0 , 2 ]
! 134: Processing [ 0 , 2 ] Strategy = 3
! 135: [ 1 , 2 ]
! 136: Processing [ 1 , 2 ] Strategy = 3
! 137: SpairAndReduction:
! 138: [ p and bases , [ [ 0 , 1 ] , [ -2*x*Dy , -3*y*Dx ] ] , [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , %[null] , %[null] ] ]
! 139: [ -2*x*Dy , -3*es*y*Dx ]
! 140: [gi, gj] = [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h ]
! 141: 1
! 142: Reduce the element 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2-6*y^2*Dx^2*h+4*x^2*Dy^2*h+2*x*y*Dy*h^2+2*x*h^4
! 143: by [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , %[null] , %[null] ]
! 144: result is [ 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , 1 , [ 2*y*h , 0 , 0 , 0 , 0 ] ]
! 145: vdegree of the original = 1
! 146: vdegree of the remainder = 1
! 147: [ 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , [ -2*x*Dy+2*y*h , -3*y*Dx , 0 , 0 , 0 ] , 2 , 3 , 1 , 1 ]
! 148: [ 1 , 3 ]
! 149: Processing [ 1 , 3 ] Strategy = 3
! 150: SpairAndReduction:
! 151: [ p and bases , [ [ 0 , 2 ] , [ -2*x*Dx , -y ] ] , [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , %[null] ] ]
! 152: [ -2*x*Dx , -es^2*y ]
! 153: [gi, gj] = [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 ]
! 154: 1
! 155: Reduce the element 4*x^2*Dx*Dy*h+6*x*y*Dy^2*h+4*x*Dy*h^3-4*x*y*Dx*h^2
! 156: by [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , %[null] ]
! 157: result is [ 0 , -1 , [ 0 , -2*x*h , 0 , 0 , 0 ] ]
! 158: vdegree of the original = 1
! 159: vdegree of the remainder = %[null]
! 160: [ 0 , [ 2*x*Dx , -2*x*h , y , 0 , 0 ] , 3 , -1 , 1 , %[null] ]
! 161: [ 1 , 6 ]
! 162: Processing [ 1 , 6 ] Strategy = 3
! 163: SpairAndReduction:
! 164: [ p and bases , [ [ 1 , 2 ] , [ -3*Dx^2 , Dy ] ] , [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , %[null] ] ]
! 165: [ -3*es*Dx^2 , es^2*Dy ]
! 166: [gi, gj] = [ -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 ]
! 167: 1
! 168: Reduce the element 9*y*Dx^2*Dy^2+18*Dx^2*Dy*h^2-6*y*Dx^3*h-6*x*Dy^3*h+6*x*Dx*Dy*h^2
! 169: by [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , %[null] ]
! 170: result is [ 0 , -1 , [ 3*Dy^2-2*Dx*h , -h^2 , 0 , 0 , 0 ] ]
! 171: vdegree of the original = 3
! 172: vdegree of the remainder = %[null]
! 173: [ 0 , [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ] , 6 , -1 , 3 , %[null] ]
! 174: [ 2 , 1 ]
! 175: Processing [ 2 , 1 ] Strategy = 3
! 176: SpairAndReduction:
! 177: [ p and bases , [ [ 2 , 3 ] , [ -Dx , Dy ] ] , [ %[null] , %[null] , [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ] , [ 2*x*Dx , -2*x*h , y , 0 , 0 ] , %[null] , %[null] , [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ] ] ]
! 178: [ es^2*Dx , -es^3*Dy ]
! 179: [gi, gj] = [ 2*x*Dy+3*es*y*Dx+es^3-2*y*h , 2*x*Dx+es^2*y-2*es*x*h ]
! 180: 1
! 181: Reduce the element 3*es*y*Dx^2-es^2*y*Dy+es^3*Dx-es^2*h^2+2*Dy*h^2-2*y*Dx*h+2*es*x*Dy*h
! 182: by [ %[null] , %[null] , [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ] , [ 2*x*Dx , -2*x*h , y , 0 , 0 ] , %[null] , %[null] , [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ] ]
! 183: result is [ -3*y*Dy^2+es^3*Dx-es^2*h^2+2*Dy*h^2+2*es*x*Dy*h+es*y*h^2 , 1 , [ 0 , 0 , 0 , 0 , 0 , 0 , -y ] ]
! 184: vdegree of the original = 2
! 185: vdegree of the remainder = 2
! 186: [ -3*y*Dy^2+es^3*Dx-es^2*h^2+2*Dy*h^2+2*es*x*Dy*h+es*y*h^2 , [ 0 , 0 , Dx , -Dy , 0 , 0 , -y ] , 1 , 5 , 2 , 2 ]
! 187: [ 0 , 3 ]
! 188: Processing [ 0 , 3 ] Strategy = 4
! 189: [ 1 , 0 ]
! 190: Processing [ 1 , 0 ] Strategy = 4
! 191: SpairAndReduction:
! 192: [ p and bases , [ [ 1 , 3 ] , [ 9*y^2*Dy , 2*x ] ] , [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , %[null] ] ]
! 193: [ 9*es*y^2*Dy , 2*es^3*x ]
! 194: [gi, gj] = [ -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 ]
! 195: 1
! 196: Reduce the element -27*y^3*Dy^3-12*x^2*Dx^2*h^2+24*x*y*Dx*Dy*h^2-45*y^2*Dy^2*h^2+18*y^3*Dx*Dy*h+8*x^3*Dy^2*h+18*y^2*Dx*h^3-4*x^2*y*Dy*h^2+4*x^2*h^4-4*x*y^2*h^3
! 197: by [ 3*y*Dx^2-2*x*Dy*h-y*h^2 , -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h , -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 , 9*y^2*Dx*Dy^2-6*x*Dx^2*h^2+12*y*Dx*Dy*h^2+4*x^2*Dy^2*h-2*x*y*Dy*h^2+2*x*h^4-2*y^2*h^3 , %[null] ]
! 198: result is [ 27*y^3*Dy^3+12*x^2*Dx^2*h^2+81*y^2*Dy^2*h^2+24*y*Dy*h^4-18*y^3*Dx*Dy*h-8*x^3*Dy^2*h-42*y^2*Dx*h^3+4*x^2*y*Dy*h^2-4*x^2*h^4+4*x*y^2*h^3 , -1 , [ 0 , -12*y*h^2 , 0 , 0 , 0 ] ]
! 199: vdegree of the original = 0
! 200: vdegree of the remainder = 0
! 201: [ 27*y^3*Dy^3+12*x^2*Dx^2*h^2+81*y^2*Dy^2*h^2+24*y*Dy*h^4-18*y^3*Dx*Dy*h-8*x^3*Dy^2*h-42*y^2*Dx*h^3+4*x^2*y*Dy*h^2-4*x^2*h^4+4*x*y^2*h^3 , [ 0 , -9*y^2*Dy-12*y*h^2 , 0 , -2*x , 0 ] , 0 , 4 , 0 , 0 ]
! 202: [ 1 , 5 ]
! 203: Processing [ 1 , 5 ] Strategy = 4
! 204: [ 2 , 0 ]
! 205: Processing [ 2 , 0 ] Strategy = 4
! 206: SpairAndReduction:
! 207: [ p and bases , [ [ 2 , 5 ] , [ 3*y*Dy , 2*x ] ] , [ [ 0 , 9*y^2*Dy+12*y*h^2 , 0 , 2*x , 1 ] , %[null] , [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ] , [ 2*x*Dx , -2*x*h , y , 0 , 0 ] , %[null] , -3*y*Dy^2+es^3*Dx-es^2*h^2+2*Dy*h^2+2*es*x*Dy*h+es*y*h^2 , [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ] ] ]
! 208: [ -3*es^2*y*Dy , -2*es^5*x ]
! 209: [gi, gj] = [ 2*x*Dy+3*es*y*Dx+es^3-2*y*h , -3*y*Dy^2+es^3*Dx-es^2*h^2+2*Dy*h^2+2*es*x*Dy*h+es*y*h^2 ]
! 210: 1
! 211: Reduce the element -9*es*y^2*Dx*Dy-2*es^3*x*Dx-3*es^3*y*Dy+2*es^2*x*h^2-4*x*Dy*h^2-9*es*y*Dx*h^2+6*y^2*Dy*h-4*es*x^2*Dy*h+6*y*h^3-2*es*x*y*h^2
! 212: by [ [ 0 , 9*y^2*Dy+12*y*h^2 , 0 , 2*x , 1 ] , %[null] , [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ] , [ 2*x*Dx , -2*x*h , y , 0 , 0 ] , %[null] , -3*y*Dy^2+es^3*Dx-es^2*h^2+2*Dy*h^2+2*es*x*Dy*h+es*y*h^2 , [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ] ]
! 213: result is [ -3*es^3*y*Dy+es^4*Dx+2*es^2*x*h^2+9*es*y*Dx*h^2+4*es^3*h^2+6*y^2*Dy*h-4*es*x^2*Dy*h+2*y*h^3-2*es*x*y*h^2 , 1 , [ Dx , 0 , 2*h^2 , 0 , 0 , 0 , 0 ] ]
! 214: vdegree of the original = 1
! 215: vdegree of the remainder = 1
! 216: [ -3*es^3*y*Dy+es^4*Dx+2*es^2*x*h^2+9*es*y*Dx*h^2+4*es^3*h^2+6*y^2*Dy*h-4*es*x^2*Dy*h+2*y*h^3-2*es*x*y*h^2 , [ Dx , 0 , -3*y*Dy+2*h^2 , 0 , 0 , -2*x , 0 ] , 0 , 1 , 1 , 1 ]
! 217: [ 3 , 0 ]
! 218: Processing [ 3 , 0 ] Strategy = 4
! 219: SpairAndReduction:
! 220: [ p and bases , [ [ 0 , 1 ] , [ -Dx , -3*y*Dy ] ] , [ [ -Dx , 1 , 3*y*Dy-2*h^2 , 0 , 0 , 2*x , 0 ] , [ 0 , 0 , -Dx , Dy , 0 , 1 , y ] , %[null] , %[null] ] ]
! 221: [ -Dx , -3*es*y*Dy ]
! 222: [gi, gj] = [ 3*es^2*y*Dy+2*es^5*x-Dx+es-2*es^2*h^2 , -es^2*Dx+es^3*Dy+es^6*y+es^5 ]
! 223: 1
! 224: Reduce the element -3*es^3*y*Dy^2-2*es^5*x*Dx+Dx^2-3*es^6*y^2*Dy-3*es^5*y*Dy-es*Dx+2*es^2*Dx*h^2-3*es^6*y*h^2-2*es^5*h^2
! 225: by [ [ -Dx , 1 , 3*y*Dy-2*h^2 , 0 , 0 , 2*x , 0 ] , [ 0 , 0 , -Dx , Dy , 0 , 1 , y ] , %[null] , %[null] ]
! 226: result is [ 3*es^3*y*Dy^2+2*es^5*x*Dx-Dx^2+3*es^6*y^2*Dy+3*es^5*y*Dy+es*Dx-2*es^3*Dy*h^2+es^6*y*h^2 , -1 , [ 0 , -2*h^2 , 0 , 0 ] ]
! 227: vdegree of the original = 2
! 228: vdegree of the remainder = 2
! 229: [ 3*es^3*y*Dy^2+2*es^5*x*Dx-Dx^2+3*es^6*y^2*Dy+3*es^5*y*Dy+es*Dx-2*es^3*Dy*h^2+es^6*y*h^2 , [ Dx , 3*y*Dy-2*h^2 , 0 , 0 ] , 0 , 2 , 2 , 2 ]
! 230: [ 0 , 4 ]
! 231: Processing [ 0 , 4 ] Strategy = 5
! 232: [ 1 , 1 ]
! 233: Processing [ 1 , 1 ] Strategy = 5
! 234: [ 2 , 2 ]
! 235: Processing [ 2 , 2 ] Strategy = 5
! 236: [ 2 , 3 ]
! 237: Processing [ 2 , 3 ] Strategy = 5
! 238: SpairAndReduction:
! 239: [ p and bases , [ [ 0 , 6 ] , [ -Dx^2 , -3*y^2*Dy ] ] , [ [ 0 , 9*y^2*Dy+12*y*h^2 , 0 , 2*x , 1 ] , -3*es^3*y*Dy+es^4*Dx+2*es^2*x*h^2+9*es*y*Dx*h^2+4*es^3*h^2+6*y^2*Dy*h-4*es*x^2*Dy*h+2*y*h^3-2*es*x*y*h^2 , [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ] , [ 2*x*Dx , -2*x*h , y , 0 , 0 ] , %[null] , -3*y*Dy^2+es^3*Dx-es^2*h^2+2*Dy*h^2+2*es*x*Dy*h+es*y*h^2 , [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ] ] ]
! 240: [ Dx^2 , -3*es^6*y^2*Dy ]
! 241: [gi, gj] = [ 9*es*y^2*Dy+2*es^3*x+es^4+12*es*y*h^2 , 3*es*Dx^2-es^2*Dy+3*Dy^2-2*Dx*h-es*h^2 ]
! 242: 1
! 243: Reduce the element 3*es^2*y^2*Dy^2+2*es^3*x*Dx^2-9*y^2*Dy^3+es^4*Dx^2+12*es*y*Dx^2*h^2+4*es^3*Dx*h^2+6*y^2*Dx*Dy*h+3*es*y^2*Dy*h^2
! 244: by [ [ 0 , 9*y^2*Dy+12*y*h^2 , 0 , 2*x , 1 ] , -3*es^3*y*Dy+es^4*Dx+2*es^2*x*h^2+9*es*y*Dx*h^2+4*es^3*h^2+6*y^2*Dy*h-4*es*x^2*Dy*h+2*y*h^3-2*es*x*y*h^2 , [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ] , [ 2*x*Dx , -2*x*h , y , 0 , 0 ] , %[null] , -3*y*Dy^2+es^3*Dx-es^2*h^2+2*Dy*h^2+2*es*x*Dy*h+es*y*h^2 , [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ] ]
! 245: result is [ 9*es^2*y^2*Dy^2+6*es^3*x*Dx^2-6*es^2*x*Dx*h^2+12*es^2*y*Dy*h^2-6*es^2*h^4+12*es*x^2*Dx*Dy*h-18*es*x*y*Dy^2*h+24*es*x*Dy*h^3+6*es*x*y*Dx*h^2 , 3 , [ 0 , -3*Dx , 0 , 0 , 0 , -9*y*Dy , -3*y*h^2 ] ]
! 246: vdegree of the original = 2
! 247: vdegree of the remainder = 2
! 248: [ 9*es^2*y^2*Dy^2+6*es^3*x*Dx^2-6*es^2*x*Dx*h^2+12*es^2*y*Dy*h^2-6*es^2*h^4+12*es*x^2*Dx*Dy*h-18*es*x*y*Dy^2*h+24*es*x*Dy*h^3+6*es*x*y*Dx*h^2 , [ 3*Dx^2 , -3*Dx , 0 , 0 , 0 , -9*y*Dy , -9*y^2*Dy-3*y*h^2 ] , 3 , 4 , 2 , 2 ]
! 249: [ 1 , 4 ]
! 250: Processing [ 1 , 4 ] Strategy = 6
! 251: [seq,level,q]=[ 6 , 1 , 4 ]
! 252: [ level, q = , 1 , 4 ]
! 253: bases=
! 254: [
! 255: [ -Dx , 1 , 3*y*Dy-2*h^2 , 0 , 0 , 2*x , 0 ]
! 256: [ 0 , 0 , -Dx , Dy , 0 , 1 , y ]
! 257: [ -Dx^2 , Dx , 0 , 3*y*Dy^2-2*Dy*h^2 , 0 , 2*x*Dx+3*y*Dy , 3*y^2*Dy+y*h^2 ]
! 258: [ -3*Dx^2 , 3*Dx , 0 , 0 , 1 , 9*y*Dy , 9*y^2*Dy+3*y*h^2 ]
! 259: ]
! 260: dr=
! 261: [ 3*Dx^2 , -3*Dx , 0 , 0 , -1 , -9*y*Dy , -9*y^2*Dy-3*y*h^2 ]
! 262: newbases=
! 263: [
! 264: [ -Dx , 1 , 3*y*Dy-2*h^2 , 0 , 0 , 2*x , 0 ]
! 265: [ 0 , 0 , -Dx , Dy , 0 , 1 , y ]
! 266: [ -Dx^2 , Dx , 0 , 3*y*Dy^2-2*Dy*h^2 , 0 , 2*x*Dx+3*y*Dy , 3*y^2*Dy+y*h^2 ]
! 267: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 268: ]
! 269: [seq,level,q]=[ 5 , 2 , 2 ]
! 270: [ level, q = , 2 , 2 ]
! 271: bases=
! 272: [
! 273: [ -Dx , -3*y*Dy+2*h^2 , 1 , 0 ]
! 274: ]
! 275: dr=
! 276: [ Dx , 3*y*Dy-2*h^2 , -1 , 0 ]
! 277: newbases=
! 278: [
! 279: [ 0 , 0 , 0 , 0 ]
! 280: ]
! 281: [seq,level,q]=[ 4 , 1 , 1 ]
! 282: [ level, q = , 1 , 1 ]
! 283: bases=
! 284: [
! 285: [ -Dx , 1 , 3*y*Dy-2*h^2 , 0 , 0 , 2*x , 0 ]
! 286: [ 0 , 0 , -Dx , Dy , 0 , 1 , y ]
! 287: [ -Dx^2 , Dx , 0 , 3*y*Dy^2-2*Dy*h^2 , 0 , 2*x*Dx+3*y*Dy , 3*y^2*Dy+y*h^2 ]
! 288: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 289: ]
! 290: dr=
! 291: [ Dx , -1 , -3*y*Dy+2*h^2 , 0 , 0 , -2*x , 0 ]
! 292: newbases=
! 293: [
! 294: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 295: [ 0 , 0 , -Dx , Dy , 0 , 1 , y ]
! 296: [ 0 , 0 , -3*y*Dx*Dy+2*Dx*h^2 , 3*y*Dy^2-2*Dy*h^2 , 0 , 3*y*Dy-2*h^2 , 3*y^2*Dy+y*h^2 ]
! 297: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 298: ]
! 299: [seq,level,q]=[ 3 , 0 , 4 ]
! 300: [ level, q = , 0 , 4 ]
! 301: bases=
! 302: [
! 303: [ 0 , 9*y^2*Dy+12*y*h^2 , 0 , 2*x , 1 ]
! 304: [ 6*y^2*Dy*h+2*y*h^3 , 9*y*Dx*h^2-4*x^2*Dy*h-2*x*y*h^2 , 2*x*h^2 , -3*y*Dy+4*h^2 , Dx ]
! 305: [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ]
! 306: [ 2*x*Dx , -2*x*h , y , 0 , 0 ]
! 307: [ 0 , 12*x^2*Dx*Dy*h-18*x*y*Dy^2*h+24*x*Dy*h^3+6*x*y*Dx*h^2 , 9*y^2*Dy^2-6*x*Dx*h^2+12*y*Dy*h^2-6*h^4 , 6*x*Dx^2 , 0 ]
! 308: [ -3*y*Dy^2+2*Dy*h^2 , 2*x*Dy*h+y*h^2 , -h^2 , Dx , 0 ]
! 309: [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ]
! 310: ]
! 311: dr=
! 312: [ 0 , -9*y^2*Dy-12*y*h^2 , 0 , -2*x , -1 ]
! 313: newbases=
! 314: [
! 315: [ 0 , 0 , 0 , 0 , 0 ]
! 316: [ 6*y^2*Dy*h+2*y*h^3 , -9*y^2*Dx*Dy-3*y*Dx*h^2-4*x^2*Dy*h-2*x*y*h^2 , 2*x*h^2 , -2*x*Dx-3*y*Dy+2*h^2 , 0 ]
! 317: [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ]
! 318: [ 2*x*Dx , -2*x*h , y , 0 , 0 ]
! 319: [ 0 , 12*x^2*Dx*Dy*h-18*x*y*Dy^2*h+24*x*Dy*h^3+6*x*y*Dx*h^2 , 9*y^2*Dy^2-6*x*Dx*h^2+12*y*Dy*h^2-6*h^4 , 6*x*Dx^2 , 0 ]
! 320: [ -3*y*Dy^2+2*Dy*h^2 , 2*x*Dy*h+y*h^2 , -h^2 , Dx , 0 ]
! 321: [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ]
! 322: ]
! 323: [seq,level,q]=[ 2 , 1 , 5 ]
! 324: [ level, q = , 1 , 5 ]
! 325: bases=
! 326: [
! 327: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 328: [ 0 , 0 , -Dx , Dy , 0 , 1 , y ]
! 329: [ 0 , 0 , -3*y*Dx*Dy+2*Dx*h^2 , 3*y*Dy^2-2*Dy*h^2 , 0 , 3*y*Dy-2*h^2 , 3*y^2*Dy+y*h^2 ]
! 330: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 331: ]
! 332: dr=
! 333: [ 0 , 0 , Dx , -Dy , 0 , -1 , -y ]
! 334: newbases=
! 335: [
! 336: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 337: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 338: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 339: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 340: ]
! 341: [seq,level,q]=[ 1 , 0 , 3 ]
! 342: [ level, q = , 0 , 3 ]
! 343: bases=
! 344: [
! 345: [ 0 , 0 , 0 , 0 , 0 ]
! 346: [ 6*y^2*Dy*h+2*y*h^3 , -9*y^2*Dx*Dy-3*y*Dx*h^2-4*x^2*Dy*h-2*x*y*h^2 , 2*x*h^2 , -2*x*Dx-3*y*Dy+2*h^2 , 0 ]
! 347: [ 2*x*Dy-2*y*h , 3*y*Dx , 0 , 1 , 0 ]
! 348: [ 2*x*Dx , -2*x*h , y , 0 , 0 ]
! 349: [ 0 , 12*x^2*Dx*Dy*h-18*x*y*Dy^2*h+24*x*Dy*h^3+6*x*y*Dx*h^2 , 9*y^2*Dy^2-6*x*Dx*h^2+12*y*Dy*h^2-6*h^4 , 6*x*Dx^2 , 0 ]
! 350: [ -3*y*Dy^2+2*Dy*h^2 , 2*x*Dy*h+y*h^2 , -h^2 , Dx , 0 ]
! 351: [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ]
! 352: ]
! 353: dr=
! 354: [ -2*x*Dy+2*y*h , -3*y*Dx , 0 , -1 , 0 ]
! 355: newbases=
! 356: [
! 357: [ 0 , 0 , 0 , 0 , 0 ]
! 358: [ 4*x^2*Dx*Dy+6*x*y*Dy^2-4*x*y*Dx*h , 6*x*y*Dx^2-4*x^2*Dy*h-2*x*y*h^2 , 2*x*h^2 , 0 , 0 ]
! 359: [ 0 , 0 , 0 , 0 , 0 ]
! 360: [ 2*x*Dx , -2*x*h , y , 0 , 0 ]
! 361: [ -12*x^2*Dx^2*Dy-24*x*Dx*Dy*h^2+12*x*y*Dx^2*h , -18*x*y*Dx^3+12*x^2*Dx*Dy*h-18*x*y*Dy^2*h+24*x*Dy*h^3+6*x*y*Dx*h^2 , 9*y^2*Dy^2-6*x*Dx*h^2+12*y*Dy*h^2-6*h^4 , 0 , 0 ]
! 362: [ -2*x*Dx*Dy-3*y*Dy^2+2*y*Dx*h , -3*y*Dx^2+2*x*Dy*h+y*h^2 , -h^2 , 0 , 0 ]
! 363: [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ]
! 364: ]
! 365: [ level= , 0 ]
! 366: [
! 367: [ 3*y*Dx^2-2*x*Dy*h-y*h^2 ]
! 368: [ -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h ]
! 369: [ -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 ]
! 370: ]
! 371: [
! 372: [ 3*y*Dx^2-2*x*Dy*h-y*h^2 ]
! 373: [ -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h ]
! 374: [ -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 ]
! 375: ]
! 376: [ level= , 1 ]
! 377: [
! 378: [ 0 , 0 , 0 , 0 , 0 ]
! 379: [ 0 , 0 , 0 , 0 , 0 ]
! 380: [ 2*x*Dx , -2*x*h , y , 0 , 0 ]
! 381: [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy , 0 , 0 ]
! 382: ]
! 383: [
! 384: [ 0 , 0 , 0 ]
! 385: [ 0 , 0 , 0 ]
! 386: [ 2*x*Dx , -2*x*h , y ]
! 387: [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy ]
! 388: ]
! 389: [ level= , 2 ]
! 390: [
! 391: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 392: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 393: [ 0 , 0 , 0 , 0 , 0 , 0 , 0 ]
! 394: ]
! 395: [
! 396: [ 0 , 0 , 0 , 0 ]
! 397: [ 0 , 0 , 0 , 0 ]
! 398: [ 0 , 0 , 0 , 0 ]
! 399: ]
! 400: [ level= , 3 ]
! 401: [
! 402: [ 0 , 0 , 0 , 0 ]
! 403: ]
! 404: [
! 405: [ 0 , 0 , 0 ]
! 406: ]
! 407: In(5)=b=a[0];
! 408: In(6)=b[1]*b[0]:
! 409: [ [ 0 ] , [ 0 ] , [ 0 ] , [ 0 ] ]
! 410: In(7)=b[2]*b[1]:
! 411: [ [ 0 , 0 , 0 ] , [ 0 , 0 , 0 ] , [ 0 , 0 , 0 ] ]
! 412: In(8)=sm1_pmat(b);
! 413: [
! 414: [
! 415: [ 3*y*Dx^2-2*x*Dy*h-y*h^2 ]
! 416: [ -2*x*Dx*Dy-3*y*Dy^2-2*Dy*h^2+2*y*Dx*h ]
! 417: [ -6*x*Dx^3-6*x*Dy^2*h+6*x*Dx*h^2 ]
! 418: ]
! 419: [
! 420: [ 0 , 0 , 0 ]
! 421: [ 0 , 0 , 0 ]
! 422: [ 2*x*Dx , -2*x*h , y ]
! 423: [ 3*Dy^2-2*Dx*h , 3*Dx^2-h^2 , -Dy ]
! 424: ]
! 425: [
! 426: [ 0 , 0 , 0 , 0 ]
! 427: [ 0 , 0 , 0 , 0 ]
! 428: [ 0 , 0 , 0 , 0 ]
! 429: ]
! 430: [
! 431: [ 0 , 0 , 0 ]
! 432: ]
! 433: ]
! 434: In(9)=
! 435:
! 436:
! 437: ------- failed example.
! 438: def Sannfs2_laScala(f) {
! 439: local p,pp;
! 440: p = Sannfs(f,"x,y");
! 441: /* Do not make laplace transform.
! 442: sm1(" p 0 get { [(x) (y) (Dx) (Dy)] laplace0 } map /p set ");
! 443: p = [p]
! 444: */
! 445: ;
! 446:
! 447: xy(x-y) の annihilating ideal の V-minimal free resolution.
! 448: In(6)=a=Sannfs2_laScala("x*y*(x-y)");
! 449:
! 450: SpairAndReduction:
! 451: [ p and bases , [ [ 0 , 1 ] , [ -3*y*Dy , Dx ] ] , [ -4*x*Dx-4*y*Dy-12*h^2 , -12*x*y*Dy+12*y^2*Dy-12*x*h^2+24*y*h^2 , %[null] ] ]
! 452: [ -3*y*Dy , es*Dx ]
! 453: [gi, gj] = [ -4*x*Dx-4*y*Dy-12*h^2 , -12*x*y*Dy+12*y^2*Dy-12*x*h^2+24*y*h^2 ]
! 454: 1
! 455: Reduce the element 12*y^2*Dx*Dy+12*y^2*Dy^2-12*x*Dx*h^2+24*y*Dx*h^2+36*y*Dy*h^2-12*h^4
! 456: by [ -4*x*Dx-4*y*Dy-12*h^2 , -12*x*y*Dy+12*y^2*Dy-12*x*h^2+24*y*h^2 , %[null] ]
! 457: result is [ -12*y^2*Dx*Dy-12*y^2*Dy^2-24*y*Dx*h^2-48*y*Dy*h^2-24*h^4 , -1 , [ 3*h^2 , 0 , 0 ] ]
! 458: vdegree of the original = 0
! 459: vdegree of the remainder = 0
! 460: [ -12*y^2*Dx*Dy-12*y^2*Dy^2-24*y*Dx*h^2-48*y*Dy*h^2-24*h^4 , [ 3*y*Dy+3*h^2 , -Dx , 0 ] , 1 , 2 , 0 , 0 ]
! 461: reductionTable_tmp=[ 2 ]
! 462: See also reductionTable, strategy, level,i
! 463: ERROR(sm): error operator : SnextI: bases[i] or bases[j] is null for all combinations.
! 464: --- Engine error or interrupt : In function : Error of class PrimitiveObject
! 465:
! 466: Type in Cleards() to exit the debug mode and Where() to see the stack trace.
! 467:
! 468: In(7)=bases:
! 469: [ %[null] , [ -3*y*Dy-3*h^2 , Dx , 1 ] , %[null] ]
! 470: In(8)=reductionTable:
! 471: [ [ 1 , 2 , 3 ] , [ 3 , 2 , 3 ] , [ 2 ] ]
! 472: In(9)=freeRes:
! 473: [ [ -4*x*Dx-4*y*Dy-12*h^2 , -12*x*y*Dy+12*y^2*Dy-12*x*h^2+24*y*h^2 , -12*y^2*Dx*Dy-12*y^2*Dy^2-24*y*Dx*h^2-48*y*Dy*h^2-24*h^4 ] , [ %[null] , [ -3*y*Dy-3*h^2 , Dx , 1 ] , %[null] ] , [ %[null] ] ]
! 474: In(10)=
! 475:
! 476: [ [ -4*x*Dx-4*y*Dy-12*h^2 , -12*x*y*Dy+12*y^2*Dy-12*x*h^2+24*y*h^2 , -12*y^2*Dx*Dy-12*y^2*Dy^2-24*y*Dx*h^2-48*y*Dy*h^2-24*h^4 ] ,
! 477: [ %[null] , [ -3*y*Dy-3*h^2 , Dx , 1 ] , %[null] ] ,
! 478: これと これの spair を計算しよう瘢雹として止まる.
! 479: [ %[null] ] ]
! 480:
! 481: これが, strategy の table.
! 482:
! 483: In(8)=reductionTable:
! 484: [ [ 1 , 2 , 3 ] , [ 3 , 2 , 3 ] , [ 2 ] ]
! 485: この元を処理中.
! 486:
! 487:
! 488:
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to debug-note.txt CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / k097 / lib / minimal