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Annotation of OpenXM/src/kan96xx/Doc/Old/bf.sm1, Revision 1.1

1.1     ! maekawa     1: (bf.sm1  Version Sep 26, 1995) message
        !             2: ( Computing b-function by the algorithm by Oaku. Type in demo1 to see a demo.)
        !             3:  message
        !             4:
        !             5: %%%% demo1 can be used as a template to compute the b-function of your own
        !             6: %%%% polynomial.
        !             7: /demo1 {
        !             8:   %%% Give your variables. s is used for FW-filtration.
        !             9:    [(s,t,x,y) ring_of_differential_operators
        !            10:   %%% Give the weight vector here.
        !            11:     [[(s) 1] [(Dx) 1 (Dy) 1 (x) 1 (y) 1]] weight_vector 0 ] define_ring
        !            12:   %%% Give the generators.  t - s f(x), Dx + s Df/Dx Dt
        !            13:    [( t- s x^2 + s y^3).
        !            14:     (  Dx + 2 s x Dt).
        !            15:     (  Dy - 3 s y^2 Dt).
        !            16:    ] /ff set
        !            17:
        !            18:   %%%%%%%%%%% Don't touch. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            19:    ff print
        !            20:    (  are generators.) message (   ) message
        !            21:    ff {[[(h). (1).]] replace} map {homogenize} map /ff set
        !            22:    (Computing groebner basis) message
        !            23:    {[ff] groebner 0 get /ans set } timer
        !            24:    (     ) message
        !            25:    ans fw_principal /ans0 set
        !            26:   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            27:
        !            28:   %%% Give variables to eliminate
        !            29:   ans0 [(Dx)  (Dy) (x)  (y) ] eliminatev
        !            30:   /ans1 set
        !            31:
        !            32:
        !            33:   (The answer [ans1] is ) message
        !            34:   ans1 print (  ) message
        !            35: } def
        !            36:
        !            37: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            38:
        !            39: %% demo2 : degree 26. Time = 355s + 60s
        !            40: /demo2 {
        !            41:   %%% Give your variables. s is used for FW-filtration.
        !            42:    [(s,t,x,y,z) ring_of_differential_operators
        !            43:   %%% Give the weight vector here.
        !            44:     [[(s) 1] [(Dx) 1 (Dy) 1 (Dz) 1 (x) 1 (y) 1 (z) 1 ]] weight_vector
        !            45:    0 ] define_ring
        !            46:   %%% Give the generators.  t - s f(x), Dx + s Df/Dx Dt
        !            47:    [( t - s (-x^2 z^2 + x^4 + y^4)).
        !            48:     (  Dx + s (-2 x z^2 + 4 x^3) Dt ).
        !            49:     (  Dy + s (4 y^3 ) Dt ).
        !            50:     (  Dz + s (-2 x^2 z) Dt).
        !            51:    ] /ff set
        !            52:
        !            53:   %%%%%%%%%%% Don't touch. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            54:    ff print
        !            55:    (  are generators.) message (   ) message
        !            56:    ff {[[(h). (1).]] replace} map {homogenize} map /ff set
        !            57:    (Computing groebner basis) message
        !            58:    {[ff] groebner 0 get /ans set } timer
        !            59:    (     ) message
        !            60:    ans fw_principal /ans0 set
        !            61:   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            62:
        !            63:   %%% Give variables to eliminate
        !            64:   ans0 [(Dx) (Dy) (Dz) (x)  (y)  (z) ] eliminatev
        !            65:   /ans1 set
        !            66:
        !            67:
        !            68:   (The answer [ans1] is ) message
        !            69:   ans1 print (  ) message
        !            70: } def
        !            71:
        !            72: /bf3_0 {
        !            73:   %%% Give your variables. s is used for FW-filtration.
        !            74:    [(s,t,x,y,z) ring_of_differential_operators
        !            75:   %%% Give the weight vector here.
        !            76:     [[(s) 1] [(Dx) 1 (Dy) 1 (Dz) 1 (x) 1 (y) 1 (z) 1 ]] weight_vector
        !            77:    0 ] define_ring
        !            78:    /s (s). def /x (x). def /y (y). def /z (z). def
        !            79:               /Dx (Dx). def /Dy (Dy). def /Dz (Dz). def
        !            80:    /t (t). def /Dt (Dt). def /h (h). def
        !            81: } def
        !            82:
        !            83: %%% Give the generators.  t - s f(x), Dx + s Df/Dx Dt as ff
        !            84:
        !            85: /bf3_1 {
        !            86:   /ff set
        !            87:   %%%%%%%%%%% Don't touch. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            88:    ff print
        !            89:    (  are generators.) message (   ) message
        !            90:    ff {[[(h). (1).]] replace} map {homogenize} map /ff set
        !            91:    (Computing groebner basis) message
        !            92:    {[ff] groebner 0 get /ans set } timer
        !            93:    (     ) message
        !            94:    ans fw_principal /ans0 set
        !            95:   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            96:
        !            97:   %%% Give variables to eliminate
        !            98:   ans0 [(Dx) (Dy) (Dz) (x)  (y)  (z) ] eliminatev
        !            99:   /ans1 set
        !           100:
        !           101:   (The answer [ans1] is ) message
        !           102:   ans1 print (  ) message
        !           103:   ans1
        !           104: } def
        !           105:
        !           106:
        !           107: %% [   ] {outputans1} map ;
        !           108: /outputans1 {
        !           109:  (t.t) (a) file /fd set
        !           110:  (string) data_conversion /tmp0 set
        !           111:  fd tmp0 writestring
        !           112:  fd (  ,) writestring
        !           113:  fd 10 (string) data_conversion writestring
        !           114:  fd closefile
        !           115: } def
        !           116:
        !           117:
        !           118:
        !           119:
        !           120: /fw_principal {
        !           121:    {[[(h). (1).]] replace} map {(s). coefficients 1 get 0 get} map
        !           122: } def
        !           123:
        !           124:
        !           125: %%%%%%%%%%%%%%%%%%%%%
        !           126: % [g1 g2 g3 ...] var eliminate0
        !           127: /eliminate0 {
        !           128:   /arg2 set /arg1 set
        !           129:   [/gb /degs /ans /n /var] pushVariables
        !           130:   [
        !           131:   /gb arg1 def
        !           132:   /var arg2 def
        !           133:   /degs gb {var . degree} map def
        !           134:   /ans [
        !           135:     0 1 << gb length 1 sub >> {
        !           136:       /n set
        !           137:       << degs n get  >>  0 eq
        !           138:       { gb n get /ff set
        !           139:         ff (0). eq
        !           140:         {  }
        !           141:         { ff } ifelse
        !           142:       }
        !           143:       {   } ifelse
        !           144:     } for
        !           145:   ] def
        !           146:   /arg1 ans def
        !           147:   ] pop
        !           148:   popVariables
        !           149:   arg1
        !           150: } def
        !           151:
        !           152:
        !           153:
        !           154:
        !           155:
        !           156:
        !           157:
        !           158:
        !           159:
        !           160:
        !           161: