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Annotation of OpenXM_contrib2/asir2000/lib/bgk, Revision 1.3

1.2       noro        1: /*
                      2:  * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
                      3:  * All rights reserved.
                      4:  *
                      5:  * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
                      6:  * non-exclusive and royalty-free license to use, copy, modify and
                      7:  * redistribute, solely for non-commercial and non-profit purposes, the
                      8:  * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
                      9:  * conditions of this Agreement. For the avoidance of doubt, you acquire
                     10:  * only a limited right to use the SOFTWARE hereunder, and FLL or any
                     11:  * third party developer retains all rights, including but not limited to
                     12:  * copyrights, in and to the SOFTWARE.
                     13:  *
                     14:  * (1) FLL does not grant you a license in any way for commercial
                     15:  * purposes. You may use the SOFTWARE only for non-commercial and
                     16:  * non-profit purposes only, such as academic, research and internal
                     17:  * business use.
                     18:  * (2) The SOFTWARE is protected by the Copyright Law of Japan and
                     19:  * international copyright treaties. If you make copies of the SOFTWARE,
                     20:  * with or without modification, as permitted hereunder, you shall affix
                     21:  * to all such copies of the SOFTWARE the above copyright notice.
                     22:  * (3) An explicit reference to this SOFTWARE and its copyright owner
                     23:  * shall be made on your publication or presentation in any form of the
                     24:  * results obtained by use of the SOFTWARE.
                     25:  * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.3     ! noro       26:  * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2       noro       27:  * for such modification or the source code of the modified part of the
                     28:  * SOFTWARE.
                     29:  *
                     30:  * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
                     31:  * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
                     32:  * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
                     33:  * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
                     34:  * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
                     35:  * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
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                     37:  * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
                     38:  * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
                     39:  * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
                     40:  * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
                     41:  * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
                     42:  * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
                     43:  * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
                     44:  * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
                     45:  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
                     46:  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
                     47:  *
1.3     ! noro       48:  * $OpenXM: OpenXM_contrib2/asir2000/lib/bgk,v 1.2 2000/08/21 08:31:40 noro Exp $
1.2       noro       49: */
1.1       noro       50: /* examples for groebner basis computations by Boege, Gebauer, Kredel */
                     51:
                     52: /* $(hairer,runge-kutta 1,05.11.83)
                     53: d=q
                     54: r=d(c2,c3,b3,b2,b1,a21,a32,a31)
                     55: opt=10 */
                     56: Hairer1 = [
                     57: [a31,a32,a21,b1,b2,b3,c3,c2],[
                     58: (+c2-a21),
                     59: (+c3-a31-a32),
                     60: (+b1+b2+b3-1),
                     61: (+b2*c2+b3*c3-1/2),
                     62: (+b2*c2^2+b3*c3^2-1/3),
                     63: (+b3*a32*c2-1/6)
                     64: ]]$
                     65:
                     66: /*$(hairer,runge-kutta*2,05.11.1983)
                     67: d=q
                     68: r=d(c2,c3,c4,b4,b3,b2,b1,a21,a31,a32,a41,a42,a43)
                     69: opt=10*/
                     70: Hairer2 = [
                     71: /* [a43,a42,a41,a32,a31,a21,b1,b2,b3,b4,c4,c3,c2],[ */
                     72: [a21,a31,a41,b1,b2,a42,a32,a43,b3,b4,c4,c3,c2],[
                     73: (+b1+b2+b3+b4-1),
                     74: (+b2*c2+b3*c3+b4*c4-1/2),
                     75: (+b2*c2^2+b3*c3^2+b4*c4^2-1/3),
                     76: (+b3*a32*c2+b4*a42*c2+b4*a43*c3-1/6),
                     77: (+b2*c2^3+b3*c3^3+b4*c4^3-1/4),
                     78: (+b3*c3*a32*c2+b4*c4*a42*c2+b4*c4*a43*c3-1/8),
                     79: (+b3*a32*c2^2+b4*a42*c2^2+b4*a43*c3^2-1/12),
                     80: (+b4*a43*a32*c2-1/24),
                     81: (+c2-a21),
                     82: (+c3-a31-a32),
                     83: (+c4-a41-a42-a43)
                     84: ]]$
                     85:
                     86:
                     87: /*$(hairer,runge-kutta 3,10.11.1983)
                     88: d=q
                     89: r=d(c2,c3,c4,c5,b2,b3,b4,b5,a32,a42,a43,a52,a53,a54)
                     90: opt=g10*/
                     91: Hairer3 = [
                     92: /* [a54,a53,a52,a43,a42,a32,b5,b4,b3,b2,c5,c4,c3,c2], */
                     93: [b2,b3,b4,b5,a52,a53,a42,a54,a32,a43,c5,c4,c3,c2],
                     94: [
                     95: (+b2*c2+b3*c3+b4*c4+b5*c5-1/2),
                     96: (+b2*c2^2+b3*c3^2+b4*c4^2+b5*c5^2-1/3),
                     97: (+b3*a32*c2+b4*a42*c2+b4*a43*c3+b5*a52*c2+b5*a53*c3+b5*a54*c4-1/6),
                     98: (+b2*c2^3+b3*c3^3+b4*c4^3+b5*c5^3-1/4),
                     99: (+b3*c3*a32*c2+b4*c4*a42*c2+b4*c4*a43*c3+b5*c5*a52*c2+b5*c5*a53*c3+b5*c5*a54*c4-1/8),
                    100: (+b3*a32*c2^2+b4*a42*c2^2+b4*a43*c3^2+b5*a52*c2^2+b5*a53*c3^2+b5*a54*c4^2-1/12),
                    101: (+b4*a43*a32*c2+b5*a53*a32*c2+b5*a54*a42*c2+b5*a54*a43*c3-1/24),
                    102: (+b2*c2^4+b3*c3^4+b4*c4^4+b5*c5^4-1/5),
                    103: (+b3*c3^2*a32*c2+b4*c4^2*a42*c2+b4*c4^2*a43*c3+b5*c5^2*a52*c2+b5*c5^2*a53*c3+b5*c5^2*a54*c4-1/10),
                    104: (+b3*c2^2*a32*c3+b4*c2^2*a42*c4+b4*c3^2*a43*c4+b5*c2^2*a52*c2+b5*c3^2*a53*c5+b5*c4^2*a54*c5-1/15),
                    105: (+b4*c4*a43*a32*c2+b5*c5*a53*a32*c2+b5*c5*a54*a42*c2+b5*c5*a54*a43*c3-1/30),
                    106: (+b3*a32^2*c2^2+b4*a42^2*c2^2+2*b4*a42*c2*a43*c3+b4*a43^2*c3^2+b5*a52^2*c2^2+b5*a53^2*c3^2+b5*a54^2*c4^2+2*b5*a52*c2*a53*c3+2*b5*a52*c2*a54*c4+2*b5*a53*c3*a54*c4-1/20),
                    107: (+b3*a32*c2^3+b4*a42*c2^3+b4*a43*c3^3+b5*a52*c2^3+b5*a53*c3^3+b5*a54*c4^3-1/20),
                    108: (+b4*a43*c3*a32*c2+b5*a53*c3*a32*c2+b5*a54*c4*a42*c2+b5*a54*c4*a43*c3-1/40),
                    109: (+b4*a43*a32*c2^2+b5*a53*a32*c2^2+b5*a54*a42*c2^2+b5*a54*a43*c3^2-1/60),
                    110: (+b5*a54*a43*a32*c2-1/120)
                    111: ]]$
                    112:
                    113: /*$(hairer,runge-kutta 4,p=5 s=6,20.12.1983)
                    114: d=q
                    115: r=d(c2,c3,c4,c5,c6,b2,b3,b4,b5,b6,a32,a42,a43,a52,a53,
                    116: a54,a62,a63,a64,a65)
                    117: opt=oil*/
                    118: Hairer4 = [
                    119: [a65,a64,a63,a62,a54,a53,a52,a43,a42,a32,b6,b5,b4,b3,b2,c6,c5,c4,c3,c2,c51],[
                    120: (+b2*c2+b3*c3+b4*c4+b5*c5+b6*c6-1/2),
                    121: (+b2*c2^2+b3*c3^2+b4*c4^2+b5*c5^2+b6*c6^2-1/3),
                    122: (+b3*a32*c2+b4*a42*c2+b4*a43*c3+b5*a52*c2+b5*a53*c3+b6*a62*c2+b6*a63*c3+b6*a64*c4+b6*a65*c5+b5*a54*c4-1/6),
                    123: (+b2*c2^3+b3*c3^3+b4*c4^3+b5*c51^3+b6*c6^3-1/4),
                    124: (+b3*c3*a32*c2+b4*c4*a42*c2+b4*c4*a43*c3+b5*c5*a52*c2+b6*c6*a62*c2+b6*c6*a63*c3+b6*c6*a64*c4+b6*c6*a65*c5+b5*c5*a53*c3+b5*c5*a54*c4-1/8),
                    125: (+b3*a32*c2^2+b4*a42*c2^2+b4*a43*c3^2+b5*a52*c2^2+b6*a62*c2^2+b6*a63*c3^2+b6*a64*c4^2+b6*a65*c5^2+b5*a53*c3^2+b5*a54*c4^2-1/12),
                    126: (+b4*a43*a32*c2+b5*a53*a32*c2+b5*a54*a42*c2+b5*a54*a43*c3+b6*a63*a32*c2+b6*a64*a42*c2+b6*a64*a43*c3+b6*a65*a52*c2+b6*a65*a53*c3+b6*a65*a54*c4-1/24),
                    127: (+b2*c2^4+b3*c3^4+b4*c4^4+b5*c5^4+b6*c6^4-1/5),
                    128: (+b3*c3^2*a32*c2+b4*c4^2*a42*c2+b4*c4^2*a43*c3+b5*c5^2*a52*c2+b5*c5^2*a53*c3+b5*c5^2*a54*c4+b6*c6^2*a62*c2+b6*c6^2*a63*c3+b6*c6^2*a64*c4+b6*c6^2*a65*c5-1/10),
                    129: (+b3*c2^2*a32*c3+b4*c2^2*a42*c4+b4*c3^2*a43*c4+b5*c2^2*a52*c5+b5*c3^2*a53*c5+b5*c4^2*a54*c5+b6*c2^2*a62*c6+b6*c3^2*a63*c6+b6*c4^2*a64*c6+b6*c5^2*a65*c6-1/15),
                    130: (+b4*c4*a43*a32*c2+b5*c5*a53*a32*c2+b5*c5*a54*a42*c2+b5*c5*a54*a43*c3+b6*c6*a63*a32*c2+b6*c6*a64*a42*c2+b6*c6*a64*a43*c2+b6*c6*a65*a52*c2+b6*c6*a65*a53*c3+b6*c6*a65*a54*c4-1/30),
                    131: (+b3*a32^2*c2^2+b4*a42^2*c2^2+2*b4*a42*c2*a43*c3+b4*a43^2*c3^2+b5*a52^2*c2^2+b5*a53^2*c3^2+b5*a54^2*c4^2+2*b5*a52*c2*a53*c3+2*b5*a52*c2*a54*c4+2*b5*a53*c3*a54*c4+b6*a62^2*c2^2+b6*a63^2*c3^2+b6*a64^2*c4^2+b6*a65^2*c5^2+2*b6*a62*c2*a63*c3+2*b6*a62*c2*a64*c4+2*b6*a62*c2*a65*c5+2*b6*a63*c3*a64*c4+2*b6*a63*c3*a65*c5+2*b6*a64*c4*a65*c5-1/20),
                    132: (+b3*a32*c2^3+b4*a42*c2^3+b4*a43*c3^3+b5*a52*c2^3+b5*a53*c3^3+b5*a54*c4^3+b6*a62*c2^3+b6*a63*c3^3+b6*a64*c4^3+b6*a65*c5^3-1/20),
                    133: (+b4*a43*c3*a32*c2+b5*a53*c3*a32*c2+b5*a54*c4*a42*c2+b5*a54*c4*a43*c3+b6*a63*c3*a32*c2+b6*a64*c4*a42*c2+b6*a64*c4*a43*c3+b6*a65*c5*a52*c2+b6*a65*c5*a53*c3+b6*a65*c5*a54*c4-1/40),
                    134: (+b4*a43*a32*c2^2+b5*a53*a32*c2^2+b5*a54*a42*c2^2+b5*a54*a43*c3^2+b6*a63*a32*c2^2+b6*a63*a42*c2^2+b6*a64*a43*c3^2+b6*a65*a52*c2^2+b6*a65*a53*c3^2+b6*a65*a54*c4^2-1/60),
                    135: (+b5*a54*a43*a32*c2+b6*a64*a43*a32*c2+b6*a65*a53*a32*c2+b6*a65*a54*a42*c2+b6*a65*a54*a43*c3-1/20)
                    136: ]]$
                    137:
                    138: /*$(butcher,runge-kutta,20 1 1984 s=3 pt=4)
                    139: d=q
                    140: r=d(b,c2,c3,a,b3,b2,a32,b1)
                    141: opt=liope10*/
                    142: Butcher = [
                    143: [b1,a32,b2,b3,a,c3,c2,b],[
                    144: (b1+b2+b3
                    145: -(a+b)),
                    146: (b2*c2+b3*c3
                    147: -(1/2+1/2*b+b^2-a*b)),
                    148: (b2*c2^2+b3*c3^2
                    149: -(a*(1/3+b^2)-4/3*b-b^2-b^3)),
                    150: (b3*a32*c2
                    151: -(a*(1/6+1/2*b+b^2)-2/3*b-b^2-b^3)),
                    152: (b2*c2^3+b3*c3^3
                    153: -(1/4+1/4*b+5/2*b^2+3/2*b^3+b^4
                    154: -a*(b+b^3))),
                    155: (b3*c3*a32*c2
                    156: -(1/8+3/8*b+7/4*b^2+3/2*b^3+b^4
                    157: -a*(1/2*b+1/2*b^2+b^3))),
                    158: (b3*a32*c2^2
                    159: -(1/12+1/12*b+7/6*b^2+3/2*b^3+b^4
                    160: -a*(2/3*b+b^2+b^3))),
                    161: (1/24+7/24*b+13/12*b^2+3/2*b^3+b^4
                    162: -a*(1/3*b+b^2+b^3))
                    163: ]]$
                    164:
                    165: /*$(gerdt,10.10.84)
                    166: d=q
                    167: r=d(l1,l2,l3,l4,l5,l6,l7)
                    168: opt=oil pe10*/
                    169: Gerdt = [
                    170: [l7,l6,l5,l4,l3,l2,l1],[
                    171: (l1*(l4-1/2*l5+l6)),
                    172: ((2/7*l1^2-l4)*(-10*l1+5*l2-l3)),
                    173: ((2/7*l1^2-l4)*(3*l4-l5+l6)),
                    174: ((-2*l1^2+l1*l2+2*l1*l3-l2^2-7*l5+21*l6) *(-3*l1+2*l2)+21*(7*l7-2*l1*l4+3/7*l1^3)),
                    175: ((-2*l1^2+l1*l2+2*l1*l3-l2^2-7*l5+21*l6) *(2*l4-2*l5)+(7*l7-2*l1*l4+3/7*l1^3) *(-45*l1+15*l2-3*l3)),
                    176: (2*(-2*l1^2+l1*l2+2*l1*l3-l2^2-7*l5+21*l6) *l7+(7*l7-2*l1*l4+3/7*l1^3)* (12*l4-3*l5+2*l6)),
                    177: ((l1*(5*l1-3*l2+l3))* (2*l2-l1) +7*(l1*(2*l6-4*l4))),
                    178: ((l1*(5*l1-3*l2+l3))* l3+7*(l1*(2*l6-4*l4))),
                    179: ((l1*(5*l1-3*l2+l3))* (-2*l4-2*l5)+(l1*(2*l6-4*l4))* (2*l2-8*l1)+84*1/2*l1*l7),
                    180: ((l1*(5*l1-3*l2+l3))* (8/3*l5+6*l6)+(l1*(2*l6-4*l4))* (11*l1-17/3*l2+5/3*l3)-168*1/2*l1*l7),
                    181: (15*l7* (l1*(5*l1-3*l2+l3)) +(l1*(2*l6-4*l4))*(5*l4-2*l5) +1/2*l1*l7*(-120*l1+30*l2-6*l3)),
                    182: (-3*(l1*(5*l1-3*l2+l3))* l7+(l1*(2*l6-4*l4))* (-1/2*l4+1/4*l5-1/2*l6)+1/2*l1*l7* (24*l1-6*l2)),
                    183: (3*(l1*(2*l6-4*l4))* l7+1/2*l1*l7* (40*l4-8*l5+4*l6))
                    184: ]]$
                    185:
                    186:
                    187: /*$(raksanyi 1,1983 rational*functions.)
                    188: d=f(a1,a2,a3,a4)
                    189: r=(x1,x2,x3,x4)
                    190: opt=oil*/
                    191: Raksanyi = [
                    192: [x4,x3,x2,x1],[
                    193: (x4-(a4-a2)),
                    194: (x1+x2+x3+x4-(a1+a3+a4)),
                    195: (x1*x3+x1*x4+x2*x3+x3*x4-(a1*a4+a1*a3+a3*a4)),
                    196: (x1*x3*x4-(a1*a3*a4))
                    197: ]]$
                    198:
                    199:
                    200: /*$(rose,general equilibrium model,1984)
                    201: d=q
                    202: r=d(u3,u4,a46)
                    203: opt=iog*/
                    204: Rose = [
                    205: [u3,u4,a46],[
                    206: /*[a46,u4,u3],[*/
                    207: (u4^4-20/7*a46^2),
                    208: (a46^2*u3^4+7/10*a46*u3^4+7/48*u3^4-50/27
                    209: *a46^2-35/27*a46-49/216),
                    210: (a46^5*u4^3+7/5*a46^4*u4^3+609/1000*a46^3
                    211: *u4^3+49/1250*a46^2*u4^3-27391/800000*a46*u4^3
                    212: -1029/160000*u4^3+3/7*a46^5*u3*u4^2+3/5*a46^6
                    213: *u3*u4^2+63/200*a46^3*u3*u4^2+147/2000*a46^2
                    214: *u3*u4^2+4137/800000*a46*u3*u4^2-7/20*a46^4
                    215: *u3^2*u4-77/125*a46^3*u3^2*u4-23863/60000*a46^2
                    216: *u3^2*u4-1078/9375*a46*u3^2*u4-24353/1920000
                    217: *u3^2*u4-3/20*a46^4*u3^3-21/100*a46^3*u3^3
                    218: -91/800*a46^2*u3^3-5887/200000*a46*u3^3
                    219: -343/128000*u3^3)
                    220: ]]$
                    221:
                    222:
                    223:
                    224: /*$(university of waterloo,19.03,1984)
                    225: d=q
                    226: r=d(a0,a2,a3,a4,a5,b0,b1,b2,b3,b4,b5,c0,c1,c2,c3,c4,c5)
                    227: opt=oil*pe10*/
                    228: Waterloo = [
                    229: [c5,c4,c3,c2,c1,c0,b5,b4,b3,b2,b1,b0,a5,a4,a3,a2,a0],[
                    230: (a4*b4),
                    231: (a5*b1+b5+a4*b3+a3*b4),
                    232: (a2*b2),
                    233: (a5*b5),
                    234: (a0*b2+b2+a4*b2+a2*b4+c2+a2*b0+a2*b1),
                    235: (a0*b0+a0*b1+a0*b4+a3*b2+b0+b1+b4+a4*b0 +a4*b1 +a2*b5+a4*b4+c1+c4+a5*b2+a2*b3+c0),
                    236: (a3*b0+a0*b3+a0*b5+a5*b0+b3+b5+a5*b4+a4*b3+ a4*b5+a3*b4+a5*b1+a3*b1+c3+c5-1),
                    237: (a5*b3+a5*b5+a3*b5+a3*b3),
                    238: (a5*b3+2*a5*b5+a3*b5),
                    239: (a0*b5+a5*b0+a3*b4+2*a5*b4+a5*b1+b5+a4*b3 +2*a4*b5+c5),
                    240: (a4*b0+2*a4*b4+a2*b5+b4+a4*b1+a5*b2+a0*b4 +c4),
                    241: (a2*b4+a4*b2),
                    242: (a4*b5+a5*b4),
                    243: (2*a3*b3+a5*b3+a3*b5),
                    244: (c3+a0*b3+2*b3+b5+a4*b3+a3*b0+2*a3*b1+ a5*b1+a3*b4),
                    245: (c1+a0*b1+2*b1+a4*b1+a2*b3+b0+a3*b2+b4),
                    246: (a2*b1+b2),
                    247: (a5*b3+a3*b5),
                    248: (b4+a4*b1)
                    249: ]]$
                    250:
                    251:
                    252: /*$(trinks 1,ideal a. 09.12.1983)
                    253: d=q
                    254: r=d(b,s,t,z,p,w)
                    255: opt=1*/
                    256: Trinks1 = [
                    257: /*[z,t,w,b,p,s],[*/
                    258: [w,p,z,t,s,b],[
                    259: (+45*p+35*s-165*b-36),
                    260: (+35*p+40*z+25*t-27*s),
                    261: (+15*w+25*p*s+30*z-18*t-165*b^2),
                    262: (-9*w+15*p*t+20*z*s),
                    263: (w*p+2*z*t-11*b^3),
                    264: (99*w-11*s*b+3*b^2)
                    265: ]]$
                    266:
                    267:
                    268: /*$(trinks 2,ideal p=a+f7lr.10.12.1983)
                    269: d=q
                    270: r=d(b,s,t,z,p,w)
                    271: opt=il*/
                    272: Trinks2 = [
                    273: [w,p,z,t,s,b],[
                    274: +45*p+35*s-165*b-36,
                    275: +35*p+40*z+25*t-27*s,
                    276: +15*w+25*p*s+30*z-18*t-165*b^2,
                    277: -9*w+15*p*t+20*z*s,
                    278: w*p+2*z*t-11*b^3,
                    279: 99*w-11*s*b+3*b^2,
                    280: b^2+33/50*b+2673/10000
                    281: ]]$
                    282:
                    283: Ge = [
                    284: [x,y,z,t,u,v,w],[
                    285: (w*(t-1/2*z+y)),
                    286: ((2/7*w^2-t)*(-10*w+5*v-u)),
                    287: ((2/7*w^2-t)*(3*t-z+y)),
                    288: ((-2*w^2+w*v+2*w*u-v^2-7*z+21*y) *(-3*w+2*v)+21*(7*x-2*w*t+3/7*w^3)),
                    289: ((-2*w^2+w*v+2*w*u-v^2-7*z+21*y) *(2*t-2*z)+(7*x-2*w*t+3/7*w^3) *(-45*w+15*v-3*u)),
                    290: (2*(-2*w^2+w*v+2*w*u-v^2-7*z+21*y) *x+(7*x-2*w*t+3/7*w^3)* (12*t-3*z+2*y)),
                    291: ((w*(5*w-3*v+u))* (2*v-w) +7*(w*(2*y-4*t))),
                    292: ((w*(5*w-3*v+u))* u+7*(w*(2*y-4*t))),
                    293: ((w*(5*w-3*v+u))* (-2*t-2*z)+(w*(2*y-4*t))* (2*v-8*w)+84*1/2*w*x),
                    294: ((w*(5*w-3*v+u))* (8/3*z+6*y)+(w*(2*y-4*t))* (11*w-17/3*v+5/3*u)-168*1/2*w*x),
                    295: (15*x* (w*(5*w-3*v+u)) +(w*(2*y-4*t))*(5*t-2*z) +1/2*w*x*(-120*w+30*v-6*u)),
                    296: (-3*(w*(5*w-3*v+u))* x+(w*(2*y-4*t))* (-1/2*t+1/4*z-1/2*y)+1/2*w*x* (24*w-6*v)),
                    297: (3*(w*(2*y-4*t))* x+1/2*w*x* (40*t-8*z+4*y))
                    298: ]]$
                    299: end$