1 | LIB "tst.lib"; |
---|
2 | |
---|
3 | tst_init(); |
---|
4 | |
---|
5 | ring r=0,(x4,x3,x2,x1,x5,y),dp; |
---|
6 | poly f2=((y+x1)*(y-2*x4)*(y+x2+x3)); |
---|
7 | ideal I= x1^2+x3*x1-x1*x4+x2^2-x2+x3*x4-x4^2-x4,x1^2+x2*x1-x1*x4+x2^2+x3*x2+x2+x4^2-x4 |
---|
8 | , 1+x1*x2-x1*x3+x1*x4+x1+x2^2-x3*x2+x2*x4-x2+x3^2+x3*x4-x4^2 , x1^2+x1*x2+x3*x1+x1*x4-x2^2+x3*x2-x2+x3^2-x3*x4-x4^2+x4; |
---|
9 | ideal J=I,f2; |
---|
10 | char_series (J); |
---|
11 | |
---|
12 | kill r; |
---|
13 | |
---|
14 | ring r=0,(x1,x2,x3,x4,x5,y),dp; |
---|
15 | poly f3=((y-2*x4^2+x3*x1+x2+1)*(y+x2^2+x3*x4+x1*x3+2)); |
---|
16 | ideal I=-1-x1^2+x3*x1+x2^2-x3*x2+x3^2-x3*x4+x4^2+x4 , 1+x2*x1+x3*x1+x1-x3*x2-x2*x4+x2-x3^2-x3*x4-x3 , 1+x1*x3+x1*x4+x1+x2^2+x2*x4-x2-x3-x4^2 , |
---|
17 | x1^2+x1*x2+x3*x1+x1*x4-x1-x2*x4-x3^2+x3*x4-x3+x4^2+x4; |
---|
18 | ideal J=I,f3; |
---|
19 | char_series (J); |
---|
20 | |
---|
21 | //examples from J. Kroeker |
---|
22 | ring rng = 0,(xz,xs,xj),(lp(1),lp(2)); |
---|
23 | ideal I = -93*xz^2*xs*xj^2+93*xz*xs*xj^2-130*xs^3*xj^2, |
---|
24 | 82*xz^3*xs*xj+90*xz*xs^2*xj^2-66*xs; |
---|
25 | char_series(I); |
---|
26 | |
---|
27 | kill rng; |
---|
28 | |
---|
29 | ring rng = 0,(xt,xl,xy),(lp(1),lp(2)); |
---|
30 | ideal I = 45*xt*xy^4+53, |
---|
31 | 84*xt^2*xy^3-84*xt*xy^3-105*xl*xy; |
---|
32 | char_series(I); |
---|
33 | |
---|
34 | kill rng; |
---|
35 | |
---|
36 | ring rng = 0,(xr,xd,xs),(lp(1),lp(2)); |
---|
37 | ideal I = -124*xr^2-9*xr*xd*xs^2, |
---|
38 | 62*xr^2*xs^2-62*xr*xs^2+126*xd; |
---|
39 | char_series(I); |
---|
40 | |
---|
41 | kill rng; |
---|
42 | |
---|
43 | ring rng = 0,(xm,xs,xg),(lp(1),lp(2)); |
---|
44 | ideal I = 51*xm^2-51*xm-130*xs^2, |
---|
45 | -27*xm^2*xs*xg^2+49*xs*xg^2-99; |
---|
46 | char_series(I); |
---|
47 | |
---|
48 | kill rng; |
---|
49 | |
---|
50 | ring rng = 0,( xv,xg,xq ),(lp(1),lp(2)); |
---|
51 | ideal I = -29*xv*xq^4-103*xg, |
---|
52 | 24*xv-105*xg^3*xq^2-24; |
---|
53 | char_series(I); |
---|
54 | |
---|
55 | kill rng; |
---|
56 | |
---|
57 | ring rng = 0, (xv, xw ,xi, xk, xn),(lp(3),lp(2)); |
---|
58 | ideal I = 32*xv^2*xk-29*xw*xk-32*xk, |
---|
59 | 99*xw*xi^2+36*xw*xk^2, |
---|
60 | 55*xw*xk-26*xw*xn^2, |
---|
61 | -44*xv*xw*xk+56*xi^2+134; |
---|
62 | char_series(I); |
---|
63 | |
---|
64 | kill rng; |
---|
65 | |
---|
66 | ring rng = 0, ( xu ,xm, xl ,xr ,xj ),(lp(3),lp(2)); |
---|
67 | ideal I = 46*xu^2*xr-86*xl^2*xj+75, |
---|
68 | -96*xj^2-91, |
---|
69 | -21*xu*xr+7*xm+61*xr^2*xj; |
---|
70 | char_series(I); |
---|
71 | |
---|
72 | kill rng; |
---|
73 | |
---|
74 | ring rng = 0, ( xk, xg, xl ,xt ,xf ),(lp(3),lp(2)); |
---|
75 | ideal I = -39*xk^2+99*xg*xl^2, |
---|
76 | 105*xl*xf^2+194, |
---|
77 | 96*xl*xf^2-14*xt+20*xf; |
---|
78 | char_series(I); |
---|
79 | |
---|
80 | kill rng; |
---|
81 | |
---|
82 | ring rng = 0,( xc, xk, xq , xx,xz ),(lp(3),lp(2)); |
---|
83 | ideal I = 7*xc*xk-123*xc*xz^2, |
---|
84 | 132*xc*xq-43*xc*xx*xz+40*xc, |
---|
85 | 34*xk*xx+115, |
---|
86 | 49*xc*xk^2-32*xk^2-122*xk*xx^2; |
---|
87 | char_series(I); |
---|
88 | |
---|
89 | kill rng; |
---|
90 | |
---|
91 | ring rng = 0,( xy, xz, xs, xe, xh),(lp(3),lp(2)); |
---|
92 | ideal I = 78*xz^2+86*xe, |
---|
93 | 118*xy*xe^2-162, |
---|
94 | 34*xz*xs+20*xz*xh-136, |
---|
95 | -119*xy^2*xz-27*xh^3-62; |
---|
96 | char_series(I); |
---|
97 | |
---|
98 | kill rng; |
---|
99 | |
---|
100 | ring rng = 0,( xn, xd, xi, xy, xf ),(lp(3),lp(2)); |
---|
101 | ideal I = -60*xn*xi-104*xd*xi+87*xf^2, |
---|
102 | -34*xn*xd*xi+118, |
---|
103 | 109*xn^2*xi+124*xn*xd, |
---|
104 | -57*xi*xy^2+47; |
---|
105 | char_series(I); |
---|
106 | |
---|
107 | kill rng; |
---|
108 | |
---|
109 | ring rng = 0,( xg, xc, xs, xo, xz),(lp(3),lp(2)); |
---|
110 | ideal I = 94*xg*xc^2+22, |
---|
111 | -129*xg*xo+138*xs*xz^2-54, |
---|
112 | -81*xo*xz^2+102, |
---|
113 | 27*xo^3-86; |
---|
114 | char_series(I); |
---|
115 | |
---|
116 | kill rng; |
---|
117 | |
---|
118 | ring rng = 0,( xa, xb, xq, xt ,xc ),(lp(3),lp(2)); |
---|
119 | ideal I = -34*xa^2+177, |
---|
120 | -52*xa*xt^2-79*xb, |
---|
121 | -24*xb*xq*xt-62, |
---|
122 | 138*xa*xc^2+117*xt; |
---|
123 | char_series(I); |
---|
124 | |
---|
125 | kill rng; |
---|
126 | |
---|
127 | ring rng = 0,( xu, xi, xw, xe, xr ),lp; |
---|
128 | ideal I = -133*xi*xw-115*xw^2*xr, |
---|
129 | -104*xw*xr^2-19*xw-17, |
---|
130 | 126*xu*xi^2-8, |
---|
131 | 94*xi*xe^2-100; |
---|
132 | char_series(I); |
---|
133 | |
---|
134 | kill rng; |
---|
135 | |
---|
136 | ring rng = 0,( xd, xx, xb, xj ,xt),lp; |
---|
137 | ideal I = 30*xx*xj*xt+125*xx+36*xj*xt^2, |
---|
138 | -36*xx+29*xb^2-79*xb, |
---|
139 | 42*xd*xx^2+65*xd*xx-76; |
---|
140 | char_series(I); |
---|
141 | |
---|
142 | kill rng; |
---|
143 | |
---|
144 | ring rng = 0,( xu ,xy, xm, xc, xs ),lp; |
---|
145 | ideal I = 23*xu*xc*xs-40, |
---|
146 | -138*xy*xm^2-97, |
---|
147 | -20*xu*xy*xc-30*xy*xs-131*xm^2*xs, |
---|
148 | -51*xu*xm^2-87*xs^2-61; |
---|
149 | char_series(I); |
---|
150 | |
---|
151 | kill rng; |
---|
152 | |
---|
153 | ring rng = 0,( xb, xm, xc, xo, xw ),lp; |
---|
154 | ideal I = -99*xb*xw^2-82, |
---|
155 | -136*xb^2*xo+77*xc^2-44*xw, |
---|
156 | -100*xm^2*xw-103*xm*xo^2-16; |
---|
157 | char_series(I); |
---|
158 | |
---|
159 | kill rng; |
---|
160 | |
---|
161 | ring rng = 0,( xm ,xo, xi ,xk ,xn ),lp; |
---|
162 | ideal I = -19*xo*xk^2-12*xn^3+114*xn, |
---|
163 | -131*xm*xi-70*xi*xn^2, |
---|
164 | -77*xm*xk*xn+28*xo+90*xi^2*xn; |
---|
165 | char_series(I); |
---|
166 | |
---|
167 | kill rng; |
---|
168 | |
---|
169 | ring rng = 0,( xz, xq, xa, xc, xl),lp; |
---|
170 | ideal I = -56*xz*xc+16*xq*xl^2+132, |
---|
171 | -6*xz-50*xq*xl+95*xc*xl, |
---|
172 | 138*xa^2+22*xc-37*xl; |
---|
173 | char_series(I); |
---|
174 | |
---|
175 | kill rng; |
---|
176 | |
---|
177 | ring rng = 0,( xz, xv, xb, xu, xp),lp; |
---|
178 | ideal I = 100*xz*xb+95*xv^2*xp, |
---|
179 | 14*xz-31*xv*xb*xp, |
---|
180 | -44*xz*xb*xp+43*xv^2-140*xu^2, |
---|
181 | -40*xz^2*xb-xp; |
---|
182 | char_series(I); |
---|
183 | |
---|
184 | kill rng; |
---|
185 | |
---|
186 | ring rng = 0,( xp, xr, xt, xq, xb),lp; |
---|
187 | ideal I = 64*xp-35*xr*xq-65*xt*xq^2, |
---|
188 | -39*xr^2*xt+85*xt*xb^2+9*xb^3, |
---|
189 | -91*xp*xt-130, |
---|
190 | -60*xp^2*xr-74*xr^2-120*xt; |
---|
191 | char_series(I); |
---|
192 | |
---|
193 | kill rng; |
---|
194 | |
---|
195 | ring rng = 0,(xg, xa, xk, xh, xu),lp; |
---|
196 | ideal I = -63*xa^2-4*xa+120, |
---|
197 | 116*xg*xa*xu-106*xg*xu-34*xa, |
---|
198 | -7*xa*xu-111*xk^2, |
---|
199 | -50*xg*xa*xu+86*xg*xh^2+56; |
---|
200 | char_series(I); |
---|
201 | |
---|
202 | kill rng; |
---|
203 | |
---|
204 | ring rng = 0,(xw,xp, xy, xo ,xz),lp; |
---|
205 | ideal I = 103*xw^2-61*xw*xy^2+43, |
---|
206 | 114*xp*xo-107*xp-107*xz, |
---|
207 | 92*xw+124*xy*xz^2; |
---|
208 | char_series(I); |
---|
209 | |
---|
210 | kill rng; |
---|
211 | |
---|
212 | ring rng = 0,( xx, xz, xp, xo ,xn),lp; |
---|
213 | ideal I = -61*xz*xn^2-10, |
---|
214 | -89*xx*xz^2-53, |
---|
215 | -22*xx*xz+71*xo, |
---|
216 | 9*xz*xp*xo+19*xp^2+119*xp*xn; |
---|
217 | char_series(I); |
---|
218 | |
---|
219 | kill rng; |
---|
220 | |
---|
221 | ring rng = 0,(xt, xd ,xa ,xp, xe),lp; |
---|
222 | ideal I = 32*xt^2*xd+51*xa^2, |
---|
223 | 135*xt*xa+62*xd*xa*xp+68*xd*xa*xe, |
---|
224 | 93*xt*xd+9*xd*xp*xe+103, |
---|
225 | -106*xt*xd^2-125; |
---|
226 | char_series(I); |
---|
227 | |
---|
228 | kill rng; |
---|
229 | |
---|
230 | ring rng = 0,(xv, xz,xx, xj, xf),dp; |
---|
231 | ideal I = 1680700*xv^5*xz^11*xx^3-15253663446*xv^13*xx^6+204205050*xv^6*xz^8*xx^3+12301875*xz^13, |
---|
232 | 2*xz*xx+3*xv*xf, |
---|
233 | -3361400*xv^4*xz^11*xx^4+30507326892*xv^12*xx^7-408410100*xv^5*xz^8*xx^4+36905625*xz^12*xf, |
---|
234 | 100842*xv^6*xx^3*xj+3430*xv^3*xz^4*xx+138915*xv^4*xz*xx+18225*xz^5*xj, |
---|
235 | 980*xv*xz^7*xx^3*xj+302526*xv^6*xx^4+39690*xv^2*xz^4*xx^3*xj+2025*xz^7*xf, |
---|
236 | 490*xv^2*xz^7*xx^2*xj+151263*xv^7*xx^3+19845*xv^3*xz^4*xx^2*xj-675*xz^8, |
---|
237 | 34300*xv^3*xz^11*xx-311299254*xv^11*xx^4+4167450*xv^4*xz^8*xx+182250*xz^12*xj+56260575*xv^5*xz^5*xx+7381125*xv*xz^9*xj, |
---|
238 | -1960*xz^7*xx^4*xj-605052*xv^5*xx^5-79380*xv*xz^4*xx^4*xj+6075*xz^6*xf^2, |
---|
239 | -201684*xv^5*xx^4*xj-6860*xv^2*xz^4*xx^2-277830*xv^3*xz*xx^2+54675*xz^4*xj*xf, |
---|
240 | 1029*xv^4*xx^2*xj+135*xz^4*xx*xj^2+35*xv*xz^4, |
---|
241 | 196*xv*xz^3*xx^3*xj^2-2058*xv^3*xx^2+405*xz^3*xj*xf, |
---|
242 | 98*xv^2*xz^3*xx^2*xj^2-1029*xv^4*xx-135*xz^4*xj, |
---|
243 | 3430*xv^3*xz^7*xx*xj+1058841*xv^8*xx^2+277830*xv^4*xz^4*xx*xj+18225*xz^8*xj^2, |
---|
244 | 57624*xv^3*xx^6*xj^2+1960*xz^4*xx^4*xj-6075*xz^3*xf^2, |
---|
245 | 28812*xv^4*xx^5*xj^2+980*xv*xz^4*xx^3*xj+2025*xz^4*xf, |
---|
246 | 14406*xv^5*xx^4*xj^2+490*xv^2*xz^4*xx^2*xj-675*xz^5, |
---|
247 | 38416*xv^2*xx^7*xj^2-1960*xz^3*xx^4*xj*xf+6075*xz^2*xf^3, |
---|
248 | -392*xz^3*xx^4*xj^2+4116*xv^2*xx^3+1215*xz^2*xj*xf^2, |
---|
249 | -2058*xv^3*xx^2*xj+405*xz^3*xj^2*xf-70*xz^4, |
---|
250 | 28*xx^4*xj^3-15*xf, |
---|
251 | 14*xv*xx^3*xj^3+5*xz, |
---|
252 | 686*xv^3*xz^3*xx*xj^2+27783*xv^4*xx*xj^2+3645*xz^4*xj^3-7203*xv^5, |
---|
253 | -153664*xz^3*xx^8*xj^2-6223392*xv*xx^8*xj^2+1613472*xv^2*xx^7+1476225*xz*xf^4, |
---|
254 | -392*xz^2*xx^4*xj^2*xf-2744*xv*xx^4+1215*xz*xj*xf^3, |
---|
255 | 54*xz^3*xx^2*xj^4+14*xv*xz^3*xx*xj^2-147*xv^3, |
---|
256 | -153664*xz^2*xx^8*xj^2*xf+4148928*xx^9*xj^2-1075648*xv*xx^8+1476225*xf^5, |
---|
257 | -1176*xz*xx^4*xj^2*xf^2+5488*xx^5+3645*xj*xf^4, |
---|
258 | 81*xz^2*xx*xj^4*xf-14*xz^3*xx*xj^2+147*xv^2, |
---|
259 | 81*xz*xj^4*xf^2-14*xz^2*xj^2*xf-98*xv, |
---|
260 | 243*xj^4*xf^3-42*xz*xj^2*xf^2+196*xx, |
---|
261 | 81*xx^3*xj^7*xf^2-14*xz*xx^3*xj^5*xf+35; |
---|
262 | char_series(I); |
---|
263 | |
---|
264 | kill rng; |
---|
265 | |
---|
266 | ring r = 0,(xi,xs,xq,xx,xm),(dp(5),C); |
---|
267 | ideal PS = |
---|
268 | -172998863839362083328*xi^24*xs^12*xq^3*xx^2-52588753158715937280*xi^19*xs^13*xq^4*xx-3996524742145603200*xi^14*xs^14*xq^5-71016487260381000*xi^14*xs^12*xq^3*xx^3+214426195095580767936*xi^16*xs^8*xq^2*xx^3+10863661177099654560*xi^11*xs^9*xq^3*xx^2-88591320048324018744*xi^8*xs^4*xq*xx^4+252588087748157329728*xi^3*xs^7*xq^4+4488379247731300740*xi^3*xs^5*xq^2*xx^3+12200657953515011617*xx^5,24316515699137447759674331724288000*xi^51*xs^25*xq^4*xx+3695906474187557573535406813440000*xi^46*xs^26*xq^5+9981993459611016739859301000000*xi^41*xs^25*xq^4*xx^2-30139492385276843294717118219456000*xi^43*xs^21*xq^3*xx^2+20554637419790732695094892000000*xi^36*xs^26*xq^6*xm-1517179299416768791697692500000*xi^36*xs^26*xq^5*xx-20687462228947419066196365168384000*xi^38*xs^22*xq^5*xm+3053966733658380347822489267520000*xi^38*xs^22*xq^4*xx+232088666866071881778962758800000*xi^33*xs^23*xq^5+12452291170898620642854475864824000*xi^35*xs^17*xq^2*xx^3-2523525114996925217629488470160000*xi^30*xs^18*xq^3*xx^2-3897278432036671489948499945040000*xi^25*xs^19*xq^5*xm+287665991882511129368141374350000*xi^25*xs^19*xq^4*xx-289524899908583838376732433488291200*xi^27*xs^15*xq^3*xx-1714910052484122227705095818057000*xi^27*xs^13*xq*xx^4-29336904602896335824336969151504000*xi^22*xs^16*xq^4+260651947180500757879705339222500*xi^22*xs^14*xq^2*xx^3+199364580575358935943124077198858000*xi^19*xs^11*xq^2*xx^2+246315529136893170561682291829121600*xi^14*xs^12*xq^4*xm-18181046656243424975945277480399000*xi^14*xs^12*xq^3*xx+6099511078728236201969507465604580416*xi^16*xs^8*xq^2*xx+927074535026828353548824509971346080*xi^11*xs^9*xq^3-32947413642589064445136259421135300*xi^11*xs^7*xq*xx^3-5040090720940539781668577178927957328*xi^8*xs^4*xq*xx^2-5189205831027538000061138633925825888*xi^3*xs^5*xq^3*xm+383025762335628023240012416637606820*xi^3*xs^5*xq^2*xx+1041170109678996593607573204356058281*xx^3,87809640024663005798823975671040000*xi^46*xs^26*xq^5*xx+13346328934566180126655635715200000*xi^41*xs^27*xq^6+36046087493039782671714142500000*xi^36*xs^26*xq^5*xx^2-108837055835721934119811815792480000*xi^38*xs^22*xq^4*xx^2+74225079571466534732287110000000*xi^31*xs^27*xq^7*xm-5478703025671665081130556250000*xi^31*xs^27*xq^6*xx-74704724715643457739042429774720000*xi^33*xs^23*xq^6*xm+11028213204877484589358989021600000*xi^33*xs^23*xq^5*xx+5549738958397177241375463369691161600*xi^35*xs^19*xq^4*xx+838097963683037350868476629000000*xi^28*xs^24*xq^6+843513782984895911949100826630208000*xi^30*xs^20*xq^5+44966607006022796765863385067420000*xi^30*xs^18*xq^3*xx^3-6834547186450005797746531273350000*xi^25*xs^19*xq^4*xx^2-6878712277138422918674780919773539200*xi^27*xs^15*xq^3*xx^2-9382336966014209142468610978800000*xi^20*xs^20*xq^6*xm+692529239717156422552932938250000*xi^20*xs^20*xq^5*xx-4721482983124597979682098146116748800*xi^22*xs^16*xq^5*xm-348502194334406472120140892161832000*xi^22*xs^16*xq^4*xx-6192730745081552488935068231872500*xi^22*xs^14*xq^2*xx^4+350754228097287862950093735434296779264*xi^24*xs^12*xq^3*xx-52969411088562828571719527634660000*xi^17*xs^17*xq^5+941243142596252736787824836081250*xi^17*xs^15*xq^3*xx^3+53311701335541656318410473415066072320*xi^19*xs^13*xq^4+2841976469305289107547844603931306800*xi^19*xs^11*xq^2*xx^3+287971060831074018584512555953906000*xi^14*xs^12*xq^3*xx^2-434747910335560835498999032117402335168*xi^16*xs^8*xq^2*xx^2+296490914701815853453876832757276000*xi^9*xs^13*xq^5*xm-21884593197330048582156352522702500*xi^9*xs^13*xq^4*xx-298406849697781401880969749855731780352*xi^11*xs^9*xq^4*xm-391392551719721817287911771399348650*xi^11*xs^7*xq*xx^4-59488385743563588581496023954827625*xi^6*xs^8*xq^2*xx^3+179618405520415443598430155669725651672*xi^8*xs^4*xq*xx^3+123288373019930126966969810992237725408*xi^3*xs^5*xq^3*xx*xm-9100163801698196828012708795286589620*xi^3*xs^5*xq^2*xx^2-24736765709269953551573032337976695021*xx^4,-14433782545996547760000*xi^30*xs^18*xq^3*xx*xm-2193813908982703800000*xi^25*xs^19*xq^4*xm+161929835175610125000*xi^25*xs^19*xq^3*xx-325952463234374213328000*xi^27*xs^15*xq^2*xx-24771020528817746820000*xi^22*xs^16*xq^3-912242952938328692990400*xi^19*xs^11*xq^2*xx*xm+202003484075704335843000*xi^19*xs^11*xq*xx^2+138653279010542621052000*xi^14*xs^12*xq^3*xm-10234278543318353842500*xi^14*xs^12*xq^2*xx-10300412820786259198678560*xi^16*xs^8*xq*xx-27819603695730349764625*xi^11*xs^7*xx^3-57655517708797884729102816*xi^8*xs^4*xq*xx*xm+4255670201252115006646740*xi^8*xs^4*xx^2+98947452492997335990404712*xs^2*xq+23820683007573432738430764*xx^2*xm,-30806568*xi^8*xs^4*xq+15271632*xi^3*xs^3*xq^2*xm^2-1127230*xi^3*xs^3*xq*xx*xm+12727897*xx,9752*xi^3*xs*xq*xx*xm^3+2990*xi^3*xs^3*xq*xm-33761; |
---|
269 | char_series(PS); |
---|
270 | |
---|
271 | //end J. Kroeker |
---|
272 | |
---|
273 | tst_status(1);$ |
---|