|
D.4.3.1 assPrimes
Procedure from library assprime.lib (see assprime_lib).
- Usage:
- assPrimes(I,[n],[a]); I ideal or module,
optional: n number of processors (for parallel computing), a
- a=1: method of Eisenbud/Hunecke/Vasconcelos
- a=2: method of Gianni/Trager/Zacharias
- a=3: mathod of Monico
assPrimes(I) chooses n=a=1
- Assume:
- I is zero-dimensional over Q[variables]
- Return:
- a list pr of associated primes of I:
Example:
| LIB "assprime.lib";
ring R=0,(a,b,c,d,e,f),dp;
ideal I=
2fb+2ec+d2+a2+a,
2fc+2ed+2ba+b,
2fd+e2+2ca+c+b2,
2fe+2da+d+2cb,
f2+2ea+e+2db+c2,
2fa+f+2eb+2dc;
assPrimes(I);
==> [1]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=27a+41b+75c+100d-24e+f
==> [2]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2-46008a-6\
9864b-115416c-183900d-184932e-270732f+8521
==> [3]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2-810a-123\
0b+10134c-16500d-225108e-269058f+20653
==> [4]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2-50382a-7\
6506b-127566c-200100d-181044e-270894f+8161
==> [5]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2-72090a-1\
09470b-187866c-280500d-161748e-271698f+34513
==> [6]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=8256ac-9000ad-36600bd+111252d2-150552ae-203616be-60696ce-84168de-\
13260e2-179352af-16512bf-24768cf-37944df-74376ef-67488f2+6966a+10578b+234\
78c+21300d-81468e-89418f+7927
==> [7]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2-51354a-7\
7982b-130266c-203700d-180180e-270930f+20497
==> [8]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=688ac-750ad-3050bd+9271d2-12546ae-16968be-5058ce-7014de-1105e2-14\
946af-1376bf-2064cf-3162df-6198ef-5624f2-702a-1066b-1606c-2975d-5649e-749\
9f+817
==> [9]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2+51354a+7\
7982b+155034c+176700d-271476e-267126f+71851
==> [10]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2+50382a+7\
6506b+152334c+173100d-270612e-267162f+58543
==> [11]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=8256ac-9000ad-36600bd+111252d2-150552ae-203616be-60696ce-84168de-\
13260e2-179352af-16512bf-24768cf-37944df-74376ef-67488f2-6966a-10578b-152\
22c-30300d-69084e-89934f+961
==> [12]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=6192ac-6750ad-27450bd+83439d2-112914ae-152712be-45522ce-63126de-9\
945e2-134514af-12384bf-18576cf-28458df-55782ef-50616f2-11502a-17466b-2885\
4c-45975d-46233e-67683f+8281
==> [13]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=8256ac-9000ad-36600bd+111252d2-150552ae-203616be-60696ce-84168de-\
13260e2-179352af-16512bf-24768cf-37944df-74376ef-67488f2-6642a-10086b-143\
22c-29100d-69372e-89922f+4957
==> [14]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=8256ac-9000ad-36600bd+111252d2-150552ae-203616be-60696ce-84168de-\
13260e2-179352af-16512bf-24768cf-37944df-74376ef-67488f2-8424a-12792b-192\
72c-35700d-67788e-89988f+1603
==> [15]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2+810a+123\
0b+14634c-10500d-226548e-268998f+21463
==> [16]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2+72090a+1\
09470b+212634c+253500d-289908e-266358f+106603
==> [17]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2-162a-246\
b+11934c-14100d-225684e-269034f+9091
==> [18]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2+71118a+1\
07994b+209934c+249900d-289044e-266394f+92911
==> [19]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2+162a+246\
b+12834c-12900d-225972e-269022f+9253
==> [20]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2+46008a+6\
9864b+140184c+156900d-266724e-267324f+54529
==> [21]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=8256ac-9000ad-36600bd+111252d2-150552ae-203616be-60696ce-84168de-\
13260e2-179352af-16512bf-24768cf-37944df-74376ef-67488f2+6642a+10086b+225\
78c+20100d-81180e-89430f+11599
==> [22]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=688ac-750ad-3050bd+9271d2-12546ae-16968be-5058ce-7014de-1105e2-14\
946af-1376bf-2064cf-3162df-6198ef-5624f2+702a+1066b+2294c+2225d-6897e-744\
7f+1519
==> [23]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=8256ac-9000ad-36600bd+111252d2-150552ae-203616be-60696ce-84168de-\
13260e2-179352af-16512bf-24768cf-37944df-74376ef-67488f2+8424a+12792b+275\
28c+26700d-82764e-89364f+10027
==> [24]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=24768ac-27000ad-109800bd+333756d2-451656ae-610848be-182088ce-2525\
04de-39780e2-538056af-49536bf-74304cf-113832df-223128ef-202464f2-71118a-1\
07994b-185166c-276900d-162612e-271662f+21793
==> [25]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=6192ac-6750ad-27450bd+83439d2-112914ae-152712be-45522ce-63126de-9\
945e2-134514af-12384bf-18576cf-28458df-55782ef-50616f2+11502a+17466b+3504\
6c+39225d-66681e-66831f+19783
==> [26]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=162a+246b+450c+600d-144e+6f-155
==> [27]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=162a+246b+450c+600d-144e+6f+1
==> [28]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=27a+41b+75c+100d-24e+f+26
==> [29]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=81a+123b+225c+300d-72e+3f-32
==> [30]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=54a+82b+150c+200d-48e+2f-73
==> [31]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=27a+41b+75c+100d-24e+f+1
==> [32]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=162a+246b+450c+600d-144e+6f+317
==> [33]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=81a+123b+225c+300d-72e+3f-29
==> [34]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=81a+123b+225c+300d-72e+3f+110
==> [35]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=27a+41b+75c+100d-24e+f+27
==> [36]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=162a+246b+450c+600d-144e+6f+161
==> [37]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=54a+82b+150c+200d-48e+2f+127
==> [38]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=162a+246b+450c+600d-144e+6f+97
==> [39]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=162a+246b+450c+600d-144e+6f+65
==> [40]:
==> _[1]=a2+d2+2ce+2bf+a
==> _[2]=2ab+2de+2cf+b
==> _[3]=b2+2ac+e2+2df+c
==> _[4]=2bc+2ad+2ef+d
==> _[5]=c2+2bd+2ae+f2+e
==> _[6]=2cd+2be+2af+f
==> _[7]=81a+123b+225c+300d-72e+3f+113
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