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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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            User manual for Singular version 3-1-1, Feb 2010, generated by texi2html.