Changeset 80a2d8 in git
- Timestamp:
- Jan 9, 2023, 4:19:16 PM (16 months ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- 69eed9010f45a15ad5528d8b504425ac16cf2743
- Parents:
- 5fd36466ec90af62d5a73de9b58addcf5cc9db70
- File:
-
- 1 edited
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Singular/LIB/primdecint.lib
r5fd364 r80a2d8 15 15 polynomial ring over the integers, Z[x_1,...,x_n]. 16 16 The first procedure 'primdecZ' can be used in parallel. 17 The coefficients must always be ZZ. 17 18 18 19 Reference: Pfister, Sadiq, Steidel , \"An Algorithm for primary decomposition in polynomial rings over the integers\" , arXiv:1008.2074 … … 39 40 "USAGE: primdecZ(I[, n]); I ideal, n integer (number of processors) 40 41 NOTE: If size(#) > 0, then #[1] is the number of available processors for 41 the computation. 42 the computation.@* 43 The coefficients must be ZZ. 42 44 RETURN: a list pr of primary ideals and their associated primes: 43 45 @format … … 48 50 " 49 51 { 52 if (coeffs(basering)!=ZZ) { ERROR("coefficoents must be ZZ"); } 50 53 if(size(I)==0){return(list(list(ideal(0),ideal(0))));} 51 54 … … 400 403 proc minAssZ(ideal I) 401 404 "USAGE: minAssZ(I); I ideal 405 The coefficients must be ZZ. 402 406 RETURN: a list pr of associated primes: 403 407 EXAMPLE: example minAssZ; shows an example 404 408 " 405 409 { 410 if (coeffs(basering)!=ZZ) { ERROR("coefficoents must be ZZ"); } 406 411 if(size(I)==0){return(list(ideal(0)));} 407 412 if(deg(I[1])==0) … … 537 542 proc heightZ(ideal I) 538 543 "USAGE: heightZ(I); I ideal 544 The coefficients must be ZZ. 539 545 RETURN: the height of the input ideal 540 546 EXAMPLE: example heightZ; shows an example 541 547 " 542 548 { 549 if (coeffs(basering)!=ZZ) { ERROR("coefficoents must be ZZ"); } 543 550 if(size(I)==0){return(0);} 544 551 if(deg(I[1])==0) … … 630 637 proc radicalZ(ideal I) 631 638 "USAGE: radicalZ(I); I ideal 639 The coefficients must be ZZ. 632 640 RETURN: the radcal of the input ideal 633 641 EXAMPLE: example radicalZ; shows an example 634 642 " 635 643 { 644 if (coeffs(basering)!=ZZ) { ERROR("coefficoents must be ZZ"); } 636 645 if(size(I)==0){return(ideal(0));} 637 646 if(deg(I[1])==0) … … 733 742 proc equidimZ(ideal I) 734 743 "USAGE: equidimZ(I); I ideal 744 The coefficients must be ZZ. 735 745 RETURN: the part of minimal height 736 746 EXAMPLE: example equidimZ; shows an example 737 747 " 738 748 { 749 if (coeffs(basering)!=ZZ) { ERROR("coefficoents must be ZZ"); } 739 750 if(size(I)==0){return(ideal(0));} 740 751 if(deg(I[1])==0) … … 914 925 proc intersectZ(ideal I, ideal J) 915 926 "USAGE: intersectZ(I,J); I,J ideals 927 The coefficients must be ZZ. 916 928 RETURN: the intersection of the input ideals 917 929 NOTE: this is an alternative to intersect(I,J) over integers, … … 919 931 EXAMPLE: example intersectZ; shows an example 920 932 { 933 if (coeffs(basering)!=ZZ) { ERROR("coefficoents must be ZZ"); } 921 934 def R = basering; 922 935 ring S=integer,( X(1..nvars(R)) ), ( dp(nvars(R)) ); … … 1501 1514 proc primdecZM(module N) 1502 1515 "USAGE: primdecZM(N); N module 1516 The coefficients must be ZZ. 1503 1517 RETURN: a list pr of primary modules and their associated primes: 1504 1518 @format
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