Changeset 5e8ee4c in git
- Timestamp:
- Oct 7, 2010, 3:48:33 PM (14 years ago)
- Branches:
- (u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '38dfc5131670d387a89455159ed1e071997eec94')
- Children:
- 8d87a654ad26db0893bc025c45fce87ebb749861
- Parents:
- 74270fcc741b7e84fe134ae44fa743f228c4c83d
- Location:
- Singular/LIB
- Files:
-
- 2 edited
-
fpadim.lib (modified) (32 diffs)
-
paraplanecurves.lib (modified) (8 diffs)
Legend:
- Unmodified
- Added
- Removed
-
Singular/LIB/fpadim.lib
r74270f r5e8ee4c 22 22 @* K-dimension. One has to check if the graph contains cycles. 23 23 @* For the whole theory we refer to [ufna]. Given a 24 @* reduced set of monomials GB one can define the basis tree, wh ichvertex24 @* reduced set of monomials GB one can define the basis tree, whose vertex 25 25 @* set V consists of all normal monomials w.r.t. GB. For every two 26 26 @* monomials m_1, m_2 in V there is a direct edge from m_1 to m_2, if and … … 41 41 @* 42 42 43 R eferences:43 REFERENCES: 44 44 45 45 @* [ufna] Ufnarovskij: Combinatorical and asymptotic methods in algebra, 1990 … … 103 103 static proc allVars(list L, intvec P, int n) 104 104 "USAGE: allVars(L,P,n); L a list of intmats, P an intvec, n an integer 105 RETURN: 0,if all variables are contained in the quotient algebra, 1 otherwise105 RETURN: int, 0 if all variables are contained in the quotient algebra, 1 otherwise 106 106 " 107 107 {int i,j,r; … … 129 129 static proc createStartMat(int d, int n) 130 130 "USAGE: createStartMat(d,n); d, n integers 131 RETURN: Anintmat131 RETURN: intmat 132 132 PURPOSE:Creating the intmat with all normal monomials in n variables and of degree d to start with 133 133 NOTE: d has to be > 0 … … 151 151 static proc createStartMat1(int n, intmat M) 152 152 "USAGE: createStartMat1(n,M); n an integer, M an intmat 153 RETURN: An intmatwith all variables except those in M153 RETURN: intmat, with all variables except those in M 154 154 " 155 155 {int i; … … 175 175 "USAGE: findDimen(V,n,L,P,degbound); V,P intvecs, n, an integer, L a list, 176 176 @* degbound an optional integer 177 RETURN: An integer177 RETURN: int 178 178 PURPOSE:Computing the K-dimension of the quotient algebra 179 179 " … … 242 242 static proc findCycle(intvec V, list L, intvec P, int n, int ld, module M) 243 243 "USAGE: 244 RETURN: 1,if Ufn-graph contains a cycle, or 0 otherwise244 RETURN: int, 1 if Ufn-graph contains a cycle, or 0 otherwise 245 245 PURPOSE:Searching the Ufnarovskij graph for cycles 246 246 " … … 323 323 static proc findHCoeff(intvec V,int n,list L,intvec P,intvec H,list #) 324 324 "USAGE: findHCoeff(V,n,L,P,H,degbound); L a list of intmats, degbound an integer 325 RETURN: Anintvec325 RETURN: intvec 326 326 PURPOSE:Computing the coefficient of the Hilbert series (upto degree degbound) 327 327 NOTE: Starting with a part of the Hilbert series we change the coefficient … … 402 402 "USAGE: findHCoeffMis(V,n,L,P,R,degbound); degbound an optional integer, L a 403 403 @* list of Intmats, R 404 RETURN: Alist404 RETURN: list 405 405 PURPOSE:Computing the coefficients of the Hilbert series and the Mistletoes all 406 406 @* at once … … 484 484 static proc findMisDim(intvec V,int n,list L,intvec P,list R,list #) 485 485 "USAGE: 486 RETURN: Alist486 RETURN: list 487 487 PURPOSE:Computing the K-dimension and the Mistletoes all at once 488 488 " … … 568 568 @* variables, L the GB, P the occuring degrees, 569 569 @* and degbound the (optional) degreebound 570 RETURN: Alist570 RETURN: list 571 571 PURPOSE:Computing mistletoes starting in V 572 572 NOTE: V has to be normal w.r.t. L, it will not be checked for being so … … 642 642 static proc isInList(intvec V, list L) 643 643 "USAGE: isInList(V,L); V an intvec, L a list of intvecs 644 RETURN: An integer644 RETURN: int 645 645 PURPOSE:Finding the position of V in L, returns 0, if V is not in M 646 646 " … … 653 653 static proc isInMat(intvec V, intmat M) 654 654 "USAGE: isInMat(V,M);V an intvec, M an intmat 655 RETURN: An integer655 RETURN: int 656 656 PURPOSE:Finding the position of V in M, returns 0, if V is not in M 657 657 " … … 668 668 static proc isInVec(int v,intvec V) 669 669 "USAGE: isInVec(v,V); v an integer,V an intvec 670 RETURN: An integer670 RETURN: int 671 671 PURPOSE:Finding the position of v in V, returns 0, if v is not in V 672 672 " … … 1065 1065 "USAGE: ivHilbert(L,n[,degbound]); L a list of intmats, n an integer, 1066 1066 @* degbound an optional integer 1067 RETURN: Anintvec, containing the coefficients of the Hilbert series1067 RETURN: intvec, containing the coefficients of the Hilbert series 1068 1068 PURPOSE:Computing the Hilbert series 1069 1069 ASSUME: - basering is a Letterplace ring. … … 1150 1150 "USAGE: ivKDim(L,n[,degbound]); L a list of intmats, 1151 1151 @* n an integer, degbound an optional integer 1152 RETURN: An integer, the K-dimension of A/<L>1152 RETURN: int, the K-dimension of A/<L> 1153 1153 PURPOSE:Computing the K-dimension of A/<L> 1154 1154 ASSUME: - basering is a Letterplace ring. … … 1231 1231 proc ivMis2Dim(list M) 1232 1232 "USAGE: ivMis2Dim(M); M a list of intvecs 1233 RETURN: An integer, the K-dimension of the given algebra1233 RETURN: int, the K-dimension of the given algebra 1234 1234 PURPOSE:Computing the K-dimension out of given mistletoes 1235 1235 ASSUME: - The mistletoes have to be ordered lexicographically -> OrdMisLex. … … 1267 1267 proc ivOrdMisLex(list M) 1268 1268 "USAGE: ivOrdMisLex(M); M a list of intvecs 1269 RETURN: Alist, containing the ordered intvecs of M1269 RETURN: list, containing the ordered intvecs of M 1270 1270 PURPOSE:Orders a given set of mistletoes lexicographically 1271 1271 ASSUME: - basering is a Letterplace ring. … … 1295 1295 "USAGE: ivSickle(L,n,[degbound]); L a list of intmats, n an int, degbound an 1296 1296 @* optional integer 1297 RETURN: Alist, containing intvecs, the mistletoes of A/<L>1297 RETURN: list, containing intvecs, the mistletoes of A/<L> 1298 1298 PURPOSE:Computing the mistletoes for a given Groebner basis L 1299 1299 ASSUME: - basering is a Letterplace ring. … … 1374 1374 "USAGE: ivSickleDim(L,n[,degbound]); L a list of intmats, n an integer, degbound 1375 1375 @* an optional integer 1376 RETURN: Alist1376 RETURN: list 1377 1377 PURPOSE:Computing mistletoes and the K-dimension 1378 1378 ASSUME: - basering is a Letterplace ring. … … 1461 1461 "USAGE:ivSickleHil(L,n[,degbound]); L a list of intmats, n an integer, 1462 1462 @* degbound an optional integer 1463 RETURN: Alist1463 RETURN: list 1464 1464 PURPOSE:Computing the mistletoes and the Hilbert series 1465 1465 ASSUME: - basering is a Letterplace ring. … … 1547 1547 proc lpDHilbert(ideal G, list #) 1548 1548 "USAGE: lpDHilbert(G[,degbound,n]); G an ideal, degbound, n optional integers 1549 RETURN: Alist1549 RETURN: list 1550 1550 PURPOSE:Computing K-dimension and Hilbert series, starting with a lp-ideal 1551 1551 ASSUME: - basering is a Letterplace ring. 1552 1552 @* - if you specify a different degree bound degbound, 1553 1553 @* degbound <= attrib(basering,uptodeg) holds. 1554 NOTE: - If L is the list returned, then L[1] is an integer, L[2] is an intvec. 1554 NOTE: - If L is the list returned, then L[1] is an integer corresponding to the 1555 @* dimension, L[2] is an intvec which contains the coefficients of the 1556 @* Hilbert series 1555 1557 @* - If degbound is set, there will be a degree bound added. 0 means no 1556 1558 @* degree bound. Default: attrib(basering,uptodeg). … … 1587 1589 "USAGE: lpDHilbertSickle(G[,degbound,n]); G an ideal, degbound, n optional 1588 1590 @* integers 1589 RETURN: Alist1591 RETURN: list 1590 1592 PURPOSE:Computing K-dimension, Hilbert series and mistletoes at once 1591 1593 ASSUME: - basering is a Letterplace ring. … … 1629 1631 proc lpHilbert(ideal G, list #) 1630 1632 "USAGE: lpHilbert(G[,degbound,n]); G an ideal, degbound, n optional integers 1631 RETURN: Anintvec, containing the coefficients of the Hilbert series1633 RETURN: intvec, containing the coefficients of the Hilbert series 1632 1634 PURPOSE:Computing the Hilbert series 1633 1635 ASSUME: - basering is a Letterplace ring. … … 1667 1669 proc lpDimCheck(ideal G) 1668 1670 "USAGE: lpDimCheck(G); 1669 RETURN: 1,if K-dimension of the factor algebra is infinite, 0 otherwise1671 RETURN: int, 1 if K-dimension of the factor algebra is infinite, 0 otherwise 1670 1672 PURPOSE:Checking a factor algebra for finiteness of the K-dimension 1671 1673 ASSUME: - basering is a Letterplace ring. … … 1695 1697 proc lpKDim(ideal G, list #) 1696 1698 "USAGE: lpKDim(G[,degbound, n]); G an ideal, degbound, n optional integers 1697 RETURN: An integer, the K-dimension of the factor algebra1699 RETURN: int, the K-dimension of the factor algebra 1698 1700 PURPOSE:Computing the K-dimension of a factor algebra, given via an ideal 1699 1701 ASSUME: - basering is a Letterplace ring … … 1730 1732 proc lpMis2Dim(ideal M) 1731 1733 "USAGE: lpMis2Dim(M); M an ideal 1732 RETURN: An integer, the K-dimension of the factor algebra1734 RETURN: int, the K-dimension of the factor algebra 1733 1735 PURPOSE:Computing the K-dimension out of given mistletoes 1734 1736 ASSUME: - basering is a Letterplace ring. … … 1754 1756 proc lpOrdMisLex(ideal M) 1755 1757 "USAGE: lpOrdMisLex(M); M an ideal of mistletoes 1756 RETURN: Anideal, containing the mistletoes, ordered lexicographically1758 RETURN: ideal, containing the mistletoes, ordered lexicographically 1757 1759 PURPOSE:A given set of mistletoes is ordered lexicographically 1758 1760 ASSUME: - basering is a Letterplace ring. … … 1775 1777 proc lpSickle(ideal G, list #) 1776 1778 "USAGE: lpSickle(G[,degbound,n]); G an ideal, degbound, n optional integers 1777 RETURN: Anideal1779 RETURN: ideal 1778 1780 PURPOSE:Computing the mistletoes of K[X]/<G> 1779 1781 ASSUME: - basering is a Letterplace ring. … … 1813 1815 proc lpSickleDim(ideal G, list #) 1814 1816 "USAGE: lpSickleDim(G[,degbound,n]); G an ideal, degbound, n optional integers 1815 RETURN: Alist1817 RETURN: list 1816 1818 PURPOSE:Computing the K-dimension and the mistletoes 1817 1819 ASSUME: - basering is a Letterplace ring. … … 1852 1854 proc lpSickleHil(ideal G, list #) 1853 1855 "USAGE: lpSickleHil(G); 1854 RETURN: Alist1856 RETURN: list 1855 1857 PURPOSE:Computing the Hilbert series and the mistletoes 1856 1858 ASSUME: - basering is a Letterplace ring. … … 1894 1896 "USAGE: sickle(G[,m, d, h, degbound]); G an ideal; m,d,h,degbound optional 1895 1897 @* integers 1896 RETURN: Alist1898 RETURN: list 1897 1899 PURPOSE:Allowing the user to access all procs with one command 1898 1900 ASSUME: - basering is a Letterplace ring. -
Singular/LIB/paraplanecurves.lib
r74270f r5e8ee4c 12 12 OVERVIEW: 13 13 14 Suppose C = {f(x,y,z)=0} is a rational plane curve, where f is homogeneous 15 of degree n with coefficients in Q and absolutely irreducible (these 14 Suppose C = {f(x,y,z)=0} is a rational plane curve, where f is homogeneous 15 of degree n with coefficients in Q and absolutely irreducible (these 16 16 conditions are checked automatically.) @* 17 17 After a first step, realized by a projective automorphism in the procedure … … 23 23 and y as algebraic and computes an integral basis in C(x)[y] of the integral 24 24 closure of C[x] in C(x,y) using the normalization algorithm from 25 @ref{normal_lib}: see @ref{integralbasis_lib}. In a future edition of the 26 library, also van Hoeij's algorithm for computing the integral basis will 25 @ref{normal_lib}: see @ref{integralbasis_lib}. In a future edition of the 26 library, also van Hoeij's algorithm for computing the integral basis will 27 27 be available. @* 28 28 From the integral basis, the adjoint ideal is obtained by linear algebra. … … 107 107 NOTE: The procedure might fail or give a wrong output if phi does 108 108 not define a birational map. 109 RETURN: ring, the coordinate ring of P, with an ideal named J and an ideal 109 RETURN: ring, the coordinate ring of P, with an ideal named J and an ideal 110 110 named psi.@* 111 111 The ideal J defines the image of phi.@* … … 663 663 } 664 664 j = j+1; 665 } 665 } 666 666 B = intersect(B,A); 667 667 i = i-1; 668 668 } 669 669 } //end else 670 B = intersect(B,homog(std(LL4),var(3))); // add nodes and cusps 670 B = intersect(B,homog(std(LL4),var(3))); // add nodes and cusps 671 671 if(sizeLL2==0) // ordinary multiple points plus cusps only 672 672 { … … 901 901 proc rncAntiCanonicalMap(ideal I) 902 902 "USAGE: rncAntiCanonicalMap(I); I ideal 903 ASSUME: I is a homogeneous ideal in the basering 903 ASSUME: I is a homogeneous ideal in the basering 904 904 defining a rational normal curve C in PP^n. 905 905 NOTE: The procedure will fail or give a wrong output if I is not the … … 945 945 proc rncItProjOdd(ideal I) 946 946 "USAGE: rncItProjOdd(I); I ideal 947 ASSUME: I is a homogeneous ideal in the basering with n+1 variables 947 ASSUME: I is a homogeneous ideal in the basering with n+1 variables 948 948 defining a rational normal curve C in PP^n with n odd. 949 949 NOTE: The procedure will fail or give a wrong output if I is not the … … 1059 1059 proc rncItProjEven(ideal I) 1060 1060 "USAGE: rncItProjEven(I); I ideal 1061 ASSUME: I is a homogeneous ideal in the basering with n+1 variables 1061 ASSUME: I is a homogeneous ideal in the basering with n+1 variables 1062 1062 defining a rational normal curve C in PP^n with n even. 1063 1063 NOTE: The procedure will fail or give a wrong output if I is not the 1064 1064 ideal of a rational normal curve. It will test whether n is odd. 1065 1065 RETURN: ring with an ideal CONIC defining a conic C2 in PP^2.@* 1066 In addition, an ideal PHI in the basering defining an isomorphic 1066 In addition, an ideal PHI in the basering defining an isomorphic 1067 1067 projection of C to C2 will be exported.@* 1068 1068 Note that the entries of PHI should be considered as … … 2537 2537 RETURN: int which is 1 if PARA defines a parametrization of the curve 2538 2538 {f=0} and 0, otherwise. 2539 THEORY: We compute the polynomial defining the image of PARA 2539 THEORY: We compute the polynomial defining the image of PARA 2540 2540 and compare it with f. 2541 2541 KEYWORDS: Parametrization, image.
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