# Changeset 4b56a8 in git

Ignore:
Timestamp:
Feb 6, 2020, 2:27:22 PM (4 years ago)
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'c7af8613769b29c741d6c338945669719f1fc4f8')
Children:
Parents:
48d798e6fa161513a1be9c743406d7c43a479b9d
Message:
`fix: avoid warning in invar.lib`
Files:
4 edited

Unmodified
Removed
• ## Singular/LIB/invar.lib

 r48d798e torusrep(list m)       representation of a torus given by the weights m[1],m[2],... finiterep()      representation of a by a list of matrices prod(l)                gives the product of all entries of list l monsum(n,d)            sum of all monomials in x(1),x(2),...,x(n) of degree d sympower(m,d)          computes the d-th symmetric power of a representation m invar(m)               computes the invariant ring of the representation m. } example {       "> SL(3);"; SL(3); "> group;"; Invar::group; "> groupideal;"; groupideal; "> print(SLrep);"; print(SLrep); {"EXAMPLE:"; echo=2; SL(3); Invar::group; groupideal; print(SLrep); } // prod() just gives the product of all entries of . //////////////////////////////////////////////////////////////////////////////// proc prod(list #) static proc prod(list #) "USAGE: prod() RETURN: the product of all entries of " // monsum(n,d) is the sum of all monomials in x(1),x(2),...,x(n) of degree d //////////////////////////////////////////////////////////////////////////////// proc monsum(int n,int d) static proc monsum(int n,int d) "USAGE: monsum(n,d) RETURNS: the sum of all monomials in x(1),x(2),...,x(n) of degree d" } example {       "> SL(2);"; SL(2); "> print(SLrep);"; print(SLrep); "> print(sympower(SLrep,3));"; print(sympower(SLrep,3));               // doesn't work in the example // environment. Bug in Singular?? // We'll have to cheat: //"g(1)^3,     3*g(1)^2*g(2),          3*g(1)*g(2)^2,          g(2)^3,"; //"g(1)^2*g(3),3*g(1)^2*g(4)-2*g(1),   3*g(1)*g(2)*g(4)-1*g(2),g(2)^2*g(4),"; //"g(1)*g(3)^2,3*g(1)*g(3)*g(4)-1*g(3),3*g(1)*g(4)^2-2*g(4),   g(2)*g(4)^2,"; //"g(3)^3,     3*g(3)^2*g(4),          3*g(3)*g(4)^2,          g(4)^3"; { "EXAMPLE:"; echo=2; SL(2); print(SLrep); print(sympower(SLrep,3)); } The base ring will be set to 'polyring' which is a global variable representing the polynomial ring on which the group acts. The variable 'representation' will be set to the input m." The variable 'representation' will be set to the input m. EXAMPLE: example invar; shows an example " { int n=nrows(m); print(invring); } example { "EXAMPLE:"; echo=2; SL(2);                          // Take the group SL_2 matrix m=dsum(SLrep,SLrep,SLrep,SLrep); // 4 copies of the standard representation invar(m);                       // empirical evidence for FFT reynolds(x(1)*x(4));            // The reynolds operator is computed using // the Omega process. } //////////////////////////////////////////////////////////////////////////////// } example {       "> torus(3);"; torus(3); "> group;"; Invar::group; "> groupideal;"; groupideal; {"EXAMPLE:"; echo=2; torus(3); Invar::group; groupideal; } RETURNS: torusrep(m) gives a matrix with entries in 'group'. This matrix represents the action of the torus with weights m[1],m[2],...,m[size(m)]" m[1],m[2],...,m[size(m)] EXAMPLE: example torusreynolds; shows an example " {       int r=size(m[1]); int n=size(m); return(mm); } example { "EXAMPLE:"; echo=2; torus(1);                  // Take the 1-dimensional torus, the multiplicative group. list weights=-2,-3,7;      // 3-dimensial action with weights -2,-3,7 matrix m=torusrep(weights);// compute the matrix of the representation invar(m);                  // compute the invariant ring } //////////////////////////////////////////////////////////////////////////////// int i=prime(n-1); while(i<>2) {if (n%i==0) {f=f*(z**(n/i)-1);}; {if (n%i==0) {f=f*(z**(n div i)-1);}; i=prime(i-1);}; if (n%2==0) {f=f*(z**(n/2)-1);}; h=h/GCD(f,h); if (n%2==0) {f=f*(z**(n div 2)-1);}; h=h/gcd(f,h); return(h/leadcoef(h)); } groupideal   of type reynolds     of type The basering will be set to 'group'." The basering will be set to 'group'. EXAMPLE: example finite; shows an example " {       ring group=0,(g(1),g(2)),dp(2); export group; // 'finitereynolds' } example {"EXAMPLE:"; echo=2; finite(6);                              // The symmetric group S_3 matrix id=unitmat(3);                   // identity matrix matrix m3[3][3]=0,1,0,0,0,1,1,0,0;      // corresponds with (1 2 3) matrix m2[3][3]=0,1,0,1,0,0,0,0,1;      // corresponds with (1 2) list a=id,m3,m3*m3,m2,m2*m3,m2*m3*m3;   // all elements of S_3 matrix rep=finiterep(a);                // compute matrix of standard repr. invar(rep);                             // compute the invariant ring } //////////////////////////////////////////////////////////////////////////////// RETURNS: finiterep(m) gives a matrix with coefficients in the ring 'group' which represents the action of the finite group where the elements of the finite group act as m[1],m[2],...m[size(m)]." of the finite group act as m[1],m[2],...m[size(m)]. EXAMPLE: example finiterep; shows an example " {       int l=size(m); int n=nrows(m[1]); return(finiterep); } example {"EXAMPLE:"; echo=2; finite(6);                              // The symmetric group S_3 matrix id=unitmat(3);                   // identity matrix matrix m3[3][3]=0,1,0,0,0,1,1,0,0;      // corresponds with (1 2 3) matrix m2[3][3]=0,1,0,1,0,0,0,0,1;      // corresponds with (1 2) list a=id,m3,m3*m3,m2,m2*m3,m2*m3*m3;   // all elements of S_3 matrix rep=finiterep(a);                // compute matrix of standard repr. invar(rep);                             // compute the invariant ring }
• ## Tst/Short/invar_lib.res.gz.uu

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• ## Tst/Short/invar_lib.stat

 r48d798e 1 >> tst_memory_0 :: 1580992983:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:133488 1 >> tst_memory_1 :: 1580992983:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:2387968 1 >> tst_memory_2 :: 1580992983:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:7054016 1 >> tst_timer_1 :: 1580992983:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:269 1 >> tst_memory_0 :: 1580995615:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:136856 1 >> tst_memory_1 :: 1580995615:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:2363392 1 >> tst_memory_2 :: 1580995615:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:7055224 1 >> tst_timer_1 :: 1580995615:4122, 64 bit:4.1.2:x86_64-Linux:nepomuck:267
• ## Tst/Short/invar_lib.tst

 r48d798e LIB "matrix.lib";               // read the libraries LIB "matrix.lib"; LIB "invar.lib"; // 4 copies of the standard representation invar(m);                       // empirical evidence for FFT reynolds(x(1)*x(4));            // The reynolds operator is computed using // the Omega process. setring Invar::polyring; // The reynolds operator is computed using the Omega process. Invar::reynolds(x(1)*x(4)); setring Invar::group; LIB "matrix.lib";               // read the libraries LIB "invar.lib"; SL(2); // Tori //////////////////////////////////////////////////////////////////////////////// LIB "invar.lib";                // read the library "EXAMPLE 1:"; //////////////////////////////////////////////////////////////////////////////// LIB "matrix.lib";               // read the libraries LIB "invar.lib"; "EXAMPLE 1:"; finite(6);                              // The symmetric group S_3 //////////////////////////////////////////////////////////////////////////////// LIB "invar.lib";                // read the library "EXAMPLE 1:"; SL(2);                          // set the current group to SL_2
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