Changeset fc46db in git
 Timestamp:
 Mar 5, 2010, 11:35:28 PM (13 years ago)
 Branches:
 (u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')
 Children:
 1f190d7136840b518cb253adbb3225c11420b6ea
 Parents:
 f8fb471ddba04b92f5fdc0432fcc4d3df1b09514
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 1 edited
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Singular/LIB/control.lib
rf8fb471 rfc46db 12 12 13 13 MAIN PROCEDURES: 14 control(R) analysis of controllabilityrelated properties of R (using Ext modules)15 controlDim(R) analysis of controllabilityrelated properties of R (using dimension)16 autonom(R) analysis of autonomyrelated properties of R (using Ext modules)17 autonomDim(R) analysis of autonomyrelated properties of R (using dimension)14 control(R); analysis of controllabilityrelated properties of R (using Ext modules) 15 controlDim(R); analysis of controllabilityrelated properties of R (using dimension) 16 autonom(R); analysis of autonomyrelated properties of R (using Ext modules) 17 autonomDim(R); analysis of autonomyrelated properties of R (using dimension) 18 18 19 19 COMPONENT PROCEDURES: 20 leftKernel(R) a left kernel of R21 rightKernel(R) a right kernel of R22 leftInverse(R) a left inverse of R23 rightInverse(R) a right inverse of R24 colrank(M) a column rank of M as of matrix25 genericity(M) analysis of the genericity of parameters26 canonize(L) Groebnerification for modules in the output of control or autonomy procs27 iostruct(R) computes an IOstructure of behavior given by a module R28 findTorsion(R, I) generators of the submodule of a module R, annihilated by the ideal I20 leftKernel(R); a left kernel of R 21 rightKernel(R); a right kernel of R 22 leftInverse(R); a left inverse of R 23 rightInverse(R); a right inverse of R 24 colrank(M); a column rank of M as of matrix 25 genericity(M); analysis of the genericity of parameters 26 canonize(L); Groebnerification for modules in the output of control or autonomy procs 27 iostruct(R); computes an IOstructure of behavior given by a module R 28 findTorsion(R, I); generators of the submodule of a module R, annihilated by the ideal I 29 29 30 30 AUXILIARY PROCEDURES: 31 controlExample(s) set up an example from the mini database inside of the library32 view() wellformatted output of lists, modules and matrices31 controlExample(s); set up an example from the mini database inside of the library 32 view(); wellformatted output of lists, modules and matrices 33 33 "; 34 34 … … 246 246 " 247 247 { 248 return(transpose(leftInverse(transpose(R)))); 248 // for comm case it suffices 249 if (isCommutative()) 250 { 251 return(transpose(leftInverse(transpose(R)))); 252 } 253 // for noncomm 254 def save = basering; def sop = opposite(save); 255 setring sop; module Mop = oppose(save,R); 256 Mop = transpose(Mop); 257 module L = leftInverse(Mop); 258 setring save; module L = oppose(sop,L); 259 L = transpose(L); 260 return(matrix(L)); 249 261 } 250 262 example … … 1604 1616 return(@r); 1605 1617 } 1618 1619 /* noncomm examples for leftInverse/rightInverse: 1620 1621 LIB "jacobson.lib"; 1622 ring w = 0,(x,d),Dp; 1623 def W=nc_algebra(1,1); 1624 setring W; 1625 matrix m[3][3]=[d2,d+1,0],[d+1,0,d3x2*d],[2d+1, d3+d2, d2]; 1626 list J=jacobson(m,0); 1627 1628 leftInverse(J[3]); // exist 1629 rightInverse(J[3]); 1630 1631 leftInverse(J[1]); // zero 1632 rightInverse(J[1]); 1633 1634 list JJ = jacobson(J[1],0); 1635 1636 leftInverse(JJ[3]); // exist 1637 rightInverse(JJ[3]); 1638 1639 leftInverse(JJ[1]); // exist 1640 rightInverse(JJ[1]); 1641 1642 leftInverse(JJ[2]); // zero 1643 rightInverse(JJ[2]); 1644 1645 */
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