Takes a list of solutions s∈Gr(k,n) in global coordinates and writes them as solutions in coordinates of the affine patch that has an identity matrix in the last k rows.
i1 : Pblm = { ({2,1}, random(RR^6,RR^6)), ({2,1}, random(RR^6,RR^6)), ({2,1}, random(RR^6,RR^6)) } o1 = {({2, 1}, | .892712 .89189 .0741835 .741046 .830833 .191734 |), ({2, | .673395 .231053 .808694 .108386 .538554 .403215 | | .29398 .461944 .362835 .348931 .873665 .615911 | | .632944 .775187 .706096 .562428 .415912 .0147867 | | .0258884 .909047 .127435 .246268 .606588 .223028 | | .714827 .314897 .254482 .153346 .848005 .388829 | ------------------------------------------------------------------------ 1}, | .557119 .96518 .0647412 .174853 .444183 .184779 |), ({2, 1}, | | .873708 .681683 .877846 .626892 .644366 .370833 | | | .7037 .914199 .0340514 .350611 .194945 .339222 | | | .681869 .887381 .507989 .379495 .518585 .062212 | | | .276259 .169813 .150294 .237252 .987173 .465736 | | | .605659 .965004 .656391 .116721 .568273 .40273 | | ------------------------------------------------------------------------ .164647 .562839 .0645275 .501243 .205375 .0821679 |)} .713493 .629991 .283709 .154289 .276652 .10394 | .909537 .479826 .977573 .467203 .0958269 .280679 | .566034 .815167 .212436 .765564 .605398 .475179 | .305423 .97723 .592747 .305946 .883549 .130004 | .732358 .0595849 .831802 .53632 .942865 .522285 | o1 : List |
i2 : S = solveSchubertProblem(Pblm, 3,6) o2 = {| .362674 5.87881 .067722 |, | .675164 .770431 -.0909566 |} | -.168148 10.2268 .359604 | | .0675706 .870501 .150312 | | .287667 5.41301 .178413 | | .390574 .658364 -.00751668 | | .399967 10.4365 .172408 | | .621526 1.17845 -.0078269 | | .893699 2.90938 .127632 | | .902762 .284467 .0636297 | | -.108865 5.44614 .099289 | | .141356 .394186 -.0692081 | o2 : List |
i3 : solutionsToAffineCoords S o3 = {| 1.17594 -.247384 -1.04186 |, | -.0717886 .515973 1.79675 |} | -2.59821 1.69933 5.94898 | | 1.97727 -.796664 -3.12795 | | -.743029 .890962 1.94183 | | .504284 .067644 .113771 | | 1 0 0 | | 1 0 0 | | 0 1 0 | | 0 1 0 | | 0 0 1 | | 0 0 1 | o3 : List |
This function may fail if the solutions are not in general position (if they cannot fit the specific local coordinates) One way to avoid this is by applying a random linear transformation to the solutions before calling this function