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lpdo [2015/02/20 16:32] kate [Orbits of Darboux transformations of type I] |
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operators defining the intertwining relation for the inverse. That is Ninv*L1=L*Minv. Operators A,G are operators that relates M and N: MA=GN (this relation is only true for invertible Darboux transformations). | operators defining the intertwining relation for the inverse. That is Ninv*L1=L*Minv. Operators A,G are operators that relates M and N: MA=GN (this relation is only true for invertible Darboux transformations). | ||

* <nowiki>LPDO__XYS_chain_of_first_order_invertible_DTs(chain,I1,I2,I3,I4,I5)</nowiki> applies Darboux transformations as indicated in argument "chain" to an operator given by its gauge invariants. Argument chain should be of the form of the list, where each element indicates Darboux transformation of certain type. Thus, e.g. [1,1,2,3] indicates the sequence: Darboux transformations with principal symbol Dx, then with Dx, then with Dy, and then with Dx+Dy. The output is a list of lists: [[invariants after first Darboux tr.],[invariants after second Darboux tr.],...] | * <nowiki>LPDO__XYS_chain_of_first_order_invertible_DTs(chain,I1,I2,I3,I4,I5)</nowiki> applies Darboux transformations as indicated in argument "chain" to an operator given by its gauge invariants. Argument chain should be of the form of the list, where each element indicates Darboux transformation of certain type. Thus, e.g. [1,1,2,3] indicates the sequence: Darboux transformations with principal symbol Dx, then with Dx, then with Dy, and then with Dx+Dy. The output is a list of lists: [[invariants after first Darboux tr.],[invariants after second Darboux tr.],...] | ||

- | * <nowiki>LPDO__XYZ_Chart(b,list_of_invs)</nowiki> computes (including plotting) b applications of all possible Darboux transformations of order 1 of type I to an operator given by its gauge invariants. Returns list of lists: [L1,L2,L3]. | + | * <nowiki>LPDO__XYZ_Chart(b,list_of_invs)</nowiki> computes (including plotting) b applications of all possible Darboux transformations of order 1 of type I to an operator given by its gauge invariants. Returns list of lists: [L1,L2,L3]. L1: if used later inside command display(L1, scaling=constrained,axes=Normal), will plot the orbit, L2: list of points (D_y up, D_x right, D_x+D_y on the diagonal), L3: list of lists of invariants (in correspondence with L2) |

- | L1: if used later inside command display(L1, scaling=constrained,axes=Normal), will plot the orbit, | + | |

- | L2: list of points (D_y up, D_x right, D_x+D_y on the diagonal), | + | |

- | L3: list of lists of invariants (in correspondence with L2) | + | |

{{:demo_chain_and_charts1.mw|Maple 16 worksheet example 1 (infinite orbit)}} | {{:demo_chain_and_charts1.mw|Maple 16 worksheet example 1 (infinite orbit)}} |

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