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egrr [2017/03/10 11:06] anna [Source] |
egrr [2017/03/29 10:02] (current) anna [EGRR package] |
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====== EGRR package ====== | ====== EGRR package ====== | ||

- | The **EGRR** package is implementing in Maple 2016 the family of algorithms for transforming a full-rank system to that with a nonsingular revealing matrix of the desired type. | + | The **EGRR** package implements in Maple 2016 a family of algorithms for transforming a full-rank system to a system having a nonsingular revealing matrix of a desired type. |

We consider an arbitrary order linear ordinary system **S** of differential equations with polynomial coefficients: | We consider an arbitrary order linear ordinary system **S** of differential equations with polynomial coefficients: | ||

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For any full rank system **S**: | For any full rank system **S**: | ||

- | - the algorithm **EG** construct an l-embracing system, but with the leading matrix coefficient being invertible, and with the set of solutions containing all the solutions of **S**; | + | - the algorithm **EG** constructs an l-embracing system, whose the leading matrix coefficient being invertible, and with the set of solutions containing all the solutions of **S**; |

- | - the algorithm **RR** construct an equivalent system, but with the frontal matrix being invertible; | + | - the algorithm **RR** constructs an equivalent system, whose the frontal matrix being invertible; |

- | - the algorithm **TriangleEG** construct an l-embracing system, but with the leading matrix coefficient being triangular, and with the set of solutions containing all the solutions of **S**; | + | - the algorithm **TriangleEG** constructs an l-embracing system, whose the leading matrix coefficient being triangular, and with the set of solutions containing all the solutions of **S**; |

- | - the algorithm **TriangleRR** construct an equivalent system, but with the frontal matrix coefficient being triangular. | + | - the algorithm **TriangleRR** constructs an equivalent system, whose the frontal matrix coefficient being triangular. |

- | The details are to be available in the paper S.A. Abramov, A.A. Ryabenko, and D. E. Khmelnov. Revealing Matrices of Linear Differential Systems of Arbitrary Order. Programming and Computer Software, 2017, to appear. | + | The details are to be available in the paper S.A. Abramov, A.A. Ryabenko, and D. E. Khmelnov. Revealing Matrices of Linear Differential Systems of Arbitrary Order. Programming and Computer Software, 2017, Vol.43, No.2, pp. 67-74. |

===== Input Parameters and Values Returned by the Procedures ===== | ===== Input Parameters and Values Returned by the Procedures ===== |

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