On the computation of the minimal polynomial of a polynomial matrix

The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples

ON THE COMPUTATION OF THE MINIMAL POLYNOMIAL OF A TWO-VARIABLE POLYNOMIAL MATRIX

The main contribution of this work is to provide an algorithm for the computation of the minimal polynomial of a two variable polynomial matrix, based on the solution of linear matrix equations. The whole theory is implemented via an illustrative example. Keywords: minimal polynomial, Cayley-Hamilton theorem, characteristic polynomial. 1

On the computation of the minimal polynomial of a polynomial matrix

The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples

On the computation of the GCD of 2-D polynomials

The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples

multivariable

RATRIX: A RATional matRIX calculator for computer aided analysis and synthesis of linea

Clinical Outcome, Socioeconomic Status and Psychological Constrains of Patients Undergoing Preimplantation Genetic Testing (PGT) in Northern Greece

Background and objectives: Preimplantation genetic testing (PGT) offers patients the possibility of having a healthy baby free of chromosomal or genetic disorders. The present study focuses on the application of PGT for patients located in Northern Greece, investigating their clinical outcomes, their motives, and their overall physical and emotional experience during the treatment, in association with their socioeconomic background. Materials and Methods: Couples who underwent PGT for a monogenic condition (PGT-M, n = 19 cycles) or aneuploidy (PGT-A, n = 22 cycles) participated in the study. Fertilization, implantation, and pregnancy rates were recorded for all cycles. The couples were asked to fill in a questionnaire about the consultation they had received prior to treatment, their sociodemographic information, and the psychological impact PGT had on both the female and male partner. Results: The fertilization, implantation, and ongoing pregnancy rates for the PGT-M and PGT-A cycles were 81.3%, 70.6%, and 52.9%, and 78.2%, 64.3%, and 57.1%, respectively. Females experienced more intense physical pain than their male partners while psychological pain was encountered by both partners and occasionally in higher instances in males. No typical socioeconomic background of the patients referred for PGT in Northern Greece was noticed. Conclusion: PGT is an attractive alternative to prenatal diagnosis (PND), aiming to establisha healthy pregnancy by identifying and avoiding the transfer of chromosomally or genetically abnormal embryos to the uterus. Although the benefits of PGT were well-received by all patients undergoing the procedure, psychological pain was evident and especially prominent in patients with a previous affected child or no normal embryos for transfer. Holistic counseling is of utmost importance in order to make patients’ experience during their journey to have a healthy baby less emotionally demanding and help them make the right choices for the future. © 2022 by the authors