A Use of Ideal Decomposition in the Computer Algebra of Tensor Expressions

1997 ◽  
Vol 16 (1) ◽  
pp. 145-164 ◽  
Author(s):  
Bernold Fiedler
Keyword(s):  
Computer Algebra ◽  
Ideal Decomposition

scholarly journals Level lines of a polynomial in the plane

2021 ◽  
pp. 1-24
Author(s):  
Alexander Dmitrievich Bruno ◽  
Alexander Borisovich Batkhin
Keyword(s):  
Finite Number ◽  
Computer Algebra ◽  
Critical Points ◽  
Real Plane ◽  
Critical Levels ◽  
Real Polynomial ◽  
Level Lines ◽  
Critical Curves ◽  
A Value ◽  
Ideal Decomposition

We propose a method for computing the position of all level lines of a real polynomial in the real plane. To do this, it is necessary to compute its critical points and critical curves, and then to compute critical values of the polynomial (there are finite number of them). Now finite number of critical levels and one representative of noncritical level corresponding to a value between two neighboring critical ones enough to compute. We propose a scheme for computing level lines based on polynomial computer algebra algorithms: Gröbner bases, primary ideal decomposition. Software for these computations are pointed out. Nontrivial examples are considered.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Computer Simulation and Computer Algebra

1989 ◽  
Author(s):  
Dietrich Stauffer ◽  
Friedrich W. Hehl ◽  
Volker Winkelmann ◽  
John G. Zabolitzky
Keyword(s):  
Computer Simulation ◽  
Computer Algebra

Computer Simulation and Computer Algebra

1988 ◽  
Author(s):  
Dietrich Stauffer ◽  
Friedrich W. Hehl ◽  
Volker Winkelmann ◽  
John G. Zabolitzky
Keyword(s):  
Computer Simulation ◽  
Computer Algebra
Sign in / Sign up

Export Citation Format

Share Document