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https://en.wikipedia.org/wiki/Canonical_form
A canonical form may simply be a convention, or a deep theorem. For example, polynomials are conventionally written with the terms in descending powers: it is more usual to write x 2 + x + 30 than x + 30 + x 2, although the two forms define the same polynomial. By contrast, the existence of Jordan canonical form for a matrix is a deep theorem.
https://link.springer.com/10.1134/S0361768819020105
This paper also gives a definition of canonical representation for polynomial (multiplicative) expressions of variables with abstract indices that results from averaging the initial expression over the action of some finite group (signature stabilizer).Author: G. Shpiz, Alexander Kryukov
https://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=704823
Canonical representation of piecewise-polynomial functions with nondegenerate linear-domain partitions Abstract: Piecewise-linear (PWL) functions are a widely used class of nonlinear approximate functions with applications in both mathematics and engineering.Cited by: 8
https://everything2.com/title/Canonical+representation+of+polynomials
Determining which equivalence class a polynomial falls into is fairly easy- assuming you write each power only once, equivalence of two polynomials holds iff their corresponding coefficients are equal. The challenge is deciding what the canonical representation should then be.
http://www.learntoprogramming.com/content/polynomial-representation-using-arrays
Polynomial Representation Using Linked List An important application of linked list is to represent polynomial and their manipulations. Main advantage of linked list for polynomial representation is that it can accommodate a number of polynomials of growing sizes so that combined size does not exceed the total memory available.
http://buzzard.ups.edu/courses/2014spring/420projects/math420-UPS-spring-2014-toomey-rational-canonical-form.pdf
3 Minimal Polynomials Before examining matrix representations of F[x]-modules, we must present one more concept: the minimal polynomial. As we will later see, minimal polynomials play an important roll in nding the Rational Canonical Form of a matrix. De nition. The minimal polynomial of a matrix A, denoted m A(x), is the unique monic
https://www.w3schools.in/data-structures-tutorial/polynomials-using-linked-list-and-arrays/
Polynomials and Sparse Matrix are two important applications of arrays and linked lists. A polynomial is composed of different terms where each of them holds a coefficient and an exponent. This tutorial chapter includes the representation of polynomials using linked lists and arrays.
https://math.stackexchange.com/questions/794295/canonical-representation-of-finite-field
Obviously, you could add some order on the polynomials and use that to make sure you get the same representation but that seems rather arbitrary. Hence my question. finite-fields
https://www.sciencedirect.com/science/article/pii/S0021999116302303
6. Canonical low-rank approximations versus sparse polynomial chaos expansions. We next confront canonical LRA to sparse PCE in the same meta-modeling applications considered in Section 5. The focus of the comparison is set on the applications involving finite-element models.Cited by: 52
https://www.python-course.eu/polynomial_class_in_python.php
Polynomials. Introduction. If you have been to highschool, you will have encountered the terms polynomial and polynomial function.This chapter of our Python tutorial is completely on polynomials, i.e. we will define a class to define polynomials.
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