SDMPolynom

Description


•

Important: The command SDMPolynom has been deprecated. A sparse distributed data structure is used by default for polynomials and is often more efficient than SDMPolynom. For information on creating and working with polynomials, see polynom.

•

SDMPolynom (Sparse Distributed Multivariate Polynomial) data structure is a dedicated data structure to represent polynomials. For example, the command a := SDMPolynom(x^3+5*x^2+11*x+15,x); creates the polynomial


This is a univariate polynomial in the variable x with integer coefficients.

•

Multivariate polynomials, and polynomials over other number rings and fields are constructed similarly. For example, a := SDMPolynom(x*y^3+sqrt(1)*y+y/2,[x,y]); creates


This is a bivariate polynomial in the variables x and y whose coefficients involve the imaginary number , which is denoted by capital I in Maple.

•

The type function can be used to test for polynomials. For example the command type(a, SDMPolynom) tests whether the expression a is a polynomial in the variable x. For details, see type/SDMPolynom.

•

Polynomials in Maple are sorted in lexicographic order, that is, in descending power of the first indeterminate.

•

The remainder of this file contains a list of operations that are available for polynomials.


Utility Functions for Manipulating Polynomials

coeff

extract a coefficient of a polynomial

coeffs

construct a sequence of all the coefficients

degree

the degree of a polynomial

lcoeff

the leading coefficient

ldegree

the low degree of a polynomial

tcoeff

the trailing coefficient

indets

the indeterminate of a polynomial




Arithmetic Operations on Polynomials


All the arithmetic operations on polynomials are wrapped inside the constructor SDMPolynom.

+,

addition and subtraction

*,^

multiplication and exponentiation

Prem

pseudoremainder of two polynomials




Mathematical Operations on Polynomials

diff

differentiate a polynomial

subs

evaluate a polynomial

eval

evaluate a polynomial




Miscellaneous Polynomial Operations

norm

norm of a polynomial

maxnorm

maximum norm of a polynomial

map

mapping an operation on the coefficients of a polynomial

convert

converting Polynomials to a Sum of Products





Thread Safety


•

The SDMPolynom command is threadsafe as of Maple 15.



Examples


Important: The command SDMPolynom has been deprecated. A sparse distributed data structure is used by default for polynomials and is often more efficient than SDMPolynom. For information on creating and working with polynomials, see polynom.
>


>


 (1) 
>


 (2) 
>


 (3) 
>


 (4) 
>


 (5) 
>


 (6) 
>


 (7) 
>


 (8) 
>


 (9) 
>


 (10) 
>


 (11) 
>


 (12) 


Download Help Document
Was this information helpful?