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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

a:=SDMPolynomx3+5x2+11x+15,x

  

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

a:=SDMPolynomxy3+12+Iy,x,y

  

This is a bivariate polynomial in the variables x and y whose coefficients involve the imaginary number 1, 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

pseudo-remainder 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 thread-safe as of Maple 15.

• 

For more information on thread safety, see index/threadsafe.

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.

a:=SDMPolynomx3+5x2+11xy6y+15,x,y:

degreea,x

3

(1)

degreea,y

1

(2)

coeffa,x,2

SDMPolynom5,y

(3)

coeffa,y,1

SDMPolynom11x6,x

(4)

coeffsa,x

6y+15,11y,5,1

(5)

subsx=3,y=2,a

141

(6)

typea,SDMPolynom

true

(7)

nopsa

17

(8)

op3,a

1

(9)

opa

1,3,0,5,2,0,11,1,1,6,0,1,15,0,0

(10)

xa

SDMPolynom3x2+10x+11y,x,y

(11)

converta,'polynom'

x3+5x2+11xy6y+15

(12)

See Also

convert, indets, polynomial, series, type, type/SDMPolynom


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