SDMPolynom - Maple Help

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

$a≔\mathrm{SDMPolynom}\left({x}^{3}+5{x}^{2}+11x+15,\left[x\right]\right)$

 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

$a≔\mathrm{SDMPolynom}\left(x{y}^{3}+\left(\frac{1}{2}+I\right)y,\left[x,y\right]\right)$

 This is a bivariate polynomial in the variables x and y whose coefficients involve the imaginary number $\sqrt{-1}$, 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

 extract a coefficient of a polynomial construct a sequence of all the coefficients the degree of a polynomial the leading coefficient the low degree of a polynomial the trailing coefficient 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 pseudo-remainder of two polynomials

 Mathematical Operations on Polynomials

 differentiate a polynomial evaluate a polynomial evaluate a polynomial

 Miscellaneous Polynomial Operations

 norm of a polynomial maximum norm of a polynomial mapping an operation on the coefficients of a polynomial converting Polynomials to a Sum of Products

 • The SDMPolynom command is thread-safe 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.

 > $a≔\mathrm{SDMPolynom}\left({x}^{3}+5{x}^{2}+11xy-6y+15,\left[x,y\right]\right):$
 > $\mathrm{degree}\left(a,x\right)$
 ${3}$ (1)
 > $\mathrm{degree}\left(a,y\right)$
 ${1}$ (2)
 > $\mathrm{coeff}\left(a,x,2\right)$
 ${\mathrm{SDMPolynom}}{}\left({5}{,}\left[{y}\right]\right)$ (3)
 > $\mathrm{coeff}\left(a,y,1\right)$
 ${\mathrm{SDMPolynom}}{}\left({11}{}{x}{-}{6}{,}\left[{x}\right]\right)$ (4)
 > $\mathrm{coeffs}\left(a,x\right)$
 ${-}{6}{}{y}{+}{15}{,}{11}{}{y}{,}{5}{,}{1}$ (5)
 > $\mathrm{subs}\left(\left[x=3,y=2\right],a\right)$
 ${141}$ (6)
 > $\mathrm{type}\left(a,\mathrm{SDMPolynom}\right)$
 ${\mathrm{true}}$ (7)
 > $\mathrm{nops}\left(a\right)$
 ${17}$ (8)
 > $\mathrm{op}\left(3,a\right)$
 ${1}$ (9)
 > $\mathrm{op}\left(a\right)$
 ${1}{,}{3}{,}{0}{,}{5}{,}{2}{,}{0}{,}{11}{,}{1}{,}{1}{,}{-6}{,}{0}{,}{1}{,}{15}{,}{0}{,}{0}$ (10)
 > $\mathrm{diff}\left(a,x\right)$
 ${\mathrm{SDMPolynom}}{}\left({3}{}{{x}}^{{2}}{+}{10}{}{x}{+}{11}{}{y}{,}\left[{x}{,}{y}\right]\right)$ (11)
 > $\mathrm{convert}\left(a,'\mathrm{polynom}'\right)$
 ${{x}}^{{3}}{+}{5}{}{{x}}^{{2}}{+}{11}{}{x}{}{y}{-}{6}{}{y}{+}{15}$ (12)