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 $\sqrt{\mathrm{-1}}$, 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

Arithmetic Operations on Polynomials

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

Mathematical Operations on Polynomials

Miscellaneous Polynomial Operations

The SDMPolynom command is thread-safe as of Maple 15.

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

$a≔\mathrm{SDMPolynom}\left(x^3+5x^2+11xy-6y+15\,\left[x\,y\right]\right)\:$

$\mathrm{degree}\left(a\,x\right)$

$3$

$\mathrm{degree}\left(a\,y\right)$

$1$

$\mathrm{coeff}\left(a\,x\,2\right)$

$\mathrm{SDMPolynom}\left(5\,\left[y\right]\right)$

$\mathrm{coeff}\left(a\,y\,1\right)$

$\mathrm{SDMPolynom}\left(11x-6\,\left[x\right]\right)$

$\mathrm{coeffs}\left(a\,x\right)$

$-6y+15,11y,5,1$

$\mathrm{subs}\left(\left[x=3\,y=2\right]\,a\right)$

$141$

$\mathrm{type}\left(a\,\mathrm{SDMPolynom}\right)$

$\mathrm{true}$

$\mathrm{nops}\left(a\right)$

$17$

$\mathrm{op}\left(3\,a\right)$

$1$

$\mathrm{op}\left(a\right)$

$1,3,0,5,2,0,11,1,1,\mathrm{-6},0,1,15,0,0$

$\mathrm{diff}\left(a\,x\right)$

$\mathrm{SDMPolynom}\left(3x^2+10x+11y\,\left[x\,y\right]\right)$

$\mathrm{convert}\left(a\,'\mathrm{polynom}'\right)$

$x^3+5x^2+11xy-6y+15$