SolveTools - Maple Programming Help

Home : Support : Online Help : Mathematics : Factorization and Solving Equations : SolveTools : SolveTools/Linear

SolveTools

 Linear
 solve linear system of equations

 Calling Sequence Linear(eqns, vars, meth, notz)

Parameters

 eqns - list or set; system of equations vars - list or set; variables to solve with respect to meth - (optional) name of the form method=Method, where Method is one of the following: AlgebraicFunction, AlgebraicNumber, ComplexFloat, ComplexRational, Float, Polynomial, RadicalFunction, RadicalNumber, Rational or RationalAlgebraicFunction; the solution process to be used notz - (optional) expressions that must not equal zero

Description

 • The Linear command solves system of linear equations.
 • Optional arguments can contain expressions which must not be zero, notz, and the method for solving the system.
 If method is not specified, Linear tries to dispatch the solution process according to the type of the system. The possible methods correspond to the following types of equations (the check is performed in this order).

 Rational - 'polynom'('rational', vars) Float -'polynom'('numeric', vars) ComplexRational - 'polynom'('complex'('rational'), vars) ComplexFloat - 'polynom'('complex'('numeric'), vars) Polynomial - 'ratpoly'('rational') AlgebraicNumber - 'polynom'('algnum', vars) RadicalNumber - 'ratpoly'('radnum', vars) RationalAlgebraicFunction - 'ratpoly'('algnum') AlgebraicFunction - 'algfun'('rational') RadicalFunction - 'radfun'('rational')

 • If the method is not specified or the system is not of one of the above types, Linear uses the default universal method, which is a primitive fraction-free algorithm.
 • All algorithms are intended to be used on large sparse systems, however, they also perform well on dense systems.
 • The algorithms used are Gaussian elimination with pivoting for stability for the numeric coefficients and primitive fraction-free for the algebraic and radical coefficients.

Examples

 > $\mathrm{with}\left(\mathrm{SolveTools}\right):$
 > $\mathrm{Linear}\left(\left\{x+y,x-y-2\right\},\left\{x,y\right\}\right)$
 $\left\{{x}{=}{1}{,}{y}{=}{-}{1}\right\}$ (1)
 > $\mathrm{Linear}\left(\left[x+y,x-y-2\right],\left[x,y\right],\left[y+1\right]\right)$
 > $\mathrm{Linear}\left(\left\{x+y-5.,4x-3y-2\right\},\left\{x,y\right\}\right)$
 $\left\{{x}{=}{2.428571428}{,}{y}{=}{2.571428571}\right\}$ (2)
 > $\mathrm{Linear}\left(\left\{x+y-5,4x-3y-2-I\right\},\left\{x,y\right\},\mathrm{method}=\mathrm{ComplexFloat}\right)$
 $\left\{{x}{=}{2.428571428}{+}{0.1428571429}{}{I}{,}{y}{=}{2.571428571}{-}{0.1428571428}{}{I}\right\}$ (3)

The following example returns NULL since the system has polynomials of y as coefficients and there is no x such that equations hold for all values of y.

 > $\mathrm{Linear}\left(\left\{x+y-5,4x-3y-2\right\},\left\{x\right\}\right)$
 > $\mathrm{Linear}\left(\left\{x+y+z-{5}^{\frac{1}{2}},4x-3y-2\right\},\left\{x,y,z\right\}\right)$
 $\left\{{x}{=}\frac{{1}}{{2}}{+}\frac{{3}}{{4}}{}{y}{,}{y}{=}{y}{,}{z}{=}{-}\frac{{1}}{{2}}{-}\frac{{7}}{{4}}{}{y}{+}\sqrt{{5}}\right\}$ (4)
 > $\mathrm{Linear}\left(\left\{x+2\mathrm{RootOf}\left({v}^{2}-w,v\right)wy,5xw-3y+7\right\},\left\{x,y\right\}\right)$
 $\left\{{x}{=}{-}\frac{{14}{}{w}{}\left({10}{}{{w}}^{{3}}{-}{3}{}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{w}\right)\right)}{{100}{}{{w}}^{{5}}{-}{9}}{,}{y}{=}\frac{{7}{}\left({10}{}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{w}\right){}{{w}}^{{2}}{-}{3}\right)}{{100}{}{{w}}^{{5}}{-}{9}}\right\}$ (5)