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Linsolve

inert matrix solve

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Linsolve(A, b) mod n

Linsolve(A, b, 'r', 't') mod n

Parameters

A

-

rectangular Matrix

b

-

Vector

'r'

-

(optional) name

't'

-

(optional) name

n

-

an integer, the modulus

Description

• 

The Linsolve function is a placeholder for representing the solution x to the linear system Ax=b.

• 

The call Linsolve(A,b) mod n computes the solution vector b if it exists of the linear system Ax=b over a finite ring of characteristic n. This includes finite fields, GFp, the integers mod p, and GFpk where elements of GFpk are expressed as polynomials in RootOfs.

• 

If an optional third parameter r is specified, and it is a name, it is assigned the rank of the matrix A.

• 

A linear system with an infinite set of solutions will be parameterized in terms of variables.  Maple uses the global names _t[1], _t[2], ...  are used by default.  If an optional fourth parameter t is specified, and it is a name, the names t[1], t[2], etc. will be used instead.

Examples

AMatrix1,2,3,1,3,0,1,4,3

A123130143

(1)

bVector1,2,3

b123

(2)

xLinsolveA,bmod5

x410

(3)

A.xbmod5

000

(4)

xLinsolveA,b,'r',tmod6

x5+3t31+3t3t3

(5)

r

2

(6)

A.xbmod6

000

(7)

An example using GF(2^4).

aliasa=RootOfy4+y+1mod2:

AMatrix1,a,a2,1,a2,1,1,a3,a2

A1aa21a211a3a2

(8)

bVector1,a,a2

b1aa2

(9)

xLinsolveA,bmod2

x0a3+10

(10)

zA.xbmod2

z1+aa3+1a2a3+1+aa3a3+1+a2

(11)

Expandconvertz,listmod2

0,0,0

(12)

See Also

Gaussjord

Inverse

mod

Modular[LinearSolve]

 


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