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RegularChains[MatrixTools]

  

MatrixMultiply

  

compute the product of two matrices modulo a regular chain

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

MatrixMultiply(A, B, rc, R)

Parameters

A

-

Matrix with coefficients in the field of fractions of R

B

-

Matrix with coefficients in the field of fractions of R

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

The command MatrixMultiply(A, B, rc, R) returns the product of A and B mod the saturated ideal of rc.

• 

The result is viewed as a matrix with coefficients in the total ring of fractions of R/I where I is the saturated ideal of rc.

• 

The implementation is based on the method proposed in the paper "On {W}inograd's Algorithm for Inner Products" by A. Waksman.

• 

It is assumed that rc is strongly normalized.

• 

This command is part of the RegularChains[MatrixTools] package, so it can be used in the form MatrixMultiply(..) only after executing the command with(RegularChains[MatrixTools]).  However, it can always be accessed through the long form of the command by using

Examples

withRegularChains:withChainTools:withMatrixTools:

RPolynomialRingy,z

R:=polynomial_ring

(1)

rcEmptyR

rc:=regular_chain

(2)

rcChainz4+1,y2z2,rc,R:

Equationsrc,R

y2z2,z4+1

(3)

mMatrix1,y+z,0,yz

m:=1y+z0yz

(4)

mimMatrixInversem,rc,R

mim:=10012z3,regular_chain,noInv,1y+z0yz,regular_chain

(5)

m1mim111

m1:=10012z3

(6)

rc1mim112

rc1:=regular_chain

(7)

MatrixMultiplym1,m,rc1,R

1001

(8)

References

  

A. Waksman "On Winograd's Algorithm for Inner Products." IEEE Transactions On Computers, C-19, (1970): 360-361.

See Also

Chain

Empty

Equations

IsStronglyNormalized

IsZeroMatrix

JacobianMatrix

LowerEchelonForm

Matrix

MatrixInverse

MatrixOverChain

MatrixTools

NormalForm

PolynomialRing

RegularChains

 


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