compute the product of two matrices modulo a regular chain - Maple Help

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RegularChains[MatrixTools][MatrixMultiply] - compute the product of two matrices modulo a regular chain

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:

R:=PolynomialRingy,z

R:=polynomial_ring

(1)

rc:=EmptyR

rc:=regular_chain

(2)

rc:=Chainz4+1,y2z2,rc,R:

Equationsrc,R

y2z2,z4+1

(3)

m:=Matrix1,y+z,0,yz

m:=1y+z0yz

(4)

mim:=MatrixInversem,rc,R

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

(5)

m1:=mim111

m1:=10012z3

(6)

rc1:=mim112

rc1:=regular_chain

(7)

MatrixMultiplym1,m,rc1,R

1001

(8)

See Also

Chain, Empty, Equations, IsStronglyNormalized, IsZeroMatrix, JacobianMatrix, LowerEchelonForm, Matrix, MatrixInverse, MatrixOverChain, MatrixTools, NormalForm, PolynomialRing, RegularChains

References

  

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


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