# 程序代写代做代考 Describe a canonical representation for dense matrices whose entries come from a

Describe a canonical representation for dense matrices whose entries come from a
domain R.

Page 90. 3.2.2 Representations of Matrices

Store a two-dimensional array (or one-dimensional array of one-dimensional arrays if our language does not support two-dimensional arrays) containing the values mi,j of the elements of the matrix.
Describe a canonical representation for sparse matrices whose entries come from a domain R.

M is stored as a list of triples (i, j, mi,j ), each non-zero element in M with one triple.
What properties do you require R to have for the previous two parts?

The elements from domain R are canonical.

Describe a canonical representation for polynomials in several variables with integer
coefficients.

Page 50.

Explain carefully how the representation of previous answer can be used to build a canonical representation for fractions of polynomials in several variables with integer coefficients.

Page 60

Then give a canonical representation for m*n matrices whose elements are fractions of polynomials in several variables.

A mxn two dimentional array A, A[i][j] contains the the canonical representation of polynomials of mi,j of the matrix.

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