Question

Design an abstract data type for a matrix with integer elements in a language that you know, including operations for addition, subtraction, and matrix multiplication. Can any one help me towrite this programme in F# language using visual studio 2019.

Answer 1

An abstract data type (ADT) is an object with a generic description independent of implementation details. This description includes a specification of the components from which the object is made and also the behavioral details of the object. Instances of abstract objects include mathematical objects (like numbers, polynomials, integrals, vectors), physical objects (like pulleys, floating bodies, missiles), animate objects (dogs, Pterodactyls, Indians) and objects (like poverty, honesty, inflation) that are abstract even in the natural language sense.

In order to define an ADT we need to specify:

• The components of an object of the ADT.
• A set of procedures that provide the behavioral description of objects belonging to the ADT.

There may be thousands of ways in which a given ADT can be implemented, even when the coding language remains constant. Any such implementation must comply with the content-wise and behavioral description of the ADT.

Examples

• Integers: An integer is an abstract data type having the standard mathematical meaning. I
• Real numbers: There are mathematically rigorous ways of defining real numbers (Dedekind cuts, completion of rational numbers, etc).
• Complex numbers: A complex number may be mathematically treated as an ordered pair of real numbers.
• Polynomials with real (or complex or integer or rational) coefficients with the standard arithmetic.
• Matrices with real (or complex or integer or rational) entries with the standard matrix arithmetic (which may include dimension, rank, nullity, etc).
• Sets are unordered collections of elements. We may restrict our study to sets of real (or complex) numbers and talk about union, intersection, complement and other standard operations on sets.

For example:-

for a complex number:-

 typedef struct { double real; double imag; } complex; 

//addition can be performed

complex cadd ( complex z1 , complex z2 ) { complex z; z.real = z1.real + z2.real; z.imag = z1.imag + z2.imag; return z; } 

//subtraction can be performed

complex csub ( complex z1 , complex z2 ) { complex z; z.real = z1.real - z2.real; z.imag = z1.imag - z2.imag; return z; } 

void cprn ( complex z ) { printf("(%lf) + i(%lf)", z.real, z.imag); } 

for the matrix:-

#define MAXROW 10 #define MAXCOL 15 typedef struct { int rowdim; int coldim; complex entry[MAXROW][MAXCOL]; } matrix; 

matrix madd ( matrix A , matrix B ) //addition { matrix C; int i, j; if ((A.rowdim != B.rowdim) || (A.coldim != B.coldim)) { fprintf(stderr, "madd: Matrices of incompatible dimensions\n"); C.rowdim = C.coldim = 0; return C; } C.rowdim = A.rowdim; C.coldim = A.coldim; for (i = 0; i < C.rowdim; ++i) for (j = 0; j < C.coldim; ++j) C.entry[i][j] = cadd(A.entry[i][j],B.entry[i][j]); return C; } 

matrix msub ( matrix A , matrix B ) { matrix C; int i, j; if ((A.rowdim != B.rowdim) || (A.coldim != B.coldim)) { fprintf(stderr, "madd: Matrices of incompatible dimensions\n"); C.rowdim = C.coldim = 0; return C; } C.rowdim = A.rowdim; C.coldim = A.coldim; for (i = 0; i < C.rowdim; ++i) for (j = 0; j < C.coldim; ++j) C.entry[i][j] = csub(A.entry[i][j],B.entry[i][j]); return C; }