Equations ( polynomials ) multiplication

[sheff]

HI everybody,
I am trying to multiply the two polynomials shown below, A using C programming language, as you know this will lead to a convolution multiplication , which means that every single element of A must be multiplied by all elements of B .
A=1+2x+3x^2+4x^3+5x^4+6x^5
B=1+2x+3x^2
This leads to C= 18 x^7 + 27 x^6 + 28 x^5 + 22 x^4 + 16 x^3 + 10 x^2 + 4 x + 1
I have tried to do this using the following code, but did not work. I would be very pleased if you could kindly let me know how this can be done.

# include <stdio.h>
# include <conio.h>
 
int main( void)
 
{
    int i,j;
   int na=100;   
   double A[1][5]; 
    double B[1][ 2];  
double C[1][2+5]  // the resultant matrix 
  A[1][0]=1;
A[1][1]=2;
 A[1][2]=3;
  A[1][3]=4;
 A[1][4]=5;
  A[1][5]=6;
B[1][0]=1.0;
 B[1][1]=2.0;
 B[1][2]=3.0;
 
for ( i=1;j<=3;j++)
     {
          for ( j=1;i<=6;i++)      
      {  
 
C[i][j]=   A[i][j]*B[i][j];  
 
      printf(" \n C  %d", C[i][j]);   
 
      }
 
  }

[newb16]

You use different variables in loop init and increment expressions
i=1;j<=3;j++)
, address C array outside its bounds (C[1][...] and c[i][j] where i>0 )
Are there any reasons for making A and B two-dimensional?

[sheff]

HI Newb16, thnx for ur reply.
regarding the increment expressions, I have corrected them, but forgot to do the same when I copied and pasted the code to this site. but still getting wrong answer .
there is no reason for the A, B being two dimensional, just though this how it can be done, any suggestions??

[sheff]

Newb16,

just to make life easy for you and everybody else who could help, lets assume you are given
A=1+2x+3x^2+4x^3+5x^4+6x^5
B=1+2x+3x^2
and you are asked to multiply them, how would you do that? and nice suggestions?

[newb16]

A,B - source polynomials, res - result.
in your example A={1,2,3,4,5,6}, B={1,2,3} Observing what power will a result of multiplying A[i] by B[j] -
foreach(i,j) res[i+j]+=A[i]*B[j];

[weaknessforcats]

A=1+2x+3x^2+4x^3+5x^4+6x^5
B=1+2x+3x^2

Consider using an ordered array. That is, an array where element 0 is for x^0, element 1 for x^1 ,etc. That would give:

int A[10] = {1,2,3,4,5,6,0,0,0,0};
int B[10] = {1,2,3,0,0,0,0,0,0,0};
int C[10] = {0,0,0,0,0,0,0,0,0,0};

Then write a nested loop to multiply an element of A to every element of B. As you go, add the product to the array C in tghe correct element. That is, the product of element 4 of A multiplied by element 3 of array B will be added to element 7 of array C.

Be sure no products need to bed added outside the range of array C.

I used 10 above to simplify coding by having the arrays be the same size. You could define the array size at run time.

[sheff]

HI weaknessforcats, thank you for you response,

the idea you suggested sounds good to me but I am not sure if you considered the fact that addition needs to be carried out after we multiply each element of A by B, so if we place it stright away into C, then how we gonna do the addition of the numbers of similar polynominal degrees. e.g
when the element 1 from B is multiplied by the element 2x from A, the result is 2x this will be added to the result of multiplying the element 2x from B with the element 1 in A leading to 4x in the second element of C. I am not sure if the program you suggested considers that, if so, plse put some more illustrations.

A=1+2x+3x^2+4x^3+5x^4+6x^5
B=1+2x+3x^2

[newb16]

Yes, it was considered -

...That is, the product of element 4 of A multiplied by element 3 of array B will be added to element 7 of array C...

Note 'added' and 3+4 = 7.