> SynDiv := proc()

local i, j, n, a, filename, fp, nd, s, b, B, I, r;

########## Prepare f(x) ###########################################

printf("***** Author: Mengnien Wu ****************************\n");

printf("* Given a polynomial *\n");

printf("* f(x)=a[1]+a[2]*x+...+a[n]*x^(n-1) *\n");

printf("* Divide it by (x-b) using \"Synthetic Division\" *\n");

printf("* and do the same thing to the quotient repeatedly. *\n");

printf("* A file contains the coefficents of *\n");

printf("* n a[1] a[2] ... a[n] *\n");

printf("* will be read. *\n");

printf("******************************************************\n");

printf("\nEnter your filename:\n");

filename := scnf("%a")[1];

fp:=fopen(filename,Read);

n := fscnf(fp,"%d")[1];

a := array(1..n);

for i from 1 to n do

a[i] := fscnf(fp,"%f")[1];

od;

fclose(fp);

########## Showing the given f(x) #################################

printf("f(x) =%f",a[1]);

for i from 2 to n do

if a[i]>0 then printf(" +%f*x^%d",a[i],i-1);

elif a[i]<0 then printf(" %f*x^%d",a[i],i-1);

fi;

od; printf("\n");

########## Divide nd many times ###################################

printf("Enter b:\n");

b:=scanf("%f")[1];

printf("Enter # of divisions:\n");

nd:=scnf("%d")[1];

for i from 1 to nd do

for j from n-1 to i by -1 do # Only this part is the core

a[j]:=a[j]+b*a[j+1]; # of synthetic division

od; #

od;

########## For showing the rewrite of f(x) only : #################

B := b;

if B<0 then B := -B; s:=`+`; else s:=`-`; fi;

printf("f(x) =");

########## Print the remainder of divisions #######################

I:=0; r:=false;

for i from 1 to nd do

if a[i]<>0 then I:=i; r:=true; break; fi;

od;

for i from 1 to nd do

if a[i]>0 and i>I then printf(" +"); fi;

if a[i]<>0 then

printf("%3.0f",a[i]);

if i=2 then printf("*(x%c%f)",s,B); fi;

if i>2 then printf("*(x%c%f)^%d",s,B,i-1); fi;

fi

od;

########## Print the final quotient of divisions ##################

I:=nd;

for i from nd+1 to n do

if a[i]<>0 then I:=i; break; fi;

od;

if nd<=n then

if r=true then printf(" + "); fi;

printf("(x%c%f)^%d * [",s,B,nd);

for i from nd+1 to n do

if a[i]>0 and i>I then printf("+"); fi;

if a[i]<>0 then

printf("%f",a[i]);

if i-nd=2 then printf("*x"); fi;

if i-nd>2 then printf("*x^%d",i-nd-1); fi;

fi;

od;

printf("]");

fi;

printf("\n");

########## Print f(b) and f'(b) ###################################

printf("f(%4.0f) =%3.0f, f'(%3.0f) = %3.0f\n",b,a[1],b,a[2]);

end:

> SynDiv();

***** Author: Mengnien Wu ****************************

* Given a polynomial *

* f(x)=a[1]+a[2]*x+...+a[n]*x^(n-1) *

* Divide it by (x-b) using "Synthetic Division" *

* and do the same thing to the remainder repeatedly. *

* A file contains the coefficents of *

* n a[1] a[2] ... a[n] *

* will be read. *

******************************************************

Enter your filename:

> "D:/Mathematics/2001fall/NumericalAnalysis/coeff.txt"

f(x) = -4 + 3*x^1 -3*x^2 + 2*x^4

Enter b:

> 1

Enter # of divisions:

> 2

f(x) = -2 + 5*(x-1) + (x-1)^2 * [ 3+ 4*x+ 2*x^2]

f(1) = -2, f'(1) = 5