arma::vec polynomial(
const arma::vec& parameter,
const arma::uword highestDegree) {
if (parameter.n_elem == 0 || highestDegree == 0) {
// By definition, the constant term is 1.
return {1.0};
}
arma::vec polynomial(polynomialSize(parameter.n_elem, highestDegree));
arma::uword n = 0;
// Generates all terms for degree > 1
for (arma::uword degree = highestDegree; degree >= 2; --degree) {
for (const auto& multicombination : multicombinations(parameter.n_elem, degree)) {
const arma::vec& partialParameter = parameter.elem(multicombination);
polynomial(n++) = arma::prod(partialParameter);
}
}
// Linear term
polynomial.subvec(n, n + parameter.n_elem - 1) = parameter;
// By definition, the constant term is 1.
polynomial(polynomial.n_elem - 1) = 1;
return polynomial;
}
//*****************************************************************************
// METHOD: ossimRpcProjection::worldToLineSample()
//
// Overrides base class implementation. Directly computes line-sample from
// the polynomials.
//*****************************************************************************
void ossimRpcProjection::worldToLineSample(const ossimGpt& ground_point,
ossimDpt& imgPt) const
{
if (traceExec()) ossimNotify(ossimNotifyLevel_DEBUG) << "DEBUG ossimRpcProjection::worldToLineSample(): entering..." << std::endl;
if(ground_point.isLatNan() ||
ground_point.isLonNan() )
{
imgPt.makeNan();
return;
}
//*
// Normalize the lat, lon, hgt:
//*
double nlat = (ground_point.lat - theLatOffset) / theLatScale;
double nlon = (ground_point.lon - theLonOffset) / theLonScale;
double nhgt;
if(ossim::isnan(ground_point.hgt))
{
nhgt = (theHgtScale - theHgtOffset) / theHgtScale;
}
else
{
nhgt = (ground_point.hgt - theHgtOffset) / theHgtScale;
}
//***
// Compute the adjusted, normalized line (U) and sample (V):
//***
double Pu = polynomial(nlat, nlon, nhgt, theLineNumCoef);
double Qu = polynomial(nlat, nlon, nhgt, theLineDenCoef);
double Pv = polynomial(nlat, nlon, nhgt, theSampNumCoef);
double Qv = polynomial(nlat, nlon, nhgt, theSampDenCoef);
double U_rot = Pu / Qu;
double V_rot = Pv / Qv;
//***
// U, V are normalized quantities. Need now to establish the image file
// line and sample. First, back out the adjustable parameter effects
// starting with rotation:
//***
double U = U_rot*theCosMapRot + V_rot*theSinMapRot;
double V = V_rot*theCosMapRot - U_rot*theSinMapRot;
//***
// Now back out skew, scale, and offset adjustments:
//***
imgPt.line = U*(theLineScale+theIntrackScale) + theLineOffset + theIntrackOffset;
imgPt.samp = V*(theSampScale+theCrtrackScale) + theSampOffset + theCrtrackOffset;
if (traceExec()) ossimNotify(ossimNotifyLevel_DEBUG) << "DEBUG ossimRpcProjection::worldToLineSample(): returning..." << std::endl;
return;
}
int main(int argc, char *argv[]) {
const int test_size = 4096 * 2;
std::normal_distribution<float> dist(0.5f, 0.5f);
rng.seed(0);
float *r_values = nullptr;
float *ret = nullptr;
float *ret2 = nullptr;
double sum = 0.0f;
std::function<float()> rnd = std::bind(dist, rng);
r_values = static_cast<float*>(_mm_malloc(sizeof(float) * test_size, 32));
ret = static_cast<float*>(_mm_malloc(sizeof(float) * test_size, 32));
ret2 = static_cast<float*>(_mm_malloc(sizeof(float) * test_size, 32));
if (!(r_values && ret && ret2))
goto exit;
std::generate_n(r_values, test_size, rnd);
for (int i = 0; i < 100000; ++i) {
polynomial(ret, r_values, test_size);
// polynomial(ret2, ret, test_size);
sum = std::accumulate(ret, ret + test_size, sum);
}
std::cout << sum << std::endl;
exit:
_mm_free(r_values);
_mm_free(ret);
_mm_free(ret2);
}
int main(void)
{
/*Repeating the main function*/
while (1)
{
int i;
/*User input 1*/
printf("Please enter the maximum degree of the polynomial: ");
scanf("%d", &max);
a = (int*) calloc(max+1, sizeof(int));
/*Terminate if a negative number*/
if(max < 0)
{
return 0;
}
/*User input 2*/
printf("Please enter the coefficients: ");
/*Input max+1 numbers*/
for (i=0; i <= max; i++)
{
scanf("%d", &a[i]);
}
power = max;
polynomial();
power = max;
derivative();
free(a);
}
}
int main(void)
{
int degree; //there will be a valiable called degree that will be an integor
int a[10]; //creates an array, a, and assigns 10 values that are integors
int i; //there will be an variable called i that will be an integor
degree=1;
while(degree>0)
{
printf("Please enter the maximum degree of the polynomial: "); //asks user to imput the degree of polynomial
scanf("%d", °ree);
if(degree<0)
{
return 0;
}
printf("Please enter the coefficients: "); //asks user to imput the coefficients
for(i=0; i<=degree; i++) //creates a loop that repeats untill the array number is equal to the degree
scanf("%d", &a[i]); //calls the coefficients of the array
printf("The polynomial is ");
polynomial(a, degree); //calls function polynomial
printf("\nIts derivative is ");
calculatederivative(a, degree);
printf("\n\n");
}
}
int main(void)
{
while(1) // the program will anew as long as this loop remains true
{
int deg; // degree
int i;
int * coeff; // array to store the coefficients as input by the user
printf("Please enter the maximum degree of the polynomial: ");
scanf("%d", °);
coeff = (int*)calloc(deg+1, sizeof(int));
if(deg >= 0) // check and carry out actions only if input is correct (degree is positive)
{
printf("Please enter the coefficients: ");
for(i=0; i<=deg ;i++) // allow the user to input coefficients as many times as required
scanf("%d", &coeff[i]);
printf("The polynomial is ");
polynomial(coeff, deg); // send the stored information to polynomial funtion
printf("\n");
printf("Its derivative is ");
derivative(coeff, deg); // send the stored information to derivative function
printf("\n\n");
free(coeff); // always free the memory for next usage after anewing the program
} else break; // breaks the operation, and hence terminates the program
}
return 0;
}
bool ArModel::check_stationary(const Vec &phi){
// The process is stationary if the roots of the polynomial
//
// 1 - phi[0]*z - ... - phi[p-1]*z^p.
//
// all lie outside the unit circle. We can do that by explicitly
// finding and checking the roots, but that's kind of expensive.
// Before doing that we can do a quick check to see if the
// coefficients are within a loose bound.
//
// Based on Rouche's theorem:
// http://en.wikipedia.org/wiki/Properties_of_polynomial_roots#Based_on_the_Rouch.C3.A9_theorem
// All the roots will be at least 1 in absolute value as long as
// sum(abs(phi)) < 1.
if(phi.abs_norm() < 1) return true;
// If that didn't work then we're stuck finding roots.
// TODO(stevescott): Really we just need to check the smallest
// root. If we had a cheap way of finding just the smallest root
// then that would be more efficient than finding them all.
Vector coefficients = concat(1, -1 * phi);
Polynomial polynomial(coefficients);
std::vector<std::complex<double> > roots(polynomial.roots());
for (int i = 0; i < roots.size(); ++i) {
if (abs(roots[i]) <= 1) return false;
}
return true;
}
int main(){
int question;
printf("This is ece177 lab2 solving 4 questions.\nPlease enter\n1 for temperature,\n2 for polynomial,\n3 for solution,\n4 for freefalldistance.\n0 for exit.\n");
scanf("%d",&question);
while(question!=0){
switch (question){
case 1:
temperature();
break;
case 2:
polynomial();
break;
case 3:
solution();
break;
case 4:
freefalldistance();
break;
default:
printf("Sorry, your choice did not match any of the four. Please try again.\n");
break;
}
printf("This is ece177 lab2 solving 4 questions.\nPlease enter\n1 for temperature,\n2 for polynomial,\n3 for solution,\n4 for freefalldistance.\n0 for exit.\n");
scanf("%d",&question);
}
return 0;
}
double zonal_pressure(double rho_value, double theta_value)
{
/*
printf("Zonal Pressure %lf %lf\n", rho_value, theta_value);
*/
return(polynomial(p_poly, 2, rho_table, theta_table, rho_value, theta_value));
}
double zonal_energy(double rho_value, double theta_value)
{
/*
printf("Zonal Energy %lf %lf\n", rho_value, theta_value);
*/
return(polynomial(e_poly, 2, rho_table, theta_table, rho_value, theta_value));
}
void deriv708a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, p, c;
do {
a = rndr(r);
b = rndr(r);
p = rndr(r);
c = rndr(r);
} while (!(a>0 && b>0));
char ax2b[BUFSZ];
polynomial(ax2b,2, a,"x^2", b,"");
char lnax2b[BUFSZ];
sprintf(lnax2b, "ln(%s)", ax2b);
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=((%s)/sqrt(%s))*cos(%d)",
polynomial(buf[0],2, 1,lnax2b, c,""),
ax2b,
p
);
sprintf(src, "y(x)=((ln(a*x^2+b)+c)/sqrt(a*x^2+b))*cos(p)");
sprintf(answ[0], "y(x)`=((%s)/sqrt((%s)^3))*cos(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x*(%s)", polynomial(buf[2],2, 2-c,"", -1,lnax2b))),
ax2b,
p
);
sprintf(answ[1], "y(x)`=((%s)/sqrt((%s)^3))*cos(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x^2*(%s)", polynomial(buf[2],2, 1-c,"", -1,lnax2b))),
ax2b,
p
);
sprintf(answ[2], "y(x)`=((%s)/sqrt((%s)^3))*sin(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x*(%s)", polynomial(buf[2],2, c-2,"", 1,lnax2b))),
ax2b,
p
);
sprintf(answ[3], "y(x)`=((%s)/(%s))*sin(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x^2*(%s)", polynomial(buf[2],2, 1,lnax2b, -2+c,""))),
ax2b,
p
);
}
int main (void)
{
int i,j;
int power;
printf("Please enter the maximum degree of polynomial: ");
scanf("%d", °ree);
if (degree<0)
{
exit(0);
}
/* Enter the coefficient */
printf("\nPlease enter the coefficient: ");
for (i = 0; i<= degree; i++)
{
scanf("%d",&coefficient[i]);
}
/* Print the polynomial */
power = degree;
printf("\nThe polynomial is");
for (i = 0; i <= degree; i++)
{
printf(" %d ", coefficient[i]);
polynomial(power); /* Print the degree */
power--;
}
/* Print the reciprocal */
power = degree;
j = i;
printf("\nThe reciprocal is");
for (j = degree; j >= 0; j--)
{
printf(" %d", coefficient[j]);
polynomial(power); /* Print the degree */
power--;
}
check_equality(i,j);
return 0;
}
void deriv413a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=sin(log(%d,%s))+cos(%d)", a,polynomial(buf[0],1,b,"x"),c);
sprintf(answ[0], "y(x)`=cos(log(%d,%d))/(x*ln(%d))",a,b,a);
sprintf(answ[1], "y(x)`=(cos(log(%d,%d))/((%s)*ln(%d)))+sin(%d)",a,b,polynomial(buf[0],1,b,"x"),a,c);
sprintf(answ[2], "y(x)`=%s", polynomial(buf[0],1,b,chprintf(buf[1],"cos(1/((%s)*ln(%d)))", polynomial(buf[2],1,b,"x"),a)));
sprintf(answ[3], "y(x)`=(cos(log(%d,%d))/(x*ln(%d)))-sin(%d)", a,b,a,c);
}
void deriv415a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b>0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=arcsin(sqrt(%d/x))+arctg(%d)", b,c);
sprintf(answ[0], "y(x)`=-(%s/(2*x*sqrt(%s)))",fraction(buf[0],1,b,1),polynomial(buf[1],2,1,"x",-b,""));
sprintf(answ[1], "y(x)`=(%s)/(2*sqrt(%s))",polynomial(buf[0],1,b,"x"),polynomial(buf[1],2,1,"x",-b,""));
sprintf(answ[2], "y(x)`=(%d)/(2*x^2*sqrt(1-(%d)/x))+arctg(%d)",-b,b,c);
sprintf(answ[0], "y(x)`=-(%s/(2*x*sqrt(%s)))+(%s)",fraction(buf[0],1,b,1),polynomial(buf[1],2,1,"x",-b,""), fraction(buf[2],1,1,1+c*c));
}
int main(void)
{
/*Intialising the variables*/
int degree;
int coefficient[11];
int i;
void polynomial(int degree, int coefficient[11]);
do
{
/*Asking the user to input values for the polynomial*/
printf("Please enter the maximum degree of the polynomial: ");
scanf("%d", °ree);
/*This while loop checks if the degree is below 0 i.e minus and terminates the program if its true*/
while(degree<0)
{
return 0;
}
/*Asking the user to input the coefficients*/
printf("Please enter the coefficients: ");
for (i=0; i <= degree; i++)
{
/*This for loop repeats the scanf the required number of times depending on the input of the degree*/
scanf("%d", &coefficient[i]);
}
/*The results of the program*/
printf("The polynomial is ");
polynomial(degree, coefficient);
printf("\n");
printf("The reciprocal is ");
reciprocal(degree, coefficient);
printf("\n");
/*Checks whether the polynomial is self-reciprocal and prints the result*/
if(selfreciprocal(degree, coefficient)==1)
printf("The polynomial is self-reciprocal \n");
if(selfreciprocal(degree, coefficient)==0)
printf("The polynomial is not self-reciprocal \n");
printf("\n\n");
}
while(selfreciprocal(degree, coefficient)==0); /*Will terminate the loop if the polynomial is self-reciprocal*/
return 0;
}
int main(void)
{
int degree; //there will be a valiable called degree that will be an integor
int a[10]; //creates an array, a, and assigns 10 values that are integors
int i; //there will be an variable called i that will be an integor
int j; //there will be a variable called j that will be an integor
degree=1;
while(degree>0)
{
printf("Please enter the maximum degree of the polynomial: "); //asks user to imput the degree of polynomial
scanf("%d", °ree);
if(degree<0)
{
return 0;
}
printf("Please enter the coefficients: "); //asks user to imput the coefficients
for(i=0; i<=degree; i++) //creates a loop that repeats untill the array number is equal to the degree
scanf("%d", &a[i]); //calls the coefficients of the array
printf("The polynomial is: ");
polynomial(a, degree); //calls function polynomial
printf("\nThe reciprocal is: ");
reciprical(a, degree); //calls function reciprical
int isreciprocal = 1; //ture
j=degree;
for(i=0; i<= degree; i++)
{
if(a[i] != a[j])
isreciprocal = 0;
j--;
}
if(isreciprocal == 1)
{
printf("\nThe polynomial is self-reciprocal");
}
else
{
printf("\nThe polynomial is not self-reciprocal");
}
printf("\n\n");
}
}
void deriv414a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=cos((%d)^(%s))^2+tg(%d)", a,polynomial(buf[0],1,b,"x"),c);
char blna[BUFSZ]; polynomial(blna,1, b,chprintf(buf[0],"ln(%d)",a));
char abx[BUFSZ]; sprintf(abx,"(%d)^(%s)", a, polynomial(buf[0],1,b,"x"));
sprintf(answ[0], "y(x)`=(-sin(2*%s))*.(%s)*.(%s)",abx,abx,blna);
sprintf(answ[1], "y(x)`=2*(cos(%s))*.(%s)+tg(%d)",abx,blna,c);
sprintf(answ[2], "y(x)`=(sin(%s)^2)*.(%s)+1/cos(%d)^2",abx,blna,c);
sprintf(answ[3], "y(x)`=2*(cos(%s))*.(sin(%s)^2)*.(%s)",abx,abx,blna);
}
void deriv412a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0));
char bx[BUFSZ];
polynomial(bx,1, b,"x");
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=(%d)^arctg(%s)+tg(%d)^2", a,bx,c);
sprintf(src, "y(x)=a^arctg(b*x)+tg(c)^2");
sprintf(answ[0], "y(x)`=(%d)^arctg(%s)*.!(ln(%d))*.(%d/(%s))", a,bx,a,b,polynomial(buf[0],2,1,"",b*b,"x^2"));
sprintf(answ[1], "y(x)`=(%d)^arctg(%s)*.!(ln(%d))+tg(%d)^2", a,bx,a,c);
sprintf(answ[2], "y(x)`=(%d)^(%d/(%s))*.!(ln(%d))+(2*tg(%d))/(cos(%d)^2)", a,b,polynomial(buf[0],2,1,"",b*b,"x^2"),a,c,c);
sprintf(answ[3], "y(x)`=arctg(%s)*(%d)^(arctg(%s)-1)*.(%d/(%s))", bx,a,bx,b,polynomial(buf[0],2,1,"",b*b,"x^2"));
}
void deriv409a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0 && c>1));
char bx[BUFSZ];
polynomial(bx,1, b,"x");
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=(%d)^tg(%s)+1/ln(%d)", a,bx,c);
sprintf(src, "y(x)=a^tg(b*x)+1/ln(c)");
sprintf(answ[0], "y(x)`=(%d)^tg(%s)*.(%d/cos(%s)^2)*.ln(%d)", a,bx,b,bx,a);
sprintf(answ[1], "y(x)`=(%d)^tg(%s)*.(%d/sin(%s)^2)*.ln(%d)", a,bx,-b,bx,a);
sprintf(answ[2], "y(x)`=(%d)^tg(%s)*.(%d/cos(%s)^2)-1/(%s)", a,bx,b,bx,polynomial(buf[0],1,c,chprintf(buf[1],"ln(%d)^2",c)));
sprintf(answ[3], "y(x)`=tg(%s)*.(%d)^(tg(%s)-1)*.(1/cos(%s)^2)+1/ln(%d)", bx, a, bx, bx, c);
}
float getRoots(float possibleRoots[],int possibleRootCounter)
{
int j=0;
for (int i=0;i<possibleRootCounter;i++)
{
if (polynomial((float)possibleRoots[i]) == 0)
{
Roots[j++]=possibleRoots[i];
printf("Roots[%d]=%f\n",j-1,Roots[j-1]);
rootsCounter++;
}
}
return rootsCounter;
}
void deriv706a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, n;
do {
a = rndr(r);
n = rndr(r);
} while (!(a!=0 && n>0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=arctg(%s)/(%s)",
memb(buf[0], 1,a,1,1,"x", false),
memb(buf[1], 1,1,n,1, polynomial(buf[2],2, a*a,"",1,"x^2"), false)
);
sprintf(src, "y(x)=arctg(x/a)/(a^2+x^2)^n");
char xarctg[BUFSZ];
sprintf(xarctg, "x*arctg(%s)", memb(buf[0], 1,a,1,1, "x", false));
sprintf(answ[0], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a,"", -2*n,xarctg),
memb(buf[1], 1,1,n+1,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[1], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a*a,"", -4*n,xarctg),
memb(buf[1], 1,1,n+1,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[2], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a,polynomial(buf[1],2, a*a,"", 1,"x^2"), -2*n,xarctg),
memb(buf[2], 1,1,n,1, polynomial(buf[3],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[3], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a*a,"", -2*n,xarctg),
memb(buf[1], 1,1,n,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
}
int main()
{
while(1){
int i; /* Give values to array by the order of i*/
int co[11]; /* The array to store the coefficients of polynomial*/
int n; /* The maximum degree of polynomial*/
int k=0; /* The variable to check reprocical*/
/* Prompt the user for maximum degree */
printf("Please enter the maximum degree of the polynomial:");
scanf("%d", &n);
/* Check whether the maximum degree is negative number
If so, terminate here. Otherwise continue the program*/
if(n<0){
return 0;}
else{
printf("Please enter the coefficients:");
for(i=0;i<=n;i++){
scanf("%d", &co[i]);}
/* Print two polynomials*/
polynomial(n,co);
reciprocal(n,co);
/* Check whether it is self-reciprocal or not.If coefficient is equal to that
after changingposition, K will get 1 increment. Otherwise 0 increment.
If k=n+1, that means p(x) = p*(x) and terminate the program*/
for(i=0;i<=n;i++){
if(co[i]==co[n-i]){
k = k+1;}
else{k = k;}}
if(k==(n+1)){
printf("The polynomial is self-reciprocal\n");
return 0;}
else{
printf("The polynomial is not self-reciprocal\n");
printf("\n");
}
}
}
}
int main(void){
int coefficient[SIZE];
int K, N, Power;
int count3 = 0;
/* Below while loop basically creat repeatatinon of Entering the polynomial */
N=1;
while (N>0){
/* asking the user to the maximum degree of polynomai, which is then taken by scanf*/
printf("Please enter the maximum degree of the polynomial:");
scanf("%d", &N);
if(N<0){
exit(0);
}
/*asking the user the input the coeff*/
printf("Please enter the coefficients:");
for(K=0; K<=N; K++)
{
scanf("%d", &coefficient[K]);
}
Power = N;
/*Here the functions are called in the main*/
polynomial(coefficient, Power, N);
reciprocal(coefficient, Power , N);
printf("\n");
}
exit(0);
}
void deriv707a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a!=0 && b>1));
char arctgxac[BUFSZ];
polynomial(arctgxac,2,
1,chprintf(buf[0],"arctg(%s)", memb(buf[1], 1,a,1,1, "x", false)),
c,""
);
char xarctgxac[BUFSZ];
sprintf(xarctgxac, "x*(%s)", arctgxac);
char a2x2[BUFSZ];
polynomial(a2x2,2, a*a,"",1,"x^2");
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=((%s)/sqrt(%s))*ln(%d)", arctgxac, a2x2, b);
sprintf(src, "y(x)=((arctg(x/a)+c)/sqrt(a*x^2+b))*ln(b)");
sprintf(answ[0], "y(x)`=((%s)/sqrt((%s)^3))*ln(%d)",
polynomial(buf[0],2, a,"", -1,xarctgxac),
a2x2,
b
);
sprintf(answ[1], "y(x)`=((%s)/sqrt((%s)^3))*ln(%d)",
polynomial(buf[0],2, a,"", -2,xarctgxac),
a2x2,
b
);
sprintf(answ[2], "y(x)`=((%s)/(%s))*ln(%d)",
polynomial(buf[0],2, a,"", -1,xarctgxac),
a2x2,
b
);
sprintf(answ[3], "y(x)`=((%s)/(%s))",
polynomial(buf[0],2, a,"", -1,xarctgxac),
polynomial(buf[1],1, b,a2x2)
);
}
// Check for identically zero polynomials using randomized polynomial identity testing
template<class R,class PerturbedT> static void
assert_last_nonzero(void(*const polynomial)(R,RawArray<const Vector<Exact<1>,PerturbedT::m>>),
R result, RawArray<const PerturbedT> X, const char* message) {
typedef Vector<Exact<1>,PerturbedT::m> EV;
const int n = X.size();
const auto Z = GEODE_RAW_ALLOCA(n,EV);
for (const int k : range(20)) {
for (int i=0;i<n;i++)
Z[i] = EV(perturbation<PerturbedT::m>(k<<10,X[i].seed()));
polynomial(result,Z);
if (last_nonzero(result)) // Even a single nonzero means we're all good
return;
}
// If we reach this point, the chance of a nonzero nonmalicious polynomial is something like (1e-5)^20 = 1e-100. Thus, we can safely assume that for the lifetime
// of this code, we will never treat a nonzero polynomial as zero. If this comes up, we can easily bump the threshold a bit further.
throw AssertionError(format("%s (there is likely a bug in the calling code), X = %s",message,str(X)));
}
int main(void)
{/*Declaring variables*/
int b;
int degree;
int coefficient[11];
int reciprocal1[11];
do/*Allows the program loop*/
{
printf("Please enter the maximum degree of the polynomial :");/*prompting user for input of maximum degree*/
scanf("%d" , °ree);
/*makes the program terminate when a negative integer is inputed*/
if(degree<0)
{
return 0;
}
printf("Please enter the coefficients:");/*prompting user for input of coefficients*/
for (b=0; b <= degree; b++)/*A for loop that repeats scanf the required number of times depending on the degree of the polynomoial*/
{
scanf("%d", &coefficient[b]);
}
printf("The polynomial is ");/*printing the polynomial*/
polynomial(degree,coefficient);
printf("Its reciprocal is ");/*Printitng the Reciprocal*/
reciprocal(degree,coefficient);
/*Determining if the polynomial is self reciprocal or not*/
if (determination(b, degree, reciprocal1, coefficient)==1)
{
printf("This not self reciprocal \n\n");
}
if (determination(b, degree, reciprocal1, coefficient)==0)
{
printf("This is self reciprocal \n\n");
}
}
while (determination(b, degree, reciprocal1, coefficient)==1);
}
int main()
{
int i,j; //update varible
int exponent; //prompt exponent by user
int *arr; //prompt coefficients by user
arr = (int *)malloc(Max_Length ); //define the max array length
if( arr == NULL ) //test whether the pointer of array points empty or not
{
return 0;
}
else
{
/* user input the exponent and coefficients which are stored in corresponding
varible and array. print the whole program. */
for (j=0;j<5;j++)
{
printf("Please enter the maximum degree of the polynomial ");
scanf("%d",&exponent); //prompt the exponent by user
if (exponent>=0)
{
printf("Please enter the coefficients ");
/* print the terms of expression */
for (i=0;i<=exponent;i++)
{
scanf("%d",&arr[i]); //prompt coefficients by use
}
polynomial(exponent,arr); //print the polynomial expression
derivative(exponent,arr); //print the derivative expression
printf("\n\n\n");
}
else
{
printf("\n\n\n");
}
}
free( arr ); //release the storage
}
return 0;
}
int main(void)
{
while(1){ //loop forever
printf("Please enter the maximum degree of the polynomial: ");
scanf("%d",°ree); //input maximum degree.
if (degree < 0 ){
break;
//the program will exit when input less then 0.
}
printf("Please enter the coefficients: ");
for (i=0;i<=degree;i++){
scanf("%d",&coef[i]);
//input all coefficients from coef[1] to coef[i].
}
polynomial(); //output all polynomial.
printf("\n");
reciprocal(); //output all reciprocal.
printf("\n");
selfreciprocal(); //output if it is self-reciprocal or not.
}
}
int main(void)
{
int i, loop, poldegree, size;
for(loop=1; loop!=0;) // loop=1 --> the program keeps on running asking for new values, loop=0 --> the program terminates
{
printf("Please enter the maximum degree of the polynomial: ");
scanf("%d", &poldegree);
if (poldegree<0) // if the polynomial degree (poldegree) entered is negative then loop=0 and the program terminates
loop=0;
else
{
size = poldegree +1 ;
int * coefficients = new int[size]; // we define the size of our array which depends on the polynomial degree entered by the user
printf("Please enter the coefficients: ");
for(i=0; i<=poldegree; i++)
scanf("%d", &coefficients[i]); // it reads tha values of the coefficients which are placed into an array
polynomial(coefficients, poldegree);
printf("\n");
reciprocal_calc(coefficients, poldegree);
printf("\n");
if(poldegree!=0)
loop=reciprocal_check(coefficients, poldegree);
else if(poldegree==0)
{
printf("The polynomial is self-reciprocal \n\n");
loop=0;
}
if (loop==1) // if the polynomial is not self-reciprocal then the array's values should be deleted sp that the next coefficients can be entered
{
free(coefficients);
printf("\n\n\n");
}
}
}
return 0;
}
int main(void)
{
while(1){ //loop forever
printf("Please enter the maximum degree of the polynomial: ");
scanf("%d",°ree); //input maximum degree.
if (degree < 0 ){
break;
//the program will exit when input less then 0.
}
printf("Please enter the coefficients: ");
for (i=0;i<=degree;i++){
scanf("%d",&*(coef+i));
//input all coefficients from coef[1] to coef[i].
}
polynomial(); //output all polynomial.
if (coef !=NULL){
free(coef);
}
printf("\n");
}
}