Find the Newton polygon of the following polynomials

Find the Newton polygon of the following polynomials:

$ (i) \ f(X)=(1-X)(1-pX)(1-p^3X)$ ,

$ (ii) \ g(X)=\prod_{i=1}^{p^2} (1-iX)$ .

Answer:

$ (i)$

To find the Newton polygon for the polynomial $ f(X)$ , we can simply multiply the linear factors as follows:

$ f(X)=(1-X)(1-pX)(1-p^3X) \ \Rightarrow f(X)=1-(p^3+p+1)X+(p^4+p^3+p)X^2-p^4 X^3$ .

Thus the Newton polygon has following vertices:

$ (0, ord_p(1)), \ (1, ord_p(-p^3+p+1)), \ (2, ord_p(p^4+p^3+p)) , \ (3,ord_p(p^4))$

i.e., $ (0,0), \ (1, 0), \ (2,1), \ (3,4)$ .

But this process we can not apply to the second polynomial $ g(X)$ in (ii) because it will be complicated.

So there should be other easy method to find the Newton polygon for the polynomials in $ (i)$ and $ (ii)$ .

Please help me find the Newton polygon for $ (ii)$ .

Find a number within a range with the less decimal places possible

Preciso encontrar um número, que esteja entre 2 números, que possua o menor quantidade de dígitos/casas decimais!

Exemplo: Número entre 0.1234 e 0.1245. A resposta é 0.124 Porque está entre os dois números, e possui o menor quantidade de dígitos possíveis.

Obs: Intervalo aberto nas duas pontas, ou seja, nem o 0.1234 e nem o 0.1245 podem ser a resposta.

Alguém consegue pensar em uma solução eficiente para esse problema?

microsoft graph api: ability to find the attachment link of a list item

is it possible to get the link of the attachment that is attached to a list item?

there is a attachment field but that only gives if there is an attachment or not. It does not give the url of the attachment.

the query looks like below:

https://graph.microsoft.com/beta/sites/mytenant.sharepoint.com:/sites/mysite:/lists/OEC_Docs?select=id,name,lastModifiedDateTime&expand=items(expand=fields(select=Title,Attachments,OptyNumber)) 

How do I find out what is causing the app “Google” to use so much background data

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What is causing this and/or how can I turn off background usage for Google for real (obviously the toggle is a placebo)

Screenshots of data usage.

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c code to find the line number in the function argument string

    #include<stdio.h>     #include<string.h>     unsigned int FindFunctionDefn( const char* strFunctionName, const char*      strSourceCode ){     int n = strlen(strSourceCode);     int m = strlen(strFunctionName);     int i = 0;     unsigned int  line = 0;     char new[300];     strcpy(new,"");     int p;     char u[1];     for(i=0;i<n;i++)     {   if (strSourceCode[i]!='\n'){     u[0] = strSourceCode[i];     strcat(new,u);     }      if (strSourceCode[i] == '\n'){     line = line + 1;     p=strstr(new,strFunctionName);     printf("%d",p);     if (p!=NULL){     printf("%s \n",p);     printf("%u",line);     return line;     }      else     {     strcpy(new,"");     }     }      }      }            int main(int argc, const char * argv[]){     const char strFunctionName[] = "func2";     const char strSourceCode[] =  "int func1(){ return 0; }\n int      func2(){ return 1; }\n" "int main(int argc, char*argv[]){ return      func2(); }\n";     FindFunctionDefn( strFunctionName, strSourceCode );     }       [![this is the code in codeblock[![\]\[1\]][1]][1]][1] 

the following C function: unsigned int FindFunctionDefn( const char* strFunctionName, const char* strSourceCode ); FindFunctionDefn takes two strings as inputs: a function name and a program string; it returns as an output the line number that contains the function definition (differentiate this with the function calls) in the program string. The program string is a valid C code; it contains a character “\n” indicate the end of a line with the line number starts from one. The program string is guaranteed not to contain any C (or C++) comments. The function FindFunctionDefn returns 0 if it fails to find the function definition. For example, char strFunctionName[] = “func2”; char strSourceCode[] = “int func1(){ return 0; }\n int func2(){ return 1; }\n” “int main(int argc, char*argv[]){ return func2(); }\n”; FindFunctionDefn( strFunctionName, strSourceCode ) should return 2. but i am not getting any output please clarify what have i done wrong thanks

Best way to find sites in google that links back to another site (backlink checker)

How can i make this happen?

for example. 

I have a site which is abc.com and i want to search google who links to my site abc.com)

perhaps ill provide anchor text?branding?naked url?root domain?

what is the best way to do this? 

it is like ahrefs a backlink checker but its a real time scraping from scrapebox?

and I can export all the backlinks to excel file and it provides the backlink lists and anchor text linked to abc.com