Re: Lists and polynomials

*To*: mathgroup at smc.vnet.net*Subject*: [mg71048] Re: [mg71023] Lists and polynomials*From*: Carl Woll <carlw at wolfram.com>*Date*: Mon, 6 Nov 2006 02:53:00 -0500 (EST)*References*: <200611050407.XAA21691@smc.vnet.net>

aland wrote: >Hi All, >Another beginner here! >I am trying to create a list based around a polynomial. >In particular, I want to work with a large-ish number based on a power >of 2 >e.g. >629 x^2 + 863 x + 271 >where x = 2^10 >What I want to do is take a number y such as y=6718213 and derive a >list where the list values are the coefficients of the polynomial. >So that if my number y=1027 (2^10 +3) >the polynomial would be >x+3 >and the list would be { 1,3 } > >I have tried NestWhileList[] and PolynomialRemainder[] but I'm really >struggling to get them to do what I want. I have a procedural >programming background; functional programming looks excellent, I just >can't get it to work! > >Any suggestions (like you're using the wrong functions, try these >others....) would be gratefully received. > >I'm also looking to convert the list back into a number once I've >finished working with the polynomial. > >Mathematica v4.2, although it probably doesn't make a lot of >difference. > >Thanks in advance, > >Alan > > If I understand your problem correctly, then the simplest solution is to use IntegerDigits and FromDigits: In[1]:= IntegerDigits[1027, 2^10] Out[1]= {1, 3} gives the list you want, and: In[2]:= FromDigits[{1, 3}, 2^10] Out[2]= 1027 converts back into your original number. You could even use FromDigits to convert to the polynomial form: In[3]:= FromDigits[{1, 3}, x] Out[3]= x + 3 Carl Woll Wolfram Research

**References**:**Lists and polynomials***From:*"aland" <alandix@yahoo.com>