Jtdylktuy

I currently taking a course in Algebra, and I find myself typing the polynomial

$a_nx^n+ldots+a_1x+a_0$ 

over and over again, and I was wondering if I could create a shortcut for such a polynomial form, such that I can control what coefficients and variables I want.

I know the polynomial package exists, but I cannot seem to incorporate the "ldots" in the commands it offers.

I think that what you need is a macro that takes two arguments: the "name" of the coefficients, and the "name" of the base of the power terms. The names will, in general, be single letters, right? (You've indicated, in a comment, that the highest and lowest order of the polynomial are always n and 0, respectively.) The macro called pn in the following example satisfies these criteria.

Incidentally, the typographic ellipsis used between binary operators (such as +) is usually of the form cdots, not ldots. (The letters "c" and "l" refer to either centered (on the math line) or low (on the typographic baseline).

documentclass{article}

%% The following macro must be used only in math mode:

newcommandpn[2]{#1_n #2^n + cdots + #1_1 #2 + #1_0}



begin{document}

$pn{a}{x}$



$pn{lambda}{z}$



$pn{alpha}{xi}$

end{document}

Addendum to address the OP's follow-up request: Suppose that not all polynomials are of order n, but that it's true that most polynomials are, in fact, order n. In that case, it makes sense to modify the pn macro that it takes 3 rather than 2 arguments, with additional argument taking on the value n by default.

documentclass{article}

%% The following macro must be used only in math mode:

newcommandpn[3][n]{#2_{#1} #3^{#1} + cdots + #2_1 #3 + #2_0}



begin{document}

$pn{a}{x}$ % use default order (n) of polynomial



$pn[4]{lambda}{z}$



$pn[q]{alpha}{xi}$

end{document}

With a fairly simple syntax:

documentclass{article}

usepackage{amsmath}

usepackage{xparse}



ExplSyntaxOn

NewDocumentCommand{poly}{O{}}

 {

  group_begin:

  keys_set:nn { poly } { #1 }

  kam_poly:

  group_end:

 }



keys_define:nn { poly }

 {

  degree  .tl_set:N   = l__poly_degree_tl,

  var     .tl_set:N   = l__poly_var_tl,

  coef    .tl_set:N   = l__poly_coef_tl,

  reverse .bool_set:N = l__poly_reverse_bool,

  degree  .initial:n  = n,

  var     .initial:n  = x,

  coef    .initial:n  = a,

  reverse .default:n  = true,

 }



cs_new_protected:Nn kam_poly:

 {

  bool_if:NTF l__poly_reverse_bool

   {

    l__poly_coef_tl sb { 0 } +

    l__poly_coef_tl sb { 1 } l__poly_var_tl +

    dots +

    l__poly_coef_tl sb { l__poly_degree_tl }

    l__poly_var_tl sp { l__poly_degree_tl }

   }

   {

    l__poly_coef_tl sb { l__poly_degree_tl }

    l__poly_var_tl sp { l__poly_degree_tl } +

    dots +

    l__poly_coef_tl sb { 1 } l__poly_var_tl +

    l__poly_coef_tl sb { 0 }

   }

 }

ExplSyntaxOff



begin{document}



$poly$



$poly[var=z]$



$poly[var=t,degree=m,coef=b]$



$poly[var=t,degree=m,coef=b,reverse]$



end{document}

The keys can be specified in any order, freeing you from the need to remember which parameter goes first; the default values are

var = x

degree = n

coef = a

You can also make shorthands with, say

newcommand{polybtn}{poly[var=t,coef=b,degree=n]}

I would propose poly{ax^n}

newcommandpoly[1]{dopoly#1^n^relax}

defdopoly#1#2^#3^#4relax{#1_{#3}#2^{#3} + dots + #1_{1}#2 + #1_{0}}

You can use poly{ax} or poly{ax^n}.