Splits an expression into two parts if possible

The series

• The series is: $\text{expr}_{1} \pm \text{expr}_{2} ...$
• $\pm$ represents plus or minus sign.
• The number of terms in the series can be 1 or more than 1.
• Each term $\text{expr}_{n}$ is an expression, and not necessarily $ax^{n}$

Use Case

• I want to transform the series by:
  • Writing a rule that split the series into 1st and remaining terms.
  • Writing another rule that transform the first term.
  • Using the two rule to transform all terms of the series.

Current Goal

• I want to split the series into:

  • the first term, and
  • the remaining terms

Constraint

• I only want the pattern to match for once.
  • There are several ways to split the expression into 2 parts
  • I only want a split that keeps the first term as simple as possible.

Test

I will use polynomials as test cases.

rule[expr_] = expr /. {Shortest[a_] + b__ :> a} test1 = x - 2x^{2} + 3x^{3}; rule[test1] test2 = -x^{4} + 2x^{2} + 3x^{3}; rule[test2] test3 = -x; rule[test3] test4 := -2 x^3 + Sum[Log[x], {n, 1, L}] 

Expected Result

• $x$
• $-x^{4}$
• $-x$
• $-2x^3$

Actual Result

• $x - 2 x^2 + 3 x^3$

• $2 x^2 + 3 x^3 - x^4$

• $-x$

• $L \log (x)-2 x^3$

Question

The rule matches with the whole series instead of the shortest first term.

How to fix the rule?

Thanks.