Polynomial Equation String Builder

A symbolic algebra service stores one polynomial term per row and needs a canonical equation string that can be fed to a downstream solver.

Table: Terms

• power: non-negative exponent of the term
• factor: signed coefficient of the term (never zero)

Each row describes one term of a polynomial in variable X.

Build a single equation string that follows this canonical protocol:

1. Put all terms on the left-hand side and append "=0".
2. Every term must be formatted as: <sign><abs(factor)>X^<power>.
3. Special formatting exceptions:
   • If power = 1, omit "^1" (example: +3X)
   • If power = 0, omit both "X" and exponent (example: -8)
4. Terms must appear in descending order of power.

Task: Return exactly one row containing exactly one column:

• equation

Supported submission environments:

• SQL (SQLite 3.27.2)
• Pandas (Python)

Terms:
| power | factor |
|-------|--------|
| 2     | 1      |
| 1     | -4     |
| 0     | 2      |

[
  {"equation":"+1X^2-4X+2=0"}
]

Terms:
| power | factor |
|-------|--------|
| 4     | -4     |
| 2     | 1      |
| 1     | -1     |

[
  {"equation":"-4X^4+1X^2-1X=0"}
]

Terms:
| power | factor |
|-------|--------|
| 0     | -7     |
| 3     | 2      |
| 1     | 5      |

[
  {"equation":"+2X^3+5X-7=0"}
]