Description
Cancel common variable exponents in an algebraic fraction.
A monomial combines a coefficient with variable exponents. Ordinary nonnegative exponents and signed Laurent exponents have different domains; exponent-vector divisibility and greatest-common-factor rules describe the variable part unless coefficients are explicitly included. Zero coefficients and absent variables need separate flags.
Cancel common variable exponents in an algebraic fraction.
When to use this tool
Use Algebraic Fraction Cancellation Exponent Term when checking the stated exponent-vector, support, coefficient or Laurent convention.
How to use the tool and how it works
- Enter numerator, denominator. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cancelled, numerator, denominator. Use the output convention below.
Cancel common variable exponents in an algebraic fraction. Require aligned nonnegative whole vectors; cancelled is the componentwise minimum, subtract it from numerator and denominator exponents.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| numerator | Numerator | Required. Array of safe integer; maximum items 256. |
| denominator | Denominator | Required. Array of safe integer; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cancelled | Componentwise minimum exponent canceled algebraically; original denominator exclusions still apply. | Required. Array of safe integer; maximum items 256. |
| numerator | Numerator | Required. Array of safe integer; maximum items 256. |
| denominator | Denominator | Required. Array of safe integer; maximum items 256. |
{
"input": {
"numerator": [
3,
1
],
"denominator": [
1,
4
]
},
"output": {
"cancelled": [
1,
1
],
"numerator": [
2,
0
],
"denominator": [
0,
3
]
}
}Limitations and assumptions
- Cancellation does not restore excluded zero-denominator points; coefficients and the original expression domain are not validated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use the complete coefficient domain and variable assumptions for symbolic simplification, full monomial divisibility or algebraic-domain conclusions.
References
Similar or alternative tools
- Algebra: Monomial Gcd Exponent Vector
Return variable-part monomial GCD exponents.
- Monomial Lcm Exponent Gap
Return exponent increments from one monomial to a variable-part LCM.