Evaluate the monomial by substituting values for variables. Args: substitutions: A single value applied to all variables, or a dict mapping variable indices to values. Returns: The evaluated result. Raises: ValueError: If
(
self,
substitutions: int | float | Fraction | dict[int, int | float | Fraction],
)
| 284 | return set(sorted(self.variables.keys())) |
| 285 | |
| 286 | def substitute( |
| 287 | self, |
| 288 | substitutions: int | float | Fraction | dict[int, int | float | Fraction], |
| 289 | ) -> Fraction: |
| 290 | """Evaluate the monomial by substituting values for variables. |
| 291 | |
| 292 | Args: |
| 293 | substitutions: A single value applied to all variables, or a |
| 294 | dict mapping variable indices to values. |
| 295 | |
| 296 | Returns: |
| 297 | The evaluated result. |
| 298 | |
| 299 | Raises: |
| 300 | ValueError: If some variables are not given values. |
| 301 | """ |
| 302 | if isinstance(substitutions, (int, float, Fraction)): |
| 303 | substitutions = { |
| 304 | v: Monomial._rationalize_if_possible(substitutions) |
| 305 | for v in self.all_variables() |
| 306 | } |
| 307 | else: |
| 308 | if not self.all_variables().issubset(set(substitutions.keys())): |
| 309 | raise ValueError("Some variables didn't receive their values.") |
| 310 | if self.coeff == 0: |
| 311 | return Fraction(0, 1) |
| 312 | ans = Monomial._rationalize_if_possible(self.coeff) |
| 313 | for k in self.variables: |
| 314 | ans *= Monomial._rationalize_if_possible( |
| 315 | substitutions[k] ** self.variables[k] |
| 316 | ) |
| 317 | return Monomial._rationalize_if_possible(ans) |
| 318 | |
| 319 | def __str__(self) -> str: |
| 320 | """Get a string representation of the monomial. |