Fixes # .

Summary/Motivation:
This PR ports the core symbolic-gradient functionality from the historical pyomo-doe-symbolic work into the current pyomo.contrib.doe implementation.

Summary/Motivation:

This PR ports the core symbolic-gradient functionality from the historical pyomo-doe-symbolic work into the current pyomo.contrib.doe implementation.

Rather than merging the old branch directly, this change transplants the symbolic DoE pieces onto current main so that symbolic sensitivities work with the newer DoE implementation already present in Pyomo, including the current objective and GreyBox-oriented code paths.

This PR is intentionally scoped to the core symbolic-gradient integration. It does not attempt to port every example, test refactor, or auxiliary change from the historical adowling2/pyomo-doe-symbolic branch in one step.

This contribution was prepared with coding assistance from OpenAI Codex. All design decisions, validation, testing, and quality-assurance responsibility remain with Shilpa Narasimhan.

Local validation included:

• pyomo/contrib/doe/tests: 133 passed, 4 skipped, 5 warnings, 10 subtests passed
• pyomo/contrib/doe/tests/test_greybox.py: 33 passed in HSL-enabled local environments

The remaining public-CI GreyBox cyipopt skips are environment-dependent and tied to MA57/HSL runtime availability.

Changes proposed in this PR:

• add GradientMethod support to DesignOfExperiments
• preserve the existing finite-difference workflow through the new gradient-method interface
• add a symbolic / pynumero gradient path for DoE
• add an analytic FIM computation path for non-optimization FIM evaluation
• export ExperimentGradients from pyomo.contrib.doe
• refactor ExperimentGradients so symbolic and automatic differentiation are set up together
• add supporting symbolic-gradient utilities for labeled experiment models
• update DoE model construction so symbolic sensitivities can be used in the Jacobian-based DoE machinery
• add a guard preventing run_doe() from being called with GradientMethod.kaug
• add the polynomial example and polynomial-focused regression coverage
• add broader symbolic-versus-automatic gradient consistency tests
• add factorial-result dataframe tests
• add reactor regression tests against expected solutions
• clarify the GreyBox cyipopt test skip reason when the MA57/HSL runtime is unavailable

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