Hi,

I’m considering proposing a *Symbolic Sensitivity Analysis* module for 
SymPy in GSoC 2025 and wanted to get your thoughts on how best to align it 
with SymPy’s goals.

The idea is to introduce *sympy.sensitivity*, a module that systematically 
handles sensitivity analysis for parametric systems—both algebraic and 
differential. While SymPy provides differentiation through diff(), there’s 
no unified framework for studying how parameter variations affect system 
behavior. This module would:

   - 
   
   *Compute symbolic sensitivities* (e.g., ∂f/∂p for parametric functions).
   - 
   
   *Support ODE sensitivity analysis*, generating sensitivity equations 
   alongside system dynamics.
   - 
   
   *Extend to higher-order sensitivities* (Hessians, second-order effects).
   - 
   
   *Provide tools for simplification and interpretation*, helping identify 
   dominant parameters.
   
This functionality would be valuable in control systems, optimization, and 
physics, where understanding parameter influence is crucial. Given SymPy’s 
existing tools in calculus, solvers, and physics, I see this as a natural 
extension—but I’d love to hear if there are specific considerations or 
integrations that would make it a stronger fit within the SymPy ecosystem.

Would this be something worth pursuing for GSoC? Are there key challenges I 
should address in my proposal to improve its viability? Any insights would 
be really helpful!

Best,
Shubham Vaghasiya

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