<p>Have results from the <a href="http://en.wikipedia.org/wiki/Calculus_of_variations" rel="nofollow">calculus of variations</a> been used previously in TCS? </p>

CC BY-SA 3.0
2011-06-18T11:34:42.707Z
The answer would be yes. Calculus of variations led to the Hamilton principle. Quantum computing captures the ability to compute arbitrary Hamiltonians. This in turn led to the discovery of polynomial time algorithms for factoring problem by Shor.
Mohammad Al-Turkistany
CC BY-SA 3.0
2011-06-19T00:41:41.460Z
@Mohammad: Thanks. But this is sort of a roundabout connection. One might naively expect more direct applications to complexity theory, where algorithms are represented as functions and the goal is to minimize some functional of them.
arnab
CC BY-SA 3.0
2011-06-20T22:07:33.467Z
Does classic calculus has applications in CS? Isn't it it strange that the field invented 400 years ago, which pops up all over the [hard] science, has such minuscule appreciation in CS. Especially compared to eager adoption of meta mathematics concepts developed last century (logic, computability).
Tegiri Nenashi
CC BY-SA 3.0
2011-06-21T17:02:06.270Z
theoryCS still focuses on the discrete. As the field evolves, more calculus will show up. For example, complex analysis is used heavily in the analysis of algorithms, especially when you care about constants (see Flajolet-Sedgewick for example)
Suresh Venkat
<reference-request><ho.history-overview>
Use of calculus of variations
arnab
# Use of calculus of variations

(Asked by: username_0 on 2011-06-18)

Have results from the [calculus of variations](http://en.wikipedia.org/wiki/Calculus_of_variations) been used previously in TCS?

**Tags:** reference-request, ho.history-overview

> **Comments:**
> **username_1**: The answer would be yes. Calculus of variations led to the Hamilton principle. Quantum computing captures the ability to compute arbitrary Hamiltonians. This in turn led to the discovery of polynomial time algorithms for factoring problem by Shor.  
> **username_0**: @Mohammad: Thanks. But this is sort of a roundabout connection. One might naively expect more direct applications to complexity theory, where algorithms are represented as functions and the goal is to minimize some functional of them.  
> **username_2**: Does classic calculus has applications in CS? Isn't it it strange that the field invented 400 years ago, which pops up all over the [hard] science, has such minuscule appreciation in CS. Especially compared to eager adoption of meta mathematics concepts developed last century (logic, computability).  
> **username_3**: theoryCS still focuses on the discrete. As the field evolves, more calculus will show up. For example, complex analysis is used heavily in the analysis of algorithms, especially when you care about constants (see Flajolet-Sedgewick for example)  

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