Nested Scheme (Help, I need a definition/explanation)

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In summary, the conversation discusses nested scheme as a method for evaluating polynomials, but the book lacks thorough explanations and the speaker is seeking a basic understanding. The expert suggests that this may be similar to Horner scheme, a technique for efficiently evaluating polynomials. They also provide a link for more information.
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Atran
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Hi, I'm reading about polynomials and I've encountered a method called nested scheme.
The tragedy is that my math book usually has no rigorous definitions and sometimes lacks definitions.
My book is only stating that nested scheme is a method for evaluating polynomials, and thereafter it continues with two examples. It does not provide an explanation.

I cannot find any proper link, for nested scheme, in google. Can you teach me the very basics, and that should be sufficient for the understanding of more advanced topics...
Thanks for help...
 
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  • #2
This sounds like something that is called Horner scheme, a technique for evaluating polynomials efficiently.

For example, f(x) = 2x3 - 6x2 + 2x - 1 can be rewritten as f(x) = x(x(2x - 6) + 2) - 1.

More information here - http://en.wikipedia.org/wiki/Horner_scheme
 
  • #3
Thanks...
 

FAQ: Nested Scheme (Help, I need a definition/explanation)

What is a Nested Scheme?

Nested Scheme is a programming concept where one Scheme expression is embedded within another, creating a hierarchy of nested expressions. It allows for more complex and flexible code structures.

How does Nested Scheme work?

In Nested Scheme, expressions are evaluated from the innermost to the outermost level. This means that the result of an inner expression can be used as input for an outer expression. It follows the same principles as regular Scheme, but with the added complexity of nested levels.

What are the benefits of using Nested Scheme?

Nested Scheme allows for more complex and flexible code structures, making it easier to write and maintain code. It also allows for the reuse of code and reduces the need for repetitive coding.

What are some examples of Nested Scheme?

An example of Nested Scheme is a function that calculates the average of a list of numbers. The function can be nested within another function that sorts the list before calculating the average, creating a more efficient and organized code structure.

Are there any drawbacks to using Nested Scheme?

The main drawback of Nested Scheme is that it can be difficult to read and understand, especially for beginners. It also requires a good understanding of regular Scheme in order to effectively use and implement nested expressions.

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