Rational Poly-Exponential Functions - Examples.

Worksheets

Below are maple worksheets, in the ".mws" format. These worksheets use and explain the code and functionality of the maple library to perform the act of multisectioning.

• Poly-exponential functions.
• Worksheet. Converting poly-exponential functions to exponential generating functions.
• Worksheet. Converting exponential generating functions to poly-exponential functions.
• Worksheet. Looking at recurrence polynomials and recurrence functions.
• Worksheet. Multisectioning the Lucas numbers.
• Worksheet. Looking at the different measures of size give for a few examples.
• Worksheet. An example where the recurrence polynomial is different depending on the value multisectioned at.
• Worksheet. An example of multisectioing the Chebyshev T polynomials.
• Worksheet. Multisectioning a poly-exponential function by using the recurrence polynomials.
• Worksheet. Multisectioning a poly-exponential function by using compression techniques
• Worksheet. Multisectioning a poly-exponential function making sure the we do the calculations over the integers.
• Worksheet. Multisectioning a poly-exponential function using linear algebra.
• Worksheet. Multisectioning a poly-exponential function by factoring out polynomials.
• Worksheet. Multisectioning a poly-exponential function by using symbolic differentiation and linear algebra.
• Worksheet. Multisectioning a poly-exponential function by using resultants.
• Rational Poly-exponential functions.
• Worksheet. Determining the top and bottom recurrence of the Bernoulli numbers, when multisectioned, using a naive method.
• Worksheet. Determining the top and bottom recurrence of the Bernoulli polynomials, when multisectioned, using a naive method.
• Worksheet. Multisectioning a rational poly-exponential function by using resultants and recurrence polynomials.
• Worksheet. Multisectioning a rational poly-exponential function by using fast polynomial multiplication, and linear algebra (method 1)
• Worksheet. Multisectioning a rational poly-exponential function by using fast polynomial multiplication, and linear algebra (method 2)
• Worksheet. Determining the top recurrence for a multisectioning a rational poly-exponential function by using information about the Taylor series expansion, and linear algebra.
• Worksheet. Determining the top and bottom recurrence for a multisectioning a rational poly-exponential function by using factoring out polynomials.
• Worksheet. Multisectioning a rational poly-exponential function by taking advantage of symmetries.