DifferenceRootReduce

✖
`DifferenceRootReduce`

✖

DifferenceRootReduce[expr,n]

attempts to reduce expr to a single DifferenceRoot object as a function of n.

Details and Options

DifferenceRootReduce will attempt to represent any expression as a DifferenceRoot object.
DifferenceRootReduce[expr,n] always gives exactly 0 when the DifferenceRoot object for expr is equivalent to the zero sequence.
DifferenceRootReduce automatically threads over lists, as well as equations and inequalities.
DifferenceRootReduce[f] operates on a pure function or pure DifferenceRoot object.

Examples

open allclose all

Basic Examples (2)Summary of the most common use cases

Reduce the Fibonacci sequence to a DifferenceRoot object:

In[9]:=9

✖

https://wolfram.com/xid/0mlbomawp1tu-euwe7v

Out[9]=9

Compare the values:

In[10]:=10

✖

https://wolfram.com/xid/0mlbomawp1tu-c50vwb

Out[10]=10

In[11]:=11

✖

https://wolfram.com/xid/0mlbomawp1tu-btushh

Out[11]=11

Prove the Cassini identity:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-fgtyrh

Out[1]=1

Scope (8)Survey of the scope of standard use cases

Polynomial functions:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-z0m9i2

Out[1]=1

Rational functions:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-i8sqzp

Out[1]=1

Hypergeometric terms:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-q856qk

Out[1]=1

Addition:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-chdlk7

Out[1]=1

Term-wise multiplication:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-yapudp

Out[1]=1

Multisection:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-2l65ek

Out[1]=1

General expressions:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-mlzuvp

Out[1]=1

DifferenceRootReduce threads automatically over lists:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-3l9qjg

Out[1]=1

Options (1)Common values & functionality for each option

Method (1)

DifferenceRootReduce can give non-homogeneous equations:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-dxzovn

Out[1]=1

Use the option Method->"Homogeneous" to get a homogeneous equation:

In[2]:=2

✖

https://wolfram.com/xid/0mlbomawp1tu-9der6v

Out[2]=2

Applications (3)Sample problems that can be solved with this function

Verify the negation formula for Fibonacci:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-ffm5mm

Out[1]=1

Addition formula:

In[2]:=2

✖

https://wolfram.com/xid/0mlbomawp1tu-86cup

Out[2]=2

Double-angle formula:

In[3]:=3

✖

https://wolfram.com/xid/0mlbomawp1tu-cye3uq

Out[3]=3

Successor relation:

In[4]:=4

✖

https://wolfram.com/xid/0mlbomawp1tu-f9at06

Out[4]=4

Conjugation relation:

In[5]:=5

✖

https://wolfram.com/xid/0mlbomawp1tu-d7zwbg

Out[5]=5

A finite sum:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-qyxipb

Out[1]=1

The difference equation shows that all the values at are odd:

In[2]:=2

✖

https://wolfram.com/xid/0mlbomawp1tu-zhmen1

Out[2]=2

In[3]:=3

✖

https://wolfram.com/xid/0mlbomawp1tu-3nodob

Out[3]=3

Define Padovan numbers:

In[1]:=1

✖

https://wolfram.com/xid/0mlbomawp1tu-wokh3f

Out[1]=1

In[2]:=2

✖

https://wolfram.com/xid/0mlbomawp1tu-32bn37

Out[2]=2

Prove recurrence relations:

In[3]:=3

✖

https://wolfram.com/xid/0mlbomawp1tu-n2dkbe

Out[3]=3

In[4]:=4

✖

https://wolfram.com/xid/0mlbomawp1tu-yr9c5y

Out[4]=4

Prove summation identity:

In[5]:=5

✖

https://wolfram.com/xid/0mlbomawp1tu-8hks69

Out[5]=5

Top