<<  ../Sigma.m

<<  ../Free.m

Structure set computation

TestTestCase[]

Examples

Example 1. The general indefinite double sum (checked)

s = SigmaSum[SigmaSum[X[i], {i, 1, k}], {k, 1, n}]

SigmaReduce[s,  SimplifyByExt -> Depth]

Example 2. Generalization of a hypergeometric identity (checked)

s = 
      SigmaSum[SigmaProduct[X[i], {i, 1, k}]*(X[k + 1] - 1), {k, 0, 
          n}]

SigmaReduce[s]

Example 3. Trivial and nontrivial examples may be close (checked)

Example 4 a)  (checked)

s = SigmaSum[X[k]*SigmaSum[X[i], {i, 1, k}], {k, 1, n}]

SigmaReduce[s,  SimplifyByExt  ->  Depth]

Example 4 b) (checked)

s = SigmaSum[X[k + 1]*SigmaSum[X[i], {i, 1, k}], {k, 1, n}]

SigmaReduce[s,  SimplifyByExt -> Depth]

Example 4. Sum-thing (checked)

s = 
      SigmaSum[SigmaProduct[
            X[i], {i, 1, k}]*(X[k] + 
              SigmaSum[X[i], {i, 1, k}]*(X[k + 1] - 1)), {k, 1, 
          n}]

SigmaReduce[s, SimplifyByExt -> Depth]

s /. X[i_] -> 1/i

SigmaReduce[%, SimplifyByExt -> Depth]

Example 5. From GKP, Exercise 5.93 (checked)

s = 
      SigmaSum[SigmaProduct[(X[j] + a)/X[j], {j, 1, k}]/(X[k] + 
              a), {k, 1, n}]

SigmaReduce[s]