Comment #30 on issue 3128 by someb...@bluewin.ch: Sum and Product
manipulations
http://code.google.com/p/sympy/issues/detail?id=3128
Ok, and now back to the original topic. From the inital list:
- [x] Addition of two sums / products with the same limits
- [x] Addition of two sums with different limits (like Sum(i, (i, 0, k)) +
Sum(i, (i, k, m)))
- [x] Change of index
- [ ] Product of Sums
- [x] Reorder multiple sums or products
- [x] Reverse order of limits
- [ ] The inverse of any of the above rules
Point 1 works:
In [117]: S1 = Sum(i, (i, a, b))
In [118]: S2 = Sum(i**2, (i, a, b))
In [119]: S1+S2
Out[119]: Sum(i, (i, a, b)) + Sum(i**2, (i, a, b))
In [120]: simplify(_)
Out[120]: Sum(i**2 + i, (i, a, b))
In [133]: P1 = Product(i, (i, a, b))
In [137]: P2 = Product(i**3+i, (i, a, b))
In [138]: P1*P2
Out[138]: Product(i, (i, a, b))*Product(i**3 + i, (i, a, b))
In [139]: simplify(_)
Out[139]: Product(i**4 + i**2, (i, a, b))
Point 2 works in special cases, could maybe be improved:
In [127]: Sum(i, (i, 0, k)) + Sum(i, (i, k+1, m))
Out[127]: Sum(i, (i, 0, k)) + Sum(i, (i, k + 1, m))
In [128]: simplify(_)
Out[128]: Sum(i, (i, 0, m))
In [125]: Sum(i, (i, 0, k)) + Sum(i, (i, k, m))
Out[125]: Sum(i, (i, 0, k)) + Sum(i, (i, k, m))
In [126]: simplify(_)
Out[126]: Sum(i, (i, 0, k)) + Sum(i, (i, k, m))
In [131]: Sum(i, (i, 0, k)) + Sum(i, (i, k+12, m))
Out[131]: Sum(i, (i, 0, k)) + Sum(i, (i, k + 12, m))
In [132]: simplify(_)
Out[132]: Sum(i, (i, 0, k)) + Sum(i, (i, k + 12, m))
In [140]: P1 = Product(i, (i, a, b))
In [143]: P2 = Product(i, (i, b+1, c))
In [144]: P1*P2
Out[144]: Product(i, (i, a, b))*Product(i, (i, b + 1, c))
In [145]: simplify(_)
Out[145]: Product(i, (i, a, c))
There are clearly bugs with point 4:
In [156]: S1
Out[156]: Sum(i, (i, a, b))
In [157]: S2
Out[157]: Sum(i**2, (i, a, b))
In [158]: S1*S2
Out[158]: Sum(i, (i, a, b))*Sum(i**2, (i, a, b))
In [159]: simplify(_)
Out[159]: Sum(i**2, (i, a, b))
In [160]: _ - S2
Out[160]: 0
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