# ore_algebra.examples.ctΒΆ

Creative telescoping

EXAMPLE:

sage: from ore_algebra.examples import ct
sage: ct.ideal.ct(ct.Dx)
([1],
[((-144*n^3*x^7 - 300*n^2*x^7 + 324*n^3*x^5 - 204*n*x^7 + 675*n^2*x^5 -
45*x^7 - 216*n^3*x^3 + 460*n*x^5 - 450*n^2*x^3 + 102*x^5 + 36*n^3*x -
308*n*x^3 + 75*n^2*x - 69*x^3 + 52*n*x + 12*x)/(-720*n^6*x^4 - 1644*n^5*x^4
+ 540*n^6*x^2 - 1320*n^4*x^4 + 1233*n^5*x^2 - 429*n^3*x^4 + 180*n^6 +
980*n^4*x^2 - 45*n^2*x^4 + 456*n^5 + 311*n^3*x^2 + 449*n^4 + 32*n^2*x^2 +
213*n^3 + 48*n^2 + 4*n))*Dx^2 + ((216*n^5 + 756*n^4 + 1020*n^3 + 660*n^2 +
204*n + 24)/(-720*n^6*x^4 - 1644*n^5*x^4 + 540*n^6*x^2 - 1320*n^4*x^4 +
1233*n^5*x^2 - 429*n^3*x^4 + 180*n^6 + 980*n^4*x^2 - 45*n^2*x^4 + 456*n^5 +
311*n^3*x^2 + 449*n^4 + 32*n^2*x^2 + 213*n^3 + 48*n^2 + 4*n))*Sn +
((-720*n^4*x^6 - 2076*n^3*x^6 + 1260*n^4*x^4 - 2220*n^2*x^6 + 3417*n^3*x^4
- 1041*n*x^6 - 576*n^4*x^2 + 3455*n^2*x^4 - 180*x^6 - 1425*n^3*x^2 +
1545*n*x^4 + 36*n^4 - 1308*n^2*x^2 + 258*x^4 + 84*n^3 - 532*n*x^2 + 73*n^2
- 82*x^2 + 28*n + 4)/(-720*n^6*x^4 - 1644*n^5*x^4 + 540*n^6*x^2 -
1320*n^4*x^4 + 1233*n^5*x^2 - 429*n^3*x^4 + 180*n^6 + 980*n^4*x^2 -
45*n^2*x^4 + 456*n^5 + 311*n^3*x^2 + 449*n^4 + 32*n^2*x^2 + 213*n^3 +
48*n^2 + 4*n))*Dx + (144*n^5*x^5 - 420*n^4*x^5 - 180*n^5*x^3 - 1584*n^3*x^5
+ 165*n^4*x^3 - 1575*n^2*x^5 - 180*n^5*x + 1163*n^3*x^3 - 633*n*x^5 -
501*n^4*x + 1303*n^2*x^3 - 90*x^5 - 599*n^3*x + 561*n*x^3 - 388*n^2*x +
84*x^3 - 132*n*x - 18*x)/(-720*n^6*x^4 - 1644*n^5*x^4 + 540*n^6*x^2 -
1320*n^4*x^4 + 1233*n^5*x^2 - 429*n^3*x^4 + 180*n^6 + 980*n^4*x^2 -
45*n^2*x^4 + 456*n^5 + 311*n^3*x^2 + 449*n^4 + 32*n^2*x^2 + 213*n^3 +
48*n^2 + 4*n)])