DEtools
AreSimilar
test if two hyperexponential functions are similar
Calling Sequence
Parameters
Description
Examples
References
AreSimilar(H1, H2, x)
H1
-
hyperexponential function of x
H2
x
variable
Let H1,H2 be hyperexponential functions of x over a field K of characteristic 0. The AreSimilar(H1,H2,x) command returns true if H1⁡x and H2⁡x are similar. Otherwise, it returns false.
H1 and H2 are similar if their ratio can be written as the product of a rational function and a constant in some extension of K.
with(DEtools):
H := exp(Int((2*x-7)/(x+4)^2,x))*(x^6+16*x^5+103*x^4+ 327*x^3+647*x^2+737*x+194)/(x-1)^2/(x+2)^4/(x+4)^2;
H≔ⅇ∫2⁢x−7x+42ⅆx⁢x6+16⁢x5+103⁢x4+327⁢x3+647⁢x2+737⁢x+194x−12⁢x+24⁢x+42
(H1,H2) := ReduceHyperexp(H,x):
H1;
−24⁢x3+143⁢x2+292⁢x+216⁢ⅇ∫−15x+42ⅆxx−1⁢x+23
H2;
x3+17⁢x2+88⁢x−231⁢ⅇ∫−23−2⁢xx+42ⅆxx−1
AreSimilar(H,H2,x);
true
AreSimilar(H1,H2,x);
Geddes, Keith; Le, Ha; and Li, Ziming. "Differential rational normal forms and a reduction algorithm for hyperexponential functions." Proceedings of ISSAC 2004. ACM Press. (2004): 183-190.
See Also
DEtools[RationalCanonicalForm]
DEtools[ReduceHyperexp]
SumTools[Hypergeometric][AreSimilar]
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