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 H1x and H2x 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.
withDEtools:
H≔expInt2x−7x+42,xx6+16x5+103x4+327x3+647x2+737x+194x−12x+24x+42
H≔ⅇ∫2x−7x+42ⅆxx6+16x5+103x4+327x3+647x2+737x+194x−12x+24x+42
H1,H2≔ReduceHyperexpH,x:
−24x3+143x2+292x+216ⅇ∫−15x+42ⅆxx−1x+23
x3+17x2+88x−231ⅇ∫−23−2xx+42ⅆxx−1
AreSimilarH,H2,x
true
AreSimilarH1,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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