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AreSimilar

  

test if two hyperexponential functions are similar

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

AreSimilar(H1, H2, x)

Parameters

H1

-

hyperexponential function of x

H2

-

hyperexponential function of x

x

-

variable

Description

• 

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.

Examples

withDEtools:

Hⅇ∫2x7x+42ⅆxx6+16x5+103x4+327x3+647x2+737x+194x12x+24x+42

H:=ⅇ∫2x7x+42ⅆxx6+16x5+103x4+327x3+647x2+737x+194x12x+24x+42

(1)

H1,H2ReduceHyperexpH,x:

H1

24x3+143x2+292x+216ⅇ∫15x+42ⅆxx+23x1

(2)

H2

x3+17x2+88x231ⅇ∫232xx+42ⅆxx1

(3)

AreSimilarH,H2,x

true

(4)

AreSimilarH1,H2,x

true

(5)

References

  

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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