Example 7.1 (Automated ApĂ©ry Asymptotics)
*This worksheet **requires** the DiagonalAsymptotics/Kronecker package available at http://diagasympt.gforge.inria.fr*

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# Import Kronecker package
read "Kronecker.mpl"; # Define the rational function F := 1/(1-w*(1+x)*(1+y)*(1+z)*(1+y+z+y*z+x*y*z)); # Compute dominant asymptotics of the main power series diagonal A, U := DiagonalAsymptotics(numer(F),denom(F),[w,x,y,z],u,n): |

(1) |

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# Asymptotics are represented by the symbolic expression
A; |

(2) |

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# When u takes the following value
# Note 1: The large numeric precision was used to verify minimality # Note 2: Random choices are used to output this result. Rerun the code to get # different expressions! (which yield the same asymptotic behaviour, of course) U; |

(3) |

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# Because u is an algebraic number of degree two in this example, we can express asymptotic behaviour exactly
evala(allvalues(subs(u=U[1],A))); |

(4) |

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