Compatibility Issues in Maple 15 - Maple Programming Help

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Compatibility Issues in Maple 15

  

The following is a brief description of the compatibility issues that affect users upgrading from Maple 14 to Maple 15.

 

Stirling numbers

finance package

DifferentialAlgebra

requires command

Plot Data Structures

Stirling numbers

• 

The Stirling numbers of the first and second kind, formerly available in the combinat package, are now top-level commands, Stirling1 and Stirling2.  For compatibility with previous releases, they can also be called as part of the combinat package as combinat[stirling1] and combinat[stirling2].

• 

To view a list of mathematical functions available as top-level commands, see initial functions.

finance package

• 

The finance package has been deprecated.  The commands formerly in that package are now part of the superseding Finance package.

DifferentialAlgebra

• 

The former ChangeRanking command got merged into RosenfeldGroebner.

  

Example 

with(DifferentialAlgebra):

  

Define a ranking for a DE system that involves two dependent variables x,y and one independent variable t

R := DifferentialRing(derivations = [t], blocks = [[x, y]]):

sys := [diff(x(t),t) = -alpha*x(t) + beta*y(t) - (rho*x(t))/(kappa+x(t)), diff(y(t),t) = alpha*x(t) - beta*y(t)];

sysⅆⅆtxt=αxt+βytρxtκ+xt,ⅆⅆtyt=αxtβyt

(1)
  

This call to RosenfeldGroebner bundles the two ODEs in a regular differential chain.

ideal := RosenfeldGroebner(sys, R);

idealregular_differential_chain

(2)

Equations(ideal, solved);

ⅆⅆtxt=αxt2βytxt+αxtκ+ρxtβytκκ+xt,ⅆⅆtyt=αxtβyt

(3)
  

As can be seen in the left-hand sides above, x' and y' are isolated, so the leading derivatives appear with degree 1, and hence the differential ideal is prime:

Is(prime, ideal);

true

(4)
  

This ideal can be rewritten in decoupled form, solving for y with respect to x, by changing the ranking for the dependent variables, from x,y to y,x. Bearing in mind that this ideal is prime, this change can be performed directly by RosenfeldGroebner passing the ideal as first argument. You only need to additionally pass to RosenfeldGroebner the piece of information that is changing

newideal := RosenfeldGroebner(ideal, blocks = [y, x]);

newidealregular_differential_chain

(5)
  

Check the Equations: they are correspondingly solved for yt with respect to xt

Equations(newideal, solved);

yt=ⅆⅆtxtxtⅆⅆtxtκαxt2αxtκρxtxtβ+βκ,ⅆ2ⅆt2xt=ⅆⅆtxtxt2α+ⅆⅆtxtxt2β+2ⅆⅆtxtxtακ+2ⅆⅆtxtxtβκ+ⅆⅆtxtακ2+ⅆⅆtxtβκ2+ⅆⅆtxtκρ+xt2βρ+xtβκρxt2+2xtκ+κ2

(6)

unwith(DifferentialAlgebra):

requires command

• 

The requires command has been deprecated.

Plot Data Structures

• 

A new _ATTRIBUTE structure has been added to certain plot data structures and its purpose is to carry information for internal use. This change does not affect usage of Maple's plotting commands and may be relevant only if you directly manipulate the plot data structures (which is generally not recommended).

See Also

Index of New Maple 15 Features

Worksheet Compatibility Issues