ApCoCoA-1:Weyl.IsHolonomic
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| This article is about a function from ApCoCoA-1. |
Weyl.IsHolonomic
Checks whether an ideal in Weyl algebra A_n is holonomic or not.
Syntax
Weyl.IsHolonomic(I:IDEAL):BOOL
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
An ideal I is holonomic if it has dimension n, the number of variables in the Weyl algebra A_n = C[x_1,...,x_n,y_1,...,y_n].
This function determines whether an ideal I is holonomic by checking its dimension.
@param I An ideal in the Weyl algebra A_n.
@return TRUE if the given ideal is holonomic.
Example
W3::=ZZ/(7)[x[1..3],d[1..3]]; Use W3; -- Cpu time = 0.00, User time = 0 ------------------------------- F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; F2:=-3x[2]d[2]^5d[3]^5+x[2]d[1]^3; F3:=-2d[1]^4d[2]^5-x[1]d[2]^7+x[3]^3d[3]^5; I:=Ideal(F1,F2,F3); Weyl.IsHolonomic(I); -- CoCoAServer: computing Cpu Time = 2.36 ------------------------------- FALSE -------------------------------
Example
A2::=QQ[x[1..2],d[1..2]]; Use A2; ------------------------------- I:=Ideal(x[1]d[1] + 2x[2]d[2] - 5, d[1]^2 - d[2]); ------------------------------- Weyl.IsHolonomic(I); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- TRUE -------------------------------
See also
