Difference between revisions of "ApCoCoA-1:Weyl.WDim"
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| − | <see>Weyl.WNormalForm</see> | + | <see>ApCoCoA-1:Weyl.WNormalForm|Weyl.WNormalForm</see> |
| − | <see>Weyl.WGB</see> | + | <see>ApCoCoA-1:Weyl.WGB|Weyl.WGB</see> |
| − | <see>Weyl.IsHolonomic</see> | + | <see>ApCoCoA-1:Weyl.IsHolonomic|Weyl.IsHolonomic</see> |
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Revision as of 08:45, 7 October 2020
Weyl.WDim
Computes the dimension of an ideal I in Weyl algebra A_n.
Syntax
Weyl.WDim(I:IDEAL):INT
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.
This function computes the dimension of an Ideal I = (f_1,f_2, ..., f_r) which represents the module A_n/I where every generator f_i should be a Weyl polynomial in Normal form. This dimension of I is equal to the dimension of the associated graded module with respect to the Bernstein filtration.
@param I An ideal in the Weyl algebra.
@return The dimension of the given ideal.
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.WDim(I); -- CoCoAServer: computing Cpu Time = 2.36 ------------------------------- 2 -------------------------------
Example
A3::=QQ[x[1..2],d[1..2]]; Use A3; ------------------------------- I:=Ideal(x[1]d[1] + 2x[2]d[2] - 5, d[1]^2 - d[2]); ------------------------------- Weyl.WDim(I); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- 2 ------------------------------- -- If the dimension is ZERO, -1 will be returned Weyl.WDim(Ideal(x[1],d[1])); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- -1 -------------------------------
See also
