Difference between revisions of "ApCoCoA-1:Weyl.IsHolonomic"
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<title>Weyl.IsHolonomic</title> | <title>Weyl.IsHolonomic</title> | ||
<short_description>Checks whether an ideal in Weyl algebra <tt>A_n</tt> is holonomic or not.</short_description> | <short_description>Checks whether an ideal in Weyl algebra <tt>A_n</tt> is holonomic or not.</short_description> | ||
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
| − | An ideal <tt>I</tt> is holonomic if it has dimension n, the number of variables in the Weyl algebra <tt>A_n = C[x_1,...,x_n,y_1,...,y_n]</tt> | + | An ideal <tt>I</tt> is holonomic if it has dimension n, the number of variables in the Weyl algebra <tt>A_n = C[x_1,...,x_n,y_1,...,y_n]</tt>. |
This function determines whether an ideal I is holonomic by checking its dimension. | This function determines whether an ideal I is holonomic by checking its dimension. | ||
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W3::=ZZ/(7)[x[1..3],d[1..3]]; | W3::=ZZ/(7)[x[1..3],d[1..3]]; | ||
Use W3; | Use W3; | ||
| − | Cpu time = 0.00, User time = 0 | + | -- Cpu time = 0.00, User time = 0 |
------------------------------- | ------------------------------- | ||
F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; | F1:=-d[1]^3d[2]^5d[3]^5+x[2]^5; | ||
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</example> | </example> | ||
</description> | </description> | ||
| − | <seealso> | + | <seealso> |
| − | <see>Weyl.WDim</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| + | <see>ApCoCoA-1:Weyl.WDim|Weyl.WDim</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| − | <type> | + | <type>apcocoaserver</type> |
<type>ideal</type> | <type>ideal</type> | ||
</types> | </types> | ||
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<key>weyl.isholonomic</key> | <key>weyl.isholonomic</key> | ||
<key>isholonomic</key> | <key>isholonomic</key> | ||
| − | <wiki-category>Package_weyl</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_weyl</wiki-category> |
</command> | </command> | ||
Latest revision as of 10:35, 7 October 2020
| 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
