Difference between revisions of "ApCoCoA-1:Weyl.WLT"
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(New page: <command> <title>Weyl.WLT</title> <short_description>Computes the leading term ideal of a D-ideal I in Weyl algebra <tt>A_n</tt>.</short_description> <syntax> Weyl.WLT(I:IDEAL):I...) |
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| Line 16: | Line 16: | ||
<example> | <example> | ||
| + | A1::=QQ[x,d];Use A1; | ||
| + | L:=x^2(x-1)(x-3)d^2-(6x^3-20x^2+12x)d+(12x^2-32x+12); | ||
| + | I:=Ideal(L,d^5); | ||
| + | Weyl.WLT(I); | ||
| + | -- CoCoAServer: computing Cpu Time = 0.016 | ||
| + | ------------------------------- | ||
| + | Ideal(xd^4, x^3d^2, x^2d^3, d^5) | ||
| + | ------------------------------- | ||
| + | ChI:=Weyl.CharI(I);ChI; | ||
| + | -- CoCoAServer: computing Cpu Time = 0 | ||
| + | ------------------------------- | ||
| + | The characteristic ideal lies in QQ[x,d] | ||
| + | -------------------------------------------------- | ||
| + | |||
| + | ------------------------------- | ||
| + | Ideal(d^5, x^4d^2 - 4x^3d^2 + 3x^2d^2, xd^3) | ||
| + | ------------------------------- | ||
</example> | </example> | ||
<example> | <example> | ||
| + | A2::=QQ[x[1..2],d[1..2]]; | ||
| + | Use A2; | ||
| + | |||
| + | I:=Ideal(x[1]d[2],x[2]d[1]); | ||
| + | Weyl.WLT(I); | ||
| + | -- CoCoAServer: computing Cpu Time = 0.016 | ||
| + | ------------------------------- | ||
| + | Ideal(x[2]^2d[2], x[2]d[2]^2, x[1]d[1], x[2]d[1], x[1]d[2]) | ||
| + | ------------------------------- | ||
</example> | </example> | ||
| Line 24: | Line 50: | ||
<seealso> | <seealso> | ||
<see>Weyl.InIw</see> | <see>Weyl.InIw</see> | ||
| + | <see>Weyl.CharI</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
Revision as of 16:13, 8 July 2009
Weyl.WLT
Computes the leading term ideal of a D-ideal I in Weyl algebra A_n.
Syntax
Weyl.WLT(I:IDEAL):IDEAL
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 ideal of leading monomials of all the polynomials of a D-ideal I in the Weyl algebra D.
@param I An ideal in the Weyl algebra.
@return An ideal, which is leading term ideal of I.
Example
A1::=QQ[x,d];Use A1; L:=x^2(x-1)(x-3)d^2-(6x^3-20x^2+12x)d+(12x^2-32x+12); I:=Ideal(L,d^5); Weyl.WLT(I); -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Ideal(xd^4, x^3d^2, x^2d^3, d^5) ------------------------------- ChI:=Weyl.CharI(I);ChI; -- CoCoAServer: computing Cpu Time = 0 ------------------------------- The characteristic ideal lies in QQ[x,d] -------------------------------------------------- ------------------------------- Ideal(d^5, x^4d^2 - 4x^3d^2 + 3x^2d^2, xd^3) -------------------------------
Example
A2::=QQ[x[1..2],d[1..2]]; Use A2; I:=Ideal(x[1]d[2],x[2]d[1]); Weyl.WLT(I); -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Ideal(x[2]^2d[2], x[2]d[2]^2, x[1]d[1], x[2]d[1], x[1]d[2]) -------------------------------
See also
