Difference between revisions of "ApCoCoA-1:Weyl.WPower"

From ApCoCoAWiki
(Change Wiki-category)
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<command>
 
<command>
 
     <title>Weyl.WPower</title>
 
     <title>Weyl.WPower</title>
     <short_description>Computes the integer-power N of a Weyl polynomial.
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     <short_description>Computes the N-th power of a Weyl polynomial.</short_description>
</short_description>
 
 
<syntax>
 
<syntax>
 
Weyl.WPower(F:POLY,N:INT):POLY
 
Weyl.WPower(F:POLY,N:INT):POLY
 
</syntax>
 
</syntax>
 
<description>
 
<description>
Computes the integer-power N of a Weyl ploynomial F:
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Computes the integer-power N of a Weyl ploynomial F.
  
'''F:''' a Weyl polynomial in normal form,
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<itemize>
 
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<item>@param <em>F</em> A Weyl polynomial in normal form.</item>
'''N:''' a positive integer, power to be calculated.
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<item>@param <em>N</em> A positive integer, power to be calculated.</item>
 
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<item>@result A Weyl polynomial F^N in Normal form.</item>
The result is a Weyl polynomial <math>F^N</math> in Normal form.
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</itemize>
  
 
<example>
 
<example>
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</example>
 
</example>
 
</description>
 
</description>
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 +
<key>Weyl.WPower</key>
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<key>WPower</key>
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 +
<types>
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<type>poly</type>
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</types>
 +
 
<wiki-category>Package_weyl</wiki-category>
 
<wiki-category>Package_weyl</wiki-category>
 
</command>
 
</command>

Revision as of 12:49, 23 April 2009

Weyl.WPower

Computes the N-th power of a Weyl polynomial.

Syntax

Weyl.WPower(F:POLY,N:INT):POLY

Description

Computes the integer-power N of a Weyl ploynomial F.

  • @param F A Weyl polynomial in normal form.

  • @param N A positive integer, power to be calculated.

  • @result A Weyl polynomial F^N in Normal form.

Example

A2::=QQ[x[1..2],y[1..2]];	--Define appropriate ring
Use A2;
F1:=x[1]^2x[2] - y[1]^3 + 3x[2]y[2] - 4;
Weyl.WPower(F1,0);
1
-------------------------------
Weyl.WPower(F1,1);
x[1]^2x[2] - y[1]^3 + 3x[2]y[2] - 4
-------------------------------
Weyl.WPower(F1,2);
x[1]^4x[2]^2 - 2x[1]^2x[2]y[1]^3 + y[1]^6 + 6x[1]^2x[2]^2y[2] - 6x[2]y[1]^3y[2] - 6x[1]x[2]y[1]^2 + 9x[2]^2y[2]^2 - 5x[1]^2x[2] + 
8y[1]^3 - 6x[2]y[1] - 15x[2]y[2] + 16
-------------------------------
Weyl.WPower(F1,3);
x[1]^6x[2]^3 - 3x[1]^4x[2]^2y[1]^3 + 3x[1]^2x[2]y[1]^6 - y[1]^9 + 9x[1]^4x[2]^3y[2] - 18x[1]^2x[2]^2y[1]^3y[2] + 9x[2]y[1]^6y[2] - 
18x[1]^3x[2]^2y[1]^2 + 18x[1]x[2]y[1]^5 + 27x[1]^2x[2]^3y[2]^2 - 27x[2]^2y[1]^3y[2]^2 - 3x[1]^4x[2]^2 + 15x[1]^2x[2]y[1]^3 - 
12y[1]^6 - 54x[1]x[2]^2y[1]^2y[2] + 27x[2]^3y[2]^3 - 42x[1]^2x[2]^2y[1] + 36x[2]y[1]^4 - 18x[1]^2x[2]^2y[2] + 45x[2]y[1]^3y[2] + 
36x[1]x[2]y[1]^2 - 54x[2]^2y[1]y[2] - 27x[2]^2y[2]^2 + 21x[1]^2x[2] - 24x[1]x[2]^2 - 48y[1]^3 + 36x[2]y[1] + 63x[2]y[2] - 64

-------------------------------
Weyl.WPower(F1,-3);
ERROR: 2nd Parameter should be a positive integer
CONTEXT: Error("2nd Parameter should be a positive integer")
-------------------------------