ApCoCoA-1:Weyl.WeylMul: Difference between revisions

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  {{Version|1}}
<command>
<command>
     <title>Weyl.Mul</title>
     <title>Weyl.WeylMul</title>
     <short_description>multiplying two WeylPolynoms</short_description>
     <short_description>Computes the product <tt>F*G</tt> of two Weyl polynomials, <tt>F</tt> and <tt>G</tt>, in normal form.</short_description>
<syntax>
<syntax>
Weyl.Mul(P,Q):WeylPolynom
Weyl.WeylMul(F:POLY,G:POLY):POLY
</syntax>
</syntax>
     <description>
     <description>
{{Beta}}
<em>Warning:</em> This function is too slow for working with polynomials in large degree and large or zero characteristic.
Use <ref>ApCoCoA-1:Weyl.WMul|Weyl.WMul</ref> instead for faster calculations.
<par/>
This method multiplies <tt>F</tt> and <tt>G</tt> and returns <tt>F*G</tt> as a Weyl polynomial in normal form.


This method multiplies P and Q and returns P*Q as a WeylPolynom.
<itemize>
<item>@param <em>F</em> A Weyl polynomial.</item>
<item>@param <em>G</em> A Weyl polynomial.</item>
<item>@result The product <tt>F*G</tt> as a Weyl polynomial in normal form.</item>
</itemize>


{{Stub}}
<example>
A1::=QQ[x,d]; --Define appropriate ring
Use A1;
F:=x; G:=d;
Weyl.WeylMul(F,G);
xd
-------------------------------
Weyl.WeylMul(G,F);
xd + 1
-------------------------------
Weyl.WeylMul(Weyl.WeylMul(G,F)-2G,F^3+G);
x^4d - 2x^3d + 4x^3 + xd^2 - 6x^2 - 2d^2 + d
-------------------------------
-- If you want to multiply Weyl polynomials that are not in normal form say for
-- example F=d^2x^3-2dx^2+7 and G=2d^3x-5xd+3, then first convert them into normal
-- form before multiplication.
-------------------------------
F:=Weyl.WNormalForm([[d^2,x^3],[-2d,x^2],[7]]);
F;
x^3d^2 + 4x^2d + 2x + 7
-------------------------------
G:=Weyl.WNormalForm([[2d^3,x],[-5x,d],[3]]);
G;
2xd^3 - 5xd + 6d^2 + 3
-------------------------------
Weyl.WeylMul(F,G);
2x^4d^5 - 5x^4d^3 + 18x^3d^4 - 27x^3d^2 + 36x^2d^3 + 14xd^3 - 18x^2d + 12xd^2 - 35xd + 42d^2 + 6x + 21
-------------------------------
Weyl.WeylMul(G,F);
2x^4d^5 - 5x^4d^3 + 32x^3d^4 - 32x^3d^2 + 148x^2d^3 + 14xd^3 - 38x^2d + 216xd^2 - 35xd + 42d^2 - 4x + 72d + 21
-------------------------------
Weyl.WeylMul(Weyl.WNormalForm([[d^2,x^3],[-2d,x^2],[7]]),Weyl.WNormalForm([[2d^3,x],[-5x,d],[3]]));
2x^4d^5 - 5x^4d^3 + 18x^3d^4 - 27x^3d^2 + 36x^2d^3 + 14xd^3 - 18x^2d + 12xd^2 - 35xd + 42d^2 + 6x + 21
-------------------------------
 
</example>
   </description>
   </description>
     <seealso>
     <seealso>
    <see>NewWeylPolynom</see>
       <see>ApCoCoA-1:Weyl.WNormalForm|Weyl.WNormalForm</see>
    <see>WeylPolynom</see>
       <see>ApCoCoA-1:Weyl.WMul|Weyl.WMul</see>
      <see>IsWeylPolynom</see>
       <see>ApCoCoA-1:Weyl.WMult|Weyl.WMult</see>
      <see>Add</see>
      <see>Sub</see>
       <see>Equals</see>
       <see>RollOver</see>
       <see>Package_Weyl</see>
     </seealso>
     </seealso>
     <wiki-category>Package_Weyl</wiki-category>
    <types>
      <type>polynomial</type>
    </types>
    <key>weyl.weylmul</key>
    <key>weylmul</key>
     <wiki-category>ApCoCoA-1:Package_weyl</wiki-category>
   </command>
   </command>

Latest revision as of 10:40, 7 October 2020

This article is about a function from ApCoCoA-1.

Weyl.WeylMul

Computes the product F*G of two Weyl polynomials, F and G, in normal form.

Syntax

Weyl.WeylMul(F:POLY,G:POLY):POLY

Description

Warning: This function is too slow for working with polynomials in large degree and large or zero characteristic.

Use Weyl.WMul instead for faster calculations.

This method multiplies F and G and returns F*G as a Weyl polynomial in normal form.

  • @param F A Weyl polynomial.

  • @param G A Weyl polynomial.

  • @result The product F*G as a Weyl polynomial in normal form.

Example

A1::=QQ[x,d];	--Define appropriate ring
Use A1;
F:=x; G:=d;
Weyl.WeylMul(F,G);
xd
-------------------------------
Weyl.WeylMul(G,F);
xd + 1
-------------------------------
Weyl.WeylMul(Weyl.WeylMul(G,F)-2G,F^3+G);
x^4d - 2x^3d + 4x^3 + xd^2 - 6x^2 - 2d^2 + d
-------------------------------
-- If you want to multiply Weyl polynomials that are not in normal form say for
-- example F=d^2x^3-2dx^2+7 and G=2d^3x-5xd+3, then first convert them into normal
-- form before multiplication.
-------------------------------
F:=Weyl.WNormalForm([[d^2,x^3],[-2d,x^2],[7]]);
F;
x^3d^2 + 4x^2d + 2x + 7
-------------------------------
G:=Weyl.WNormalForm([[2d^3,x],[-5x,d],[3]]);
G;
2xd^3 - 5xd + 6d^2 + 3
-------------------------------
Weyl.WeylMul(F,G);
2x^4d^5 - 5x^4d^3 + 18x^3d^4 - 27x^3d^2 + 36x^2d^3 + 14xd^3 - 18x^2d + 12xd^2 - 35xd + 42d^2 + 6x + 21
-------------------------------
Weyl.WeylMul(G,F);
2x^4d^5 - 5x^4d^3 + 32x^3d^4 - 32x^3d^2 + 148x^2d^3 + 14xd^3 - 38x^2d + 216xd^2 - 35xd + 42d^2 - 4x + 72d + 21
-------------------------------
Weyl.WeylMul(Weyl.WNormalForm([[d^2,x^3],[-2d,x^2],[7]]),Weyl.WNormalForm([[2d^3,x],[-5x,d],[3]]));
2x^4d^5 - 5x^4d^3 + 18x^3d^4 - 27x^3d^2 + 36x^2d^3 + 14xd^3 - 18x^2d + 12xd^2 - 35xd + 42d^2 + 6x + 21
-------------------------------

See also

Weyl.WNormalForm

Weyl.WMul

Weyl.WMult




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