ApCoCoA-1:Weyl.WeylMul
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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
