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Functions and commands 341
Groebner Basis Returns the Groebner basis of the ideal spanned by a list of
polynomials.
gbasis(LstPoly,LstVar)
Example:
gbasis([x^2-y^3,x+y^2],[x,y]) gives [y^4-
y^3,x+y^2]
Groebner
Remainder
Returns the remainder of the division of a polynomial by the
Groebner basis of a list of polynomials.
greduce(Poly,LstPoly,LstVar)
Example:
greduce(x*y-1,[x^2-y^2,2*x*y-y^2,y^3],[x,y])
gives 1/2*y^2-1
Hermite Returns the Hermite polynomial of degree n.
hermite(Intg(n))where n ≤ 1556
Example:
hermite(3) gives 8*x^3-12*x
Lagrange Returns the Lagrange polynomial for two lists. The list in the
first argument corresponds to the abscissa values, and the list
in the second argument corresponds to the ordinate values.
lagrange((Lst_xk,Lst_yk)
or
lagrange(Mtrx_2*n)
Example:
lagrange([1,3],[0,1]) gives (x-1)/2
Laguerre Returns the Laguerre polynomial of degree n.
laguerre(Intg(n))
Example:
laguerre(4) gives 1/24*a^4+(-1/6)*a^3*x+5/
12*a^3+1/4*a^2*x^2+(-3/2)*a^2*x+35/24*a^2+(-
1/6)*a*x^3+7/4*a*x^2+(-13/3)*a*x+25/12*a+1/
24*x^4+(-2/3)*x^3+3*x^2-4*x+1