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Removed manual section for CoefficientMultivariatePolynomial which do…
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…cuments a function that never existed???
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osj1961 committed Jan 4, 2025
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Expand Up @@ -12240,70 +12240,6 @@ DegreesMultivariatePolynomial(poly,R2);
-->

<ManSection>
<Func Name="CoefficientMultivariatePolynomial" Arg ="f, var, power, R"/>

<Description>
The command <C>CoefficientMultivariatePolynomial</C>
takes four arguments: a multivariant polynomial
<A>f</A>, a variable name <A>var</A>, an integer
<A>power</A>, and a polynomial ring <A>R</A> containing <A>f</A>.
For example, if <A>f</A> is a multivariate polynomial in
<M>R</M> = <M>F</M>[<M>x_1,x_2,...,x_n</M>] then <A>var</A> must be
one of the <M>x_i</M>.
The output is the coefficient of <M>x_i^{power}</M>
in <A>f</A>.
<P/>
(Not sure if <M>F</M> needs to be a field in fact ...)
<P/>
Related to the GAP command <C>PolynomialCoefficientsPolynomial</C>.

</Description>
</ManSection>

<Example>
gap> F:=GF(11);;
gap> R2:=PolynomialRing(F,2);
PolynomialRing(..., [ x_1, x_2 ])
gap> vars:=IndeterminatesOfPolynomialRing(R2);;
gap> x:=vars[1];; y:=vars[2];;
gap> poly:=y^2-x*(x^2-1);;
gap> PolynomialCoefficientsOfPolynomial(poly,x);
[ x_2^2, Z(11)^0, 0*Z(11), -Z(11)^0 ]
gap> PolynomialCoefficientsOfPolynomial(poly,y);
[ -x_1^3+x_1, 0*Z(11), Z(11)^0 ]
gap> CoefficientMultivariatePolynomial(poly,y,0,R2);
-x_1^3+x_1
gap> CoefficientMultivariatePolynomial(poly,y,1,R2);
0*Z(11)
gap> CoefficientMultivariatePolynomial(poly,y,2,R2);
Z(11)^0
gap> CoefficientMultivariatePolynomial(poly,x,0,R2);
x_2^2
gap> CoefficientMultivariatePolynomial(poly,x,1,R2);
Z(11)^0
gap> CoefficientMultivariatePolynomial(poly,x,2,R2);
0*Z(11)
gap> CoefficientMultivariatePolynomial(poly,x,3,R2);
-Z(11)^0
</Example>
<!--
F:=GF(11);;
R2:=PolynomialRing(F,2);
vars:=IndeterminatesOfPolynomialRing(R2);;
x:=vars[1];; y:=vars[2];;
poly:=y^2-x*(x^2-1);;
PolynomialCoefficientsOfPolynomial(poly,x);
PolynomialCoefficientsOfPolynomial(poly,y);
CoefficientMultivariatePolynomial(poly,y,0,R2);
CoefficientMultivariatePolynomial(poly,y,1,R2);
CoefficientMultivariatePolynomial(poly,y,2,R2);
CoefficientMultivariatePolynomial(poly,x,0,R2);
CoefficientMultivariatePolynomial(poly,x,1,R2);
CoefficientMultivariatePolynomial(poly,x,2,R2);
CoefficientMultivariatePolynomial(poly,x,3,R2);
-->


<ManSection>
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