Polynomials
Expand(expr)
Expand(expr) : expands a univariate. Example: Expand((1+x)^2)
would evaluate to 1+2*x+x^2.
If the expression depends on more than one variable, you can
specify which variable to expand to using Expand(expr,var);
Also, you can expand to multiple variables, by specifying the
order in which to expand, in a list, using Expand(expr,{varlist}).
Degree(expr) or Degree(expression, variable)
Degree(expr) : return the degree of a polynomial. Example: Degree((1+x)^2); evaluates to 2.
The version accepting an additional variable as an argument can be
used to get the degree of a multivariate polynomial with respect to
that variable. Example: Degree(a+b*x^3,a);returns 1.
Coef(expr,var,order)
Coef(expr,var,order) : return the coefficient of order for expression
expr treated as a univariate with respect to the variable var.
The argument to parameter order can also be a list of integers, in
which case this function returns a list of coefficients.
PSolve(expr,var)
PSolve(expr,var) : solve expr=0, treating expr as a polynomial in
the variable var. The result returned is the value var should take
for expr=0 to be true. This has been implemented for polynomials
upto degree 2.
Div(n,m)
Div(n,m) : div is also defined for polynomials.
Mod(n,m)
Mod(n,m) : mod is also defined for polynomials.
Content(poly)
Content(poly) : determine the content of a univariate polynomial.
The content is the greatest common divisor of each term in the
polynomial. The content of 2*x^2+4*x should be 2*x for instance.
PrimitivePart(poly)
PrimitivePart(poly) : determine the primitive part of a univariate polynomial.
This is defined as PrimitivePart(poly)*Content(poly) = poly, and can
easily be checked with Expand(PrimitivePart(poly)*Content(poly))
which should be equal to Expand(poly).
RandomPoly(var,deg,coefmin,coefmax)
RandomPoly(var,deg,coefmin,coefmax) :
generate a random polynomial in variable var, of degree deg,
with coefficients ranging from coefmin to coefmax (inclusive).
LeadingCoef(poly)
LeadingCoef(poly) : get the leading coefficient of the polynomial poly.
If there are more variables in poly, you can specify which variable
is the main one, by adding it as an argument:
In> LeadingCoef(a*x^2+2,x)
Out> a; |
Monic(poly)
Monic(poly) : return the monic part of the polynomial poly.
This is poly/LeadingCoef(poly). This function also accepts
a second argument, specifying the variable of the univariate
polynomial:
In> f:=a*x^2+b
Out> a*x^2+b;
In> PrettyForm(Monic(f,x))
b 2
- + x
a
Out> True;
|
BigOh(_uv,_var,_degree)
BigOh(poly,var,degree) : Given a polynomial poly in variable var,
drop all terms of order degree or higher.