Ground term (constant coefficient) of a polynomial
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ground(p) returns the constant coefficient p(0,
0, …) of the polynomial p.
The first argument can either be a polynomial expression, or
a polynomial generated by
or an element of some polynomial domain overloading
If the first argument
f is not element of
a polynomial domain, then
ground converts the expression
to a polynomial via
poly(f). If a list of indeterminates
is specified, then the polynomial
poly(f, vars) is
The constant coefficient is returned as an arithmetical expression.
be converted to a polynomial in the specified indeterminates. Cf. Example 3.
We demonstrate how the indeterminates influence the result:
f := 2*x^2 + 3*y + 1: ground(f), ground(f, [x]), ground(f, [y]), ground(poly(f)), ground(poly(f, [x])), ground(poly(f, [y]))
The result is the evaluation at the origin:
subs(f, x = 0, y = 0), subs(f, x = 0), subs(f, y = 0)
Note the difference between
g := 2*x^2 + 3*y: ground(g), ground(g, [x]); tcoeff(g), tcoeff(g, [x]);
delete f, g:
The result of
ground is not fully evaluated:
p := poly(27*x^2 + a, [x]): a := 5: ground(p), eval(ground(p))
delete p, a:
The following expression is syntactically not a polynomial expression,
f := (x^2 - 1)/(x - 1): ground(f)
After cancellation via
compute the constant coefficient: