fspace.spad line 1 [edit on github]
An expression space is a set which is closed under certain operators.
belong?(op) tests if % accepts op as applicable to its elements.
box(f) returns f with a 'box' around it that prevents f from being evaluated when operators are applied to it. For example, log(1) returns 0, but log(box 1) returns the formal kernel log(1).
definingPolynomial(x) returns an expression p such that p(x) = 0.
distribute(f) expands all the kernels in f that are formally enclosed by a box or paren expression.
distribute(f, g) expands all the kernels in f that contain g in their arguments and that are formally enclosed by a box or a paren expression.
elt(op, x) or op(x) applies the unary operator op to x.
elt(op, x, y) or op(x, y) applies the binary operator op to x and y.
elt(op, x, y, z) or op(x, y, z) applies the ternary operator op to x, y and z.
elt(op, x, y, z, t) or op(x, y, z, t) applies the 4-ary operator op to x, y, z and t.
elt(op, x, y, z, t, s) applies the 5-ary operator op to x, y, z, t and s
elt(op, x, y, z, t, s, r) applies the 6-ary operator op to x, y, z, t, s and r
elt(op, x, y, z, t, s, r, q) applies the 7-ary operator op to x, y, z, t, s, r and q
elt(op, x, y, z, t, s, r, q, p) applies the 8-ary operator op to x, y, z, t, s, r, q and p
elt(op, x, y, z, t, s, r, q, p, o) applies the 9-ary operator op to x, y, z, t, s, r, q, p and o
elt(op, [x1, ..., xn]) or op([x1, ..., xn]) applies the n-ary operator op to x1, ..., xn.
eval(x, s, f) replaces every s(a) in x by f(a) for any a.
eval(x, s, f) replaces every s(a1, .., am) in x by f(a1, .., am) for any a1, ..., am.
eval(x, [s1, ..., sm], [f1, ..., fm]) replaces every si(a)x by fi(a)a.
eval(x, [s1, ..., sm], [f1, ..., fm]) replaces every si(a1, ..., an)x by fi(a1, ..., an)a1, ..., an.
eval(x, [s1, ..., sm], [f1, ..., fm]) replaces every si(a)x by fi(a)a.
eval(x, [s1, ..., sm], [f1, ..., fm]) replaces every si(a1, ..., an)x by fi(a1, ..., an)a1, ..., an.
eval(x, s, f) replaces every s(a) in x by f(a) for any a.
eval(x, s, f) replaces every s(a1, .., am) in x by f(a1, .., am) for any a1, ..., am.
even? x is true if x is an even integer.
freeOf?(x, y) tests if x does not contain any occurrence of y, where y is a single kernel.
freeOf?(x, s) tests if x does not contain any operator whose name is s.
height(f) returns the highest nesting level appearing in f. Constants have height 0. Symbols have height 1. For any operator op and expressions f1, ..., fn, op(f1, ..., fn) has height equal to 1 + max(height(f1), ..., height(fn)).
is?(x, op) tests if x is a kernel and if its operator is op.
is?(x, s) tests if x is a kernel and if the name of its operator is s.
kernel(op, x) constructs op(x) without evaluating it.
kernel(op, [f1, ..., fn]) constructs op(f1, ..., fn) without evaluating it.
kernels(f) returns the list of all the top-level kernels appearing in f, but not the ones appearing in the arguments of the top-level kernels.
kernels([f1,...,fn]) returns the list of all the top-level kernels appearing in f1, ..., fn but not the ones appearing in the arguments of the top-level kernels.
mainKernel(f) returns a kernel of f with maximum nesting level, or "failed" if f has no kernels (i.e. f is a constant).
map(f, k) returns op(f(x1), ..., f(xn)) where k = op(x1, ..., xn).
minPoly(k) returns p such that p(k) = 0.
odd? x is true if x is an odd integer.
operator(op) returns a copy of op with the domain-dependent properties appropriate for %.
operators(f) returns all the basic operators appearing in f, no matter what their levels are.
paren(f) returns (f). This prevents f from being evaluated when operators are applied to it. For example, log(1) returns 0, but log(paren 1) returns the formal kernel log((1)).
subst(f, k = g) replaces the kernel k by g formally in f.
subst(f, [k1..., kn], [g1, ..., gn]) replaces the kernels k1, ..., kn by g1, ..., gn formally in f.
subst(f, [k1 = g1, ..., kn = gn]) replaces the kernels k1, ..., kn by g1, ..., gn formally in f.
tower(f) returns all the kernels appearing in f, no matter what their levels are.
tower([f1,...,fn]) returns all the kernels appearing in f1, ..., fn no matter what their levels are.
Evalable(%)
InnerEvalable(K, %)
InnerEvalable(%, %)