|
|
Taylor (t) |
Complex
Taylor (ct) |
Real
Polymorph (rp) |
Complex
Polymorph (cp) |
:f:
(f) |
FΧΡ (F) |
Damap/Gmap (M) |
1 |
Derivative
dt/dxi |
t=t.d.i |
ct=ct.d.i |
|
|
|
|
|
2 |
Extract an
order |
t=t.sub.i |
ct=ct.sub.i |
rp=rp.sub.i |
cp=cp.sub.i |
f=f.sub.i |
F.sub.i |
M.sub.i |
3 |
Truncate order i and above |
t=t.cut.i |
ct=ct.cut.i |
rp=rp.cut.i |
cp=cp.cut.i |
f=f.cut.i |
F.cut.i |
M.cut.i |
4 |
Create Monomial |
r x1j(1)...xnvj(nv) |
r x1j(1)...xnvj(nv) |
r xi |
|
|
|
5 |
Peek
coefficient r of monomial r x1j(1)...xnvj(nv) |
|
|
|
|
6 |
Peek coefficient of x1j(1)...xnj(n) as a Taylor series whenre n<nv |
|
|
|
|
7 |
Generalization of .par. (item 6) |
t=t.part.info |
t=t.part.info |
t=t.part.info |
t=t.part.info |
8 |
Shift
exponents downwards by k |
t=t<=k |
ct=ct<=k |
9 |
Peek and
shift (6+8 combined): t=(t.par.j(n))<=n |
|
|
10 |
Tiny Real Polynomials |
r+ xi |
r(1)+r(2) xi |
|
|
11 |
Tiny Complex Polynomials |
Re(c) xj(1) +Im(c) xj(2)
|
c(1)+c(2) (xj(1)+i xj(2)) |
|
|
|
12 |
Pseudo-derivative
dxn/dxi=xin-1 |
t=t.k.i |
ct=ct.k.i |
13 |
Poisson Bracket |
t= t.pb.t |
|
|
|
|
|
|