HTML manual of the Full Polymorphic Package or FPP

Etienne Forest and Yukiko Nogiwa

For some PTC specific documents click here

For ICAP2006 pdfs, please click here

Initializing FPP : for pure TPSA calculations and for phase space calculations involving type DAMAP. (with examples)

Fundamental Types: Taylor, Real Polymorph, Complex Taylor and Complex Polymorph: Including the Knob State of Polymorphs

Functions acting on the four fundamental types: Exponential, Logarithm, trigonometric and more...

 Links to Tables pointing to the operations (+,-,*,/) on these types

1. Taylor
2. Complex Taylor
3. Real Polymorphs
4. Complex Polymorphs

Reading and Printing Objects

1. Generally one can use for input:

CALL DAINPUT(object,Filenumber) or CALL READ(object,Filenumber).

CALL DAINPUT(object,Filenumber) or CALL READ(object,Filenumber).

2. Generally one can use for output

CALL DAPRINT(object,Filenumber,prec) or CALL PRINT(object,Filenumber,prec).

CALL DAPRINT(object,Filenumber,prec) or CALL PRINT(object,Filenumber,prec). prec is an optional small number. Coefficient smaller than prec are not printed.

N.B: It is not possible to read real or complex polymorph.

Big Table Summarizing many useful Operations with lots of trivial examples for each operation

Taylor Maps

Taylor Maps: what is that good for?

The three  map Types of FPP

1. Plain DAMAP
2. DAMAPSPIN
3. Gmap : an all purpose map

Tables Summarizing many useful Operations related to DAMAP with lots of trivial and not so examples for each operation

Factorization of the Normal Form A into a "Lagrangian Canonical form": Teng-Edwards and more!

• The big Table also described useful representation of the maps: Dragt-Finn, Reverse Dragt-Finn, One-Lie-Exponent. The Normal Form, which is made out of plain DAMAP and the two Dragt-Finns is described separately. It must be pointed out that the Dragt-Finn representation appears naturally in the order-by-order normalization process.
• Orbital Normal Form: A type Central to Accelerator Calculations
• Spin Normal Form for DAMAPSIN
• Factorization of the Normal Form A ☻(Orbital case: new pedagogically important routine of FPP)☻
• Phase Advance  ☻(Orbital case: new pedagogically important routine of FPP)☻

Resonance Basis for Taylor Series, Poisson Bracket Operators and Vector Fields

If a Taylor series is Floquet basis, that is to say, if we expect the phase space variables to move on circles, then it makes sense to replace (q,p) in each plane by a new set of variables:

(x₁,x₂)=(x+ip,x-ip)=B^-1(x,p). For example, if T is of type Taylor and Tres of type Taylorresonance, then    Tres=t transforms t into the new basis. In fact, Tres= Tres%cos + i Tres%sin.

1. Type Taylorresonance
2. Type Pbresonance

The same applies to types Pbfield and Pbresonance. For type Vecfield and Vecresonance, the relationship between a vector field and its resonance basis representation is slightly more complex.

3. Type Vecresonance

A vector field V•Grad turns into the resonance basis W•Grad:           W(x)=B^-1V(Bx).             (See the following Jpeg for the definition of B.)

The two sets of Tables contain a lot of useful information and tons of example programs