diff --git a/changelog b/changelog
index 04a4914..377aa85 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,13 @@
+20080818 tpd src/input/Makefile biquat.input added
+20080818 dxc src/input/biquat.input added
+20080818 dxc "David Cyganski" (no known email)
+20080818 tpd src/input/Makefile ifthenelse.input added
+20080818 fxs src/input/ifthenelse.input added
+20080818 tpd src/interp/setq.lisp add Fabio Stumbo
+20080818 tpd readme add Fabio Stumbo
+20080818 fxs "Fabio Stumbo" (no known email)
+20080818 tpd src/input/Makefile sqrt3.input added
+20080818 rhx src/input/sqrt3.input added
 20080818 tpd src/input/Makefile typetower.input added
 20080818 rhx src/input/typetower.input added
 20080817 tpd src/algebra/vector.spad doc ravel from CartesianTensor
diff --git a/readme b/readme
index b2e20ab..7735016 100644
--- a/readme
+++ b/readme
@@ -240,8 +240,8 @@ at the axiom command prompt will prettyprint the list.
 "Gerhard Schneider      Martin Schoenert       Marshall Schor"
 "Frithjof Schulze       Fritz Schwarz          Nick Simicich"
 "William Sit            Elena Smirnova         Jonathan Steinbach"
-"Christine Sundaresan   Robert Sutor           Moss E. Sweedler"
-"Eugene Surowitz"
+"Fabio Stumbo           Christine Sundaresan   Robert Sutor"
+"Moss E. Sweedler       Eugene Surowitz"
 "Max Tegmark            James Thatcher         Balbir Thomas"
 "Mike Thomas            Dylan Thurston         Barry Trager"
 "Themos T. Tsikas"
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index e70b0d9..0d919d6 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -278,7 +278,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     arrows.regress    asinatan.regress asinhatanh.regress \
     assign.regress    atansqrt.regress \
     asec.regress      bags.regress     bbtree.regress   besselk.regress \
-    binary.regress    bop.regress      bstree.regress   bouquet.regress \
+    binary.regress    biquat.regress \
+    bop.regress       bstree.regress   bouquet.regress \
     bug100.regress    bug101.regress \
     bug103.regress    bug10069.regress \
     bugs.regress      bug10312.regress bug6357.regress  bug9057.regress \
@@ -315,7 +316,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     gstbl.regress     heap.regress     heat.regress     help.regress \
     herm.regress      heugcd.regress \
     hexadec.regress   ico.regress      ideal.regress \
-    ifact.regress     infprod.regress  intaf.regress    intbypart.regress \
+    ifact.regress     ifthenelse.regress \
+    infprod.regress  intaf.regress    intbypart.regress \
     intdeq.regress \
     intef2.regress    intef.regress    intg0.regress    intheory.regress \
     intmix2.regress   intmix.regress   int.regress      intrf.regress \
@@ -363,7 +365,8 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     series2.regress   series.regress   sersolve.regress set.regress \
     sincos.regress    sinhcosh.regress \
     sincosex.regress  sint.regress     skew.regress     slowint.regress \
-    solvetra.regress  space3.regress   sqmatrix.regress sregset.regress \
+    solvetra.regress  space3.regress   sqmatrix.regress sqrt3.regress \
+    sregset.regress \
     stbl.regress      stream2.regress  stream.regress   streams.regress \
     string.regress    strtbl.regress   summation.regress \
     symbol.regress    t111293.regress  table.regress    tancot.regress \
@@ -518,7 +521,8 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/asec.input \
        ${OUT}/bags.input     ${OUT}/bbtree.input     ${OUT}/besselk.input \
        ${OUT}/bern.input \
-       ${OUT}/bernpoly.input ${OUT}/binary.input     ${OUT}/bop.input \
+       ${OUT}/bernpoly.input ${OUT}/binary.input     ${OUT}/biquat.input \
+       ${OUT}/bop.input \
        ${OUT}/bouquet.input  ${OUT}/bstree.input     ${OUT}/bug6357.input \
        ${OUT}/bug9057.input  ${OUT}/bug100.input     ${OUT}/bug101.input \
        ${OUT}/bug103.input \
@@ -574,6 +578,7 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/herm.input     ${OUT}/heugcd.input \
        ${OUT}/hexadec.input    ${OUT}/huang.input \
        ${OUT}/ico.input      ${OUT}/ideal.input      ${OUT}/ifact.input \
+       ${OUT}/ifthenelse.input \
        ${OUT}/images1.input  ${OUT}/images1a.input   ${OUT}/images3a.input \
        ${OUT}/images3.input  ${OUT}/images6.input    ${OUT}/images6a.input \
        ${OUT}/images7.input  ${OUT}/images7a.input   ${OUT}/infprod.input \
@@ -652,7 +657,8 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/sinsin2.input  ${OUT}/sint.input       ${OUT}/skew.input \
        ${OUT}/slowint.input  ${OUT}/solvetra.input   ${OUT}/space3.input \
        ${OUT}/spiral.input \
-       ${OUT}/sqmatrix.input ${OUT}/sregset.input    ${OUT}/stbl.input \
+       ${OUT}/sqmatrix.input ${OUT}/sqrt3.input \
+       ${OUT}/sregset.input  ${OUT}/stbl.input \
        ${OUT}/stream2.input  ${OUT}/stream.input     ${OUT}/streams.input \
        ${OUT}/string.input   ${OUT}/strtbl.input     ${OUT}/summation.input \
        ${OUT}/symbol.input \
@@ -722,6 +728,7 @@ DOCFILES= \
   ${DOC}/bbtree.input.dvi      ${DOC}/besselk.input.dvi    \
   ${DOC}/bern.input.dvi       \
   ${DOC}/bernpoly.input.dvi    ${DOC}/binary.input.dvi     \
+  ${DOC}/biquat.input.dvi \
   ${DOC}/bop.input.dvi         ${DOC}/bouquet.input.dvi    \
   ${DOC}/bstree.input.dvi      ${DOC}/bug10069.input.dvi   \
   ${DOC}/bug100.input.dvi      ${DOC}/bug101.input.dvi     \
@@ -860,6 +867,7 @@ DOCFILES= \
   ${DOC}/hexadec.input.dvi     ${DOC}/hilbert.as.dvi       \
   ${DOC}/huang.input.dvi       ${DOC}/ico.input.dvi        \
   ${DOC}/ideal.input.dvi       ${DOC}/ifact.input.dvi      \
+  ${DOC}/ifthenelse.input.dvi \
   ${DOC}/images1a.input.dvi    ${DOC}/images1.input.dvi    \
   ${DOC}/images2a.input.dvi    ${DOC}/images2.input.dvi    \
   ${DOC}/images3a.input.dvi    ${DOC}/images3.input.dvi    \
@@ -993,7 +1001,8 @@ DOCFILES= \
   ${DOC}/skew.input.dvi        ${DOC}/slowint.input.dvi    \
   ${DOC}/solvetra.input.dvi    ${DOC}/space3.input.dvi     \
   ${DOC}/spadprof.input.dvi    ${DOC}/spiral.input.dvi     \
-  ${DOC}/sqmatrix.input.dvi    ${DOC}/sregset.input.dvi    \
+  ${DOC}/sqmatrix.input.dvi    ${DOC}/sqrt3.input.dvi      \
+  ${DOC}/sregset.input.dvi    \
   ${DOC}/stbl.input.dvi        ${DOC}/stream2.input.dvi    \
   ${DOC}/stream.input.dvi      ${DOC}/streams.input.dvi    \
   ${DOC}/string.input.dvi      ${DOC}/strtbl.input.dvi     \
diff --git a/src/input/biquat.input.pamphlet b/src/input/biquat.input.pamphlet
new file mode 100644
index 0000000..bfb3165
--- /dev/null
+++ b/src/input/biquat.input.pamphlet
@@ -0,0 +1,790 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input biquat.input}
+\author{D. Cyganski}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+@
+<<*>>=
+)spool biquat.output
+)set message test on
+)set message auto off
+)clear all
+ 
+@
+\section{Hamiltonian Biquaternions}
+
+Define the type $Q$ of Hamiltonian biquaternions (not to be confused with
+Clifford biquaternions which are an entirely different object)
+<<*>>=
+
+--S 1 of 43
+C:=Complex Expression Integer
+--R 
+--R
+--R   (1)  Complex Expression Integer
+--R                                                                 Type: Domain
+--E 1
+
+--S 2 of 43
+Q:=Quaternion C
+--R 
+--R
+--R   (2)  Quaternion Complex Expression Integer
+--R                                                                 Type: Domain
+--E 2
+
+--S 3 of 43
+q:Q:=quatern(q0,q1,q2,q3)
+--R 
+--R
+--R   (3)  q0 + q1 i + q2 j + q3 k
+--R                                  Type: Quaternion Complex Expression Integer
+--E 3
+
+@
+Define a function that takes a complex list (parameter l) into a 
+quaternion
+<<*>>=
+
+--S 4 of 43
+qlist(l:List C):Q==quatern(1.1,1.2,1.3,1.4)
+--R 
+--R   Function declaration qlist : List Complex Expression Integer -> 
+--R      Quaternion Complex Expression Integer has been added to 
+--R      workspace.
+--R                                                                   Type: Void
+--E 4
+
+@
+Define a function that takes a quaternion into a list
+<<*>>=
+
+--S 5 of 43
+listq(x:Q):List C == [real x, imagI x, imagJ x, imagK x]
+--R 
+--R   Function declaration listq : Quaternion Complex Expression Integer
+--R       -> List Complex Expression Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 5
+
+@
+Define a function that takes a biquat into a matrix
+<<*>>=
+
+--S 6 of 43
+matrixq(x:Q):Matrix C == matrix _
+             [[real x + %i*imagI(x), imagJ x + %i*imagK(x)],_
+             [-imagJ(x) + %i*imagK(x), real x - %i*imagI(x)]]
+--R 
+--R   Function declaration matrixq : Quaternion Complex Expression Integer
+--R       -> Matrix Complex Expression Integer has been added to 
+--R      workspace.
+--R                                                                   Type: Void
+--E 6
+
+@
+\section{The Pauli basis Biquaternions}
+
+The quaternion package in axiom is based upon the Hamiltonian basis,
+i, j, k, in contrast to the Pauli basis used in the Morgan papers which
+make certain operations correspond more closely (in the sense of
+visualization as ordering of components is more natural so that 
+classical operations can be easily identified) to vector calculus
+functions and connect with more directly with various spinor QM
+formulations. To both follow these papers and obtain these visualization
+benefits, we will define and use the Pauli basis also.
+
+The Pauli basis in terms of the Hamiltonian quaternion basis
+<<*>>=
+
+--S 7 of 43
+sig0:=quatern(1,0,0,0)::Q
+--R 
+--R
+--R   (7)  1
+--R                                  Type: Quaternion Complex Expression Integer
+--E 7
+
+--S 8 of 43
+sig1:=%i*quatern(0,0,0,1)::Q
+--R 
+--R
+--R   (8)  %i k
+--R                                  Type: Quaternion Complex Expression Integer
+--E 8
+
+--S 9 of 43
+sig2:=%i*quatern(0,0,1,0)::Q
+--R 
+--R
+--R   (9)  %i j
+--R                                  Type: Quaternion Complex Expression Integer
+--E 9
+
+--S 10 of 43
+sig3:=-%i*quatern(0,1,0,0)::Q
+--R 
+--R
+--R   (10)  - %i i
+--R                                  Type: Quaternion Complex Expression Integer
+--E 10
+
+@
+For purposes of manipulation and display it would be best if we either
+\begin{enumerate}
+\item Copy the quaternion source code and edit it to use $\sigma_i$ as
+symbols for the basis rather than i, j, k and change the definition of
+multiplication to correspond to this Pauli basis so that all current
+display and entry functions are flipped to the new basis
+\item Use the $\sigma$ basis above with the existing package but define a
+new display function, say sigrep, that can show us the results in Pauli
+form at will, but otherwise show it in Hamiltonian basis
+\end{enumerate}
+
+While 2 is not as natural and convenient, it is easier to code and would
+automatically provide a development that could be seen in the visually 
+appealing Pauli form, or in the standard Hamiltonian form of biquaternions.
+
+After a quick review and finding no fast path to 2, and not wishing to get
+into the mechanics of compiling an axiom package instead of working on
+the physics, I have taken the yet easier path and simply defined the
+simplest display function that gives me access to seeing Pauli basis
+results: a list of the four Pauli basis coefficients.
+
+Define a function that produces the Pauli basis representation of the
+biquaternion.
+<<*>>=
+
+--S 11 of 43
+siglist(x:Q):List C == [real x, -imagK(x)*%i, -imagJ(x)*%i, %i*imagI(x)]
+--R 
+--R   Function declaration siglist : Quaternion Complex Expression Integer
+--R       -> List Complex Expression Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 11
+
+@
+\section{Biquaternion Calculus}
+
+Define the quaternion derivative (Morgan, 2001, Eq. 2)
+<<*>>=
+
+--S 12 of 43
+D(q:Q,x:Symbol,y:Symbol,z:Symbol):Q==sig1*D(q,x)+sig2*D(q,y)+sig3*D(q,z)
+--R 
+--R   Function declaration D : (Quaternion Complex Expression Integer,
+--R      Symbol,Symbol,Symbol) -> Quaternion Complex Expression Integer 
+--R      has been added to workspace.
+--R                                                                   Type: Void
+--E 12
+
+@
+For testing the derivative we define this set of operators
+<<*>>=
+
+--S 13 of 43
+Ft:=operator 'Ft
+--R 
+--R
+--R   (13)  Ft
+--R                                                          Type: BasicOperator
+--E 13
+
+--S 14 of 43
+Fx:=operator 'Fx
+--R 
+--R
+--R   (14)  Fx
+--R                                                          Type: BasicOperator
+--E 14
+
+--S 15 of 43
+Fy:=operator 'Fy
+--R 
+--R
+--R   (15)  Fy
+--R                                                          Type: BasicOperator
+--E 15
+
+--S 16 of 43
+Fz:=operator 'Fz
+--R 
+--R
+--R   (16)  Fz
+--R                                                          Type: BasicOperator
+--E 16
+
+@
+Now form a general quaternion which is a function of x, y, z
+<<*>>=
+
+--S 17 of 43
+F:Q:=Ft(x,y,z)*sig0+Fx(x,y,z)*sig1+Fy(x,y,z)*sig2+Fz(x,y,z)*sig3
+--R 
+--R
+--R   (17)  Ft(x,y,z) - Fz(x,y,z)%i i + Fy(x,y,z)%i j + Fx(x,y,z)%i k
+--R                                  Type: Quaternion Complex Expression Integer
+--E 17
+
+@
+In the Pauli basis the derivative of this biquat should produce
+(Morgan 2001, eq 1):
+\begin{verbatim}
+  D(Ft+F.sigma)=div(F)+(grad(Ft)+%i*curl(F)).sigma
+\end{verbatim}
+<<*>>=
+
+--S 18 of 43
+siglist(D(F,x,y,z))
+--R 
+--R   Compiling function D with type (Quaternion Complex Expression 
+--R      Integer,Symbol,Symbol,Symbol) -> Quaternion Complex Expression 
+--R      Integer 
+--R   Compiling function siglist with type Quaternion Complex Expression 
+--R      Integer -> List Complex Expression Integer 
+--R
+--R   (18)
+--R   [Fz  (x,y,z) + Fy  (x,y,z) + Fx  (x,y,z),
+--R      ,3            ,2            ,1
+--R    Ft  (x,y,z) + (Fz  (x,y,z) - Fy  (x,y,z))%i,
+--R      ,1             ,2            ,3
+--R    Ft  (x,y,z) + (- Fz  (x,y,z) + Fx  (x,y,z))%i,
+--R      ,2               ,1            ,3
+--R    Ft  (x,y,z) + (Fy  (x,y,z) - Fx  (x,y,z))%i]
+--R      ,3             ,1            ,2
+--R                                        Type: List Complex Expression Integer
+--E 18
+
+@
+\section{Biquaternion Exponential}
+
+Define a function that evaluates the Biquat exponential by beginning
+with the biquat rotation.
+
+First let's introduce some refinement to the language we will use. In
+many texts and papers, the i, j, k or $\sigma_1$, $\sigma_2$, $\sigma_3$
+components of the biquaternion are called the imaginary components while
+the scalar or $\sigma_0$ component are called real. This introduces vast
+confusion when dealing with biquaternions in which there is a ``true''
+imaginary unit, \%i being used. We will adopt a variation on the language
+used by Gsponer and others. A biquat $[{\bf a}, {\bf b}, {\bf c}, {\bf d}]$
+has scalar component ${\bf a}$ which may have itself an imaginary component.
+The component $[{\bf 0}, {\bf b}, {\bf c}, {\bf d}]$ is its vector 
+component which again may be complex:
+\begin{verbatim}
+ [0,b,c,d]=[0,Re(b),Re(c),Re(d)]+[0,Im(b),Im(c),Im(d)]=Re(Vec(q))+Im(Vec(q))
+\end{verbatim}
+Thus, for us, a ``real quaternion'' has real scalar and vector components
+and does not refer to a quaternion with only a scalar component as it would
+in the language adopted by the quatern package in Axiom.
+
+The rotation is a function of real number, theta and a unit norm, real
+vector quaternion. It's form is that of a simple complex quaternion
+exponential, R($\theta$,q)=$e^a$ where $a$ is an Imaginary Vector quaternions
+are like exponentials of pure imaginary numbers, resulting in each case in a
+unit norm object of the same type. For many of our purposes in the
+representation of relativistic and quantum mechanics it is the only type
+of quaternion for which we will have to evaluate the exponential.
+
+Define a biquaternion rotation operator that takes a biquat through a
+rotation of $\theta$ radians about the axis defined by the unit $q$ biquat
+(Morgan 2001, Eq 3).
+<<*>>=
+
+--S 19 of 43
+rot(theta:Expression Integer,q:Q):Q==cos(theta/2)-%i::Q*q*sin(theta/2)
+--R 
+--R   Function declaration rot : (Expression Integer,Quaternion Complex 
+--R      Expression Integer) -> Quaternion Complex Expression Integer has 
+--R      been added to workspace.
+--R                                                                   Type: Void
+--E 19
+
+@
+The rotation is a basis for defining the general exponential, since we
+can always extract the unit vector corresponding to a given biquaternion,
+all we need is the biquaternion abs operation, not provided by axiom
+(note, many texts and papers label the abs which is a complex valued
+$norm^2$ by the name ``norm'' -- very bad form -- I've adopted abs as
+the name to avoid this confusion.
+<<*>>=
+
+--S 20 of 43
+((x:Q)/(y:Q)):Q == x*inv(y)
+--R 
+--R   Function declaration ?/? : (Quaternion Complex Expression Integer,
+--R      Quaternion Complex Expression Integer) -> Quaternion Complex 
+--R      Expression Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 20
+
+--S 21 of 43
+abs(q:Q):C == sqrt((q*conjugate(q))::C)
+--R 
+--R   Function declaration abs : Quaternion Complex Expression Integer -> 
+--R      Complex Expression Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 21
+
+--S 22 of 43
+exp(q:Q):Q == (_
+  q-conjugate(q)=0 => exp( (q+conjugate(q))::C/2)$C * sig0; _
+  exp( (q+conjugate(q))::C/2)$C * (sig0*cos(abs(q)) +_
+  (q-conjugate(q))/abs(q-conjugate(q))*sin(abs(q))) )
+--R 
+--R   Function declaration exp : Quaternion Complex Expression Integer -> 
+--R      Quaternion Complex Expression Integer has been added to 
+--R      workspace.
+--R                                                                   Type: Void
+--E 22
+
+@
+If I've defined these correctly, then the rotation about the x axis
+defined by qx below by 2 radians should give the same answer as
+exponentiation of \%i*qx (not a very complete test).
+<<*>>=
+
+--S 23 of 43
+qx:=sig1
+--R 
+--R
+--R   (23)  %i k
+--R                                  Type: Quaternion Complex Expression Integer
+--E 23
+
+--S 24 of 43
+mm:=siglist(rot(2,qx))
+--R 
+--R   Compiling function / with type (Quaternion Complex Expression 
+--R      Integer,Quaternion Complex Expression Integer) -> Quaternion 
+--R      Complex Expression Integer 
+--R   There are 2 exposed and 6 unexposed library operations named cos 
+--R      having 1 argument(s) but none was determined to be applicable. 
+--R      Use HyperDoc Browse, or issue
+--R                               )display op cos
+--R      to learn more about the available operations. Perhaps 
+--R      package-calling the operation or using coercions on the arguments
+--R      will allow you to apply the operation.
+--R   Cannot find a definition or applicable library operation named cos 
+--R      with argument type(s) 
+--R                    Quaternion Complex Expression Integer
+--R      
+--R      Perhaps you should use "@" to indicate the required return type, 
+--R      or "$" to specify which version of the function you need.
+--R   AXIOM will attempt to step through and interpret the code.
+--R   Compiling function rot with type (Expression Integer,Quaternion 
+--R      Complex Expression Integer) -> Quaternion Complex Expression 
+--R      Integer 
+--R
+--R   (24)
+--R                2         3                  3          2
+--R    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
+--R   [-------------------------------- + ----------------------------- %i,
+--R                  2          2                     2          2
+--R           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
+--R                  2         3                    3            2
+--R    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
+--R    ---------------------------------- + --------------------------------- %i,
+--R                   2          2                        2          2
+--R            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
+--R    0, 0]
+--R                                        Type: List Complex Expression Integer
+--E 24
+
+--S 25 of 43
+nn:=siglist(exp(-%i::Q*qx))
+--R 
+--R   There are 2 exposed and 7 unexposed library operations named exp 
+--R      having 1 argument(s) but none was determined to be applicable. 
+--R      Use HyperDoc Browse, or issue
+--R                               )display op exp
+--R      to learn more about the available operations. Perhaps 
+--R      package-calling the operation or using coercions on the arguments
+--R      will allow you to apply the operation.
+--R   Cannot find a definition or applicable library operation named exp 
+--R      with argument type(s) 
+--R                    Quaternion Complex Expression Integer
+--R      
+--R      Perhaps you should use "@" to indicate the required return type, 
+--R      or "$" to specify which version of the function you need.
+--R   AXIOM will attempt to step through and interpret the code.
+--R   Compiling function exp with type Quaternion Complex Expression 
+--R      Integer -> Quaternion Complex Expression Integer 
+--R   Compiling function abs with type Quaternion Complex Expression 
+--R      Integer -> Complex Expression Integer 
+--R
+--R   (25)
+--R                2         3                  3          2
+--R    cos(1)sin(1)  + cos(1)  + cos(1)   sin(1)  + (cos(1)  - 1)sin(1)
+--R   [-------------------------------- + ----------------------------- %i,
+--R                  2          2                     2          2
+--R           2sin(1)  + 2cos(1)               2sin(1)  + 2cos(1)
+--R                  2         3                    3            2
+--R    - cos(1)sin(1)  - cos(1)  + cos(1)   - sin(1)  + (- cos(1)  - 1)sin(1)
+--R    ---------------------------------- + --------------------------------- %i,
+--R                   2          2                        2          2
+--R            2sin(1)  + 2cos(1)                  2sin(1)  + 2cos(1)
+--R    0, 0]
+--R                                        Type: List Complex Expression Integer
+--E 25
+
+--S 26 of 43
+(mm=nn)@Boolean
+--R 
+--R
+--R   (26)  true
+--R                                                                Type: Boolean
+--E 26
+
+@
+To express a proof of equality such as:
+\begin{verbatim}
+  rot(theta,q) = exp((-theta/2)*%i*q)
+\end{verbatim}
+for arbitrary real $\theta$ and biquaternion real using vector $q$ as one 
+would in Maple, we need to express the fact that $q$ is a vector quantity
+with real coefficients in the Pauli basis representing a unit magnitude
+vector. One way to represent this is to create a quaternion called $qnv$,
+representing a general normalized (unit length) vector part only biquat with
+two independent variables $q1$ and $q2$ representing its only degrees of
+freedom.
+<<*>>=
+
+--S 27 of 43
+qnv:=q1*sig1+q2*sig2+sqrt(1-q1^2-q2^2)*sig3
+--R 
+--R
+--R            +---------------+
+--R            |    2     2
+--R   (27)  - \|- q2  - q1  + 1 %i i + q2 %i j + q1 %i k
+--R                                  Type: Quaternion Complex Expression Integer
+--E 27
+
+@
+\section{Assumptions about Variables}
+
+Now, in the equations that will result, we will obtain subexpressions of the
+form $\sqrt{\theta^2}$. The positive root will always be appropriate in
+this formula and one way to get it (in other computer algebra systems) 
+would be to restrict $\theta$ to positive values so as to avoid branches
+that would otherwise have to be properly selected to get an equality. Thus,
+one means to get the desired simplification is to perform the restriction
+of $\theta$ to positive values. My current understanding is: Axiom does not
+support variables with properties in the sense that Maple does (the 
+*assume* facility).
+
+\section{Problems}
+
+Returning to the case at hand, let's expand a test of equality to the
+four biquat components and seek a way to prove that each component 
+is zero.
+<<*>>=
+
+--S 28 of 43
+theta:=_\theta
+--R 
+--R
+--R   (28)  \theta
+--R                                                        Type: Variable \theta
+--E 28
+
+--S 29 of 43
+testqeq:=map(simplify,siglist(rot(theta,qnv)-exp((-theta/2)*%i*qnv)))_
+         ::List Expression Complex Integer
+--R 
+--R
+--R   (29)
+--R           +-------+
+--R           |      2
+--R          \|\theta          \theta
+--R   [- cos(----------) + cos(------),
+--R               2               2
+--R                        +-------+
+--R          +-------+     |      2
+--R          |      2     \|\theta                       \theta
+--R    %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
+--R                            2                            2
+--R    ---------------------------------------------------------,
+--R                              \theta
+--R                        +-------+
+--R          +-------+     |      2
+--R          |      2     \|\theta                       \theta
+--R    %i q2\|\theta  sin(----------) - %i \theta q2 sin(------)
+--R                            2                            2
+--R    ---------------------------------------------------------,
+--R                              \theta
+--R
+--R                                            +-------+
+--R            +---------------+ +-------+     |      2
+--R            |    2     2      |      2     \|\theta
+--R         %i\|- q2  - q1  + 1 \|\theta  sin(----------)
+--R                                                2
+--R       + 
+--R                                 +---------------+
+--R                         \theta  |    2     2
+--R         - %i \theta sin(------)\|- q2  - q1  + 1
+--R                            2
+--R    /
+--R       \theta
+--R     ]
+--R                                        Type: List Expression Complex Integer
+--E 29
+
+@
+As is quite obvious from this result, the two equations would have been
+shown to be equal if positivity of the theta variable was enforced. This
+raises two questions
+\begin{enumerate}
+\item How would one perform a proof such as the above within the
+allowed operations of Axiom?
+\item How can Axiom be called a symbolic algebra system if basic notions
+of algebraic proof such as restrictions of a variable to the semiring
+of non-negative integers is disallowed?
+\end{enumerate}
+How are symbolic manipulations, proofs and solutions to be carried out
+without this basic notion? I am let to think that Axiom can only be
+considered a semi-numerical software system.
+
+\section{Rules and Pattern Matching}
+
+Let's try another way to answer question 1 by using symbolic pattern
+matching ``rules''. Define a rule that recognizes the specific case of
+the variable theta appearing in a construct that should be simplified
+given its positivity.
+<<*>>=
+
+--S 30 of 43
+posthetaRule:=rule sqrt(theta^2)==theta
+--R 
+--R
+--R          +------+
+--R          |     2
+--R   (30)  \|theta   == theta
+--R                        Type: RewriteRule(Integer,Integer,Expression Integer)
+--E 30
+
+@
+But, now we encounter two new problems. First, apparently ``map'' does
+not work with rules, so I can't apply this rule in a simple fashion to
+the entire List generated by our test case above for any x.
+
+The ``map'' function only maps functions but we can easily turn a rule 
+into an anonymous function.
+<<*>>=
+
+--S 31 of 43
+map(x+->posthetaRule(x), [0,sqrt(theta^2),0,sqrt(theta^2)])
+--R 
+--R
+--R   (31)  [0,\theta,0,\theta]
+--R                                                Type: List Expression Integer
+--E 31
+
+@
+But even if we were to split our list above, and try to apply this rule
+to a component, we get this disappointing result:
+<<*>>=
+
+--S 32 of 43
+posthetaRule testqeq.1
+--R 
+--R   There are no library operations named posthetaRule 
+--R      Use HyperDoc Browse or issue
+--R                            )what op posthetaRule
+--R      to learn if there is any operation containing " posthetaRule " in
+--R      its name.
+--R 
+--RDaly Bug
+--R   Cannot find a definition or applicable library operation named 
+--R      posthetaRule with argument type(s) 
+--R                         Expression Complex Integer
+--R      
+--R      Perhaps you should use "@" to indicate the required return type, 
+--R      or "$" to specify which version of the function you need.
+--E 32
+
+@
+Apparently rules have builtin assumptions about the construction of
+the expression. If I override this for a real element of the list
+we are testing I can successfully get one answer.
+<<*>>=
+
+--S 33 of 43
+[posthetaRule (testqeq.i::Expression Integer) for i in 1..1]
+--R 
+--R
+--R   (32)  [0]
+--R                                                Type: List Expression Integer
+--E 33
+
+@
+But this doesn't extend to the remainder of the list.
+<<*>>=
+
+--S 34 of 43
+[posthetaRule (testqeq.i::Expression Integer) for i in 1..4]
+--R 
+--R 
+--RDaly Bug
+--R   Cannot convert from type Expression Complex Integer to Expression 
+--R      Integer for value
+--R                       +-------+
+--R         +-------+     |      2
+--R         |      2     \|\theta                       \theta
+--R   %i q1\|\theta  sin(----------) - %i \theta q1 sin(------)
+--R                           2                            2
+--R   ---------------------------------------------------------
+--R                             \theta
+--R
+--E 34
+
+@
+because obviously we can't coerce an actually complex value into the
+Expression Integer type that the rule seems to want.
+
+Here is one way to create the necessary rule. Like everything else in
+Axiom rules are objects in some domain. We need to specify a domain
+for the rule that is compatible with the domain we wish to manipulate.
+So let's find out more about this domain:
+<<*>>=
+
+--S 35 of 43
+)show RewriteRule
+--R 
+--R RewriteRule(Base: SetCategory,R: Join(Ring,PatternMatchable Base,OrderedSet,ConvertibleTo Pattern Base),F: Join(FunctionSpace R,PatternMatchable Base,ConvertibleTo Pattern Base))  is a domain constructor
+--R Abbreviation for RewriteRule is RULE 
+--R This constructor is exposed in this frame.
+--R Issue )edit rule.spad.pamphlet to see algebra source code for RULE 
+--R
+--R------------------------------- Operations --------------------------------
+--R ?=? : (%,%) -> Boolean                coerce : Equation F -> %
+--R coerce : % -> OutputForm              elt : (%,F,PositiveInteger) -> F
+--R ?.? : (%,F) -> F                      hash : % -> SingleInteger
+--R latex : % -> String                   lhs : % -> F
+--R pattern : % -> Pattern Base           retract : % -> Equation F
+--R rhs : % -> F                          rule : (F,F,List Symbol) -> %
+--R rule : (F,F) -> %                     ?~=? : (%,%) -> Boolean
+--R quotedOperators : % -> List Symbol
+--R retractIfCan : % -> Union(Equation F,"failed")
+--R suchThat : (%,List Symbol,(List F -> Boolean)) -> %
+--R
+--E 35
+
+@
+We can provide satisfactory parameters of this domain constructor as follows:
+<<*>>=
+
+--S 36 of 43
+Complex Integer has PatternMatchable Integer
+--R 
+--R
+--R   (33)  true
+--R                                                                Type: Boolean
+--E 36
+
+--S 37 of 43
+Expression Complex Integer has FunctionSpace Complex Integer
+--R 
+--R
+--R   (34)  true
+--R                                                                Type: Boolean
+--E 37
+
+--S 38 of 43
+Expression Complex Integer has PatternMatchable Integer
+--R 
+--R
+--R   (35)  true
+--R                                                                Type: Boolean
+--E 38
+
+@
+So the following simplification works as hoped:
+<<*>>=
+
+--S 39 of 43
+posxRule:=(rule sqrt('theta^2)==theta)$RewriteRule(Integer,Complex Integer,_
+            Expression Complex Integer)
+--R 
+--R
+--R          +------+
+--R          |     2
+--R   (36)  \|theta   == theta
+--R        Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer)
+--E 39
+
+--S 40 of 43
+map(x+->posxRule x, testqeq)
+--R 
+--R
+--R   (37)  [0,0,0,0]
+--R                                        Type: List Expression Complex Integer
+--E 40
+
+@
+\section{Algebraic Domain of Computation}
+
+Recall that Axiom does things in a fundamentally {\sl algebraic} rather
+than {\sl symbolic} way. So although the pattern matching approach
+works, it goes somewhat against the overall philosophy of Axiom. It is
+possible to do almost anything by using rewrite rules including things
+that are mathematically incorrect. In this case the rule is simple and
+the results obvious but if it gets more complicated this can be a problem.
+
+Is there some ``axiomatic'', i.e. algebraic way to express the fact that
+$\theta$ is a positive real? well, what we really need is that
+$$\sqrt{\theta^2} = \theta$$
+be satisfied. Now consider that by definition $\sqrt{}$:
+<<*>>=
+
+--S 41 of 43
+test (sqrt(x)^2=x)
+--R 
+--R
+--R   (38)  true
+--R                                                                Type: Boolean
+--E 41
+
+@
+and so
+<<*>>=
+
+--S 42 of 43
+test (sqrt(sqrt(x)^2)=sqrt(x))
+--R 
+--R
+--R   (39)  true
+--R                                                                Type: Boolean
+--E 42
+
+@
+for any $x$. So the expression $\sqrt{(x)}$ is one such thing that has
+the desired property in the Expression domain. {\sl With exactly the
+appropriate loss of generality}, let us just suppose that $\theta$ is
+$\sqrt{(\beta)}$ for some $\beta$. Then if necessary we can also
+perform a change of variable back to $\theta$.
+<<*>>=
+
+--S 43 of 43
+eval(eval(testqeq,theta=sqrt(beta)),sqrt(beta)=theta)
+--R 
+--R
+--R   (40)  [0,0,0,0]
+--R                                        Type: List Expression Complex Integer
+--E 43
+
+)spool 
+)lisp (bye)
+ 
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/input/ifthenelse.input.pamphlet b/src/input/ifthenelse.input.pamphlet
new file mode 100644
index 0000000..29c75b4
--- /dev/null
+++ b/src/input/ifthenelse.input.pamphlet
@@ -0,0 +1,299 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input ifthenelse.input}
+\author{Fabio Stumbo}
+\maketitle
+\begin{abstract}
+{\bf if-then-else: what is wrong?}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+@
+<<*>>=
+)spool ifthenelse.output
+)set message test on
+)set message auto off
+)clear all
+
+@
+I am having some problem with the if-then-else syntax in .input files
+
+{\bf Problem 1}: I refer to the Axiom book which ships with the program
+(version 2005/09). At page 204 it says that the usual rules for piling
+are suspended in conditional expressions and it gives 5 different ways
+which should be equivalent, namely:
+\begin{verbatim}
+
+  if i>0 then output("positive") else output("nonpositive")
+
+  if i>0 then output("positive") 
+    else output("nonpositive")
+
+  if i>0 then output("positive") 
+  else output("nonpositive")
+
+  if i>0 
+  then output("positive") 
+  else output("nonpositive")
+
+  if i>0 
+    then output("positive") 
+    else output("nonpositive")
+\end{verbatim}
+
+Well, I tried all of them, creating each time a blank r.input file with 
+inside only:
+<<*>>=
+ 
+--S 1 of 20
+i:=2
+--R 
+--R
+--R   (1)  2
+--R                                                        Type: PositiveInteger
+--E 1
+
+@
+followed by one of the ``if$\ldots$''.
+
+The result of the first two are ok, whereas the other three
+give some syntax error (different each time).
+<<*>>=
+
+--S 2 of 20
+for i in 2..2 repeat
+  if i>0 then output("positive") else output("nonpositive")
+--R 
+--R   positive
+--R                                                                   Type: Void
+--E 2
+
+--S 3 of 20
+for i in 2..2 repeat
+  if i>0 then output("positive") 
+    else output("nonpositive")
+--R 
+--R   positive
+--R                                                                   Type: Void
+--E 3
+
+--S 4 of 20
+for i in 2..2 repeat
+  if i>0 then output("positive") 
+  else output("nonpositive")
+--R 
+--R   positive
+--R                                                                   Type: Void
+--E 4
+
+--S 5 of 20
+for i in 2..2 repeat
+  if i>0 
+  then output("positive") 
+  else output("nonpositive")
+--R 
+--R   positive
+--R                                                                   Type: Void
+--E 5
+
+--S 6 of 20
+for i in 2..2 repeat
+  if i>0 
+    then output("positive") 
+    else output("nonpositive")
+--R 
+--R  Line  47: --R 
+--R  Line  48: --R   positive
+--R  Line  49: --R                                                                   Type: Void
+--R  Line  50: --E 5
+--R  Line  51: 
+--R  Line  52: --S 6 of 20
+--R  Line  53: for i in 2..2 repeat
+--R  Line  54:   if i>0 
+--R           ..A
+--R  Error  A: (from #\A and on) Ignored from here
+--R  Line  55:     then output("positive") 
+--R           ....A
+--R  Error  A: Improper syntax.
+--R  Error  A: (from #\A up to ) Ignored.
+--R  Line  56:     else output("nonpositive")
+--R           ....A........................B
+--R  Error  A: Improper syntax.
+--R  Error  A: (from #\A up to #\B) Ignored.
+--R  Error  B: Possibly missing a then 
+--R  Error  B: (up to #\B) to here.
+--R   7 error(s) parsing 
+--E 6
+
+--S 7 of 20
+i:=2
+--R 
+--R
+--R   (6)  2
+--R                                                        Type: PositiveInteger
+--E 7
+
+--S 8 of 20
+for i in 2..2 repeat
+  if i>0 then
+    output(i)
+    output("positive") 
+  else
+    output(i)
+    else output("nonpositive")
+--R 
+--R  Line  83: --R 
+--R  Line  84: --R
+--R  Line  85: --R   (6)  2
+--R  Line  86: --R                                                        Type: PositiveInteger
+--R  Line  87: --E 7
+--R  Line  88: 
+--R  Line  89: --S 8 of 20
+--R  Line  90: for i in 2..2 repeat
+--R  Line  91:   if i>0 then
+--R  Line  92:     output(i)
+--R  Line  93:     output("positive") 
+--R  Line  94:   else
+--R  Line  95:     output(i)
+--R  Line  96:     else output("nonpositive")
+--R           ....A
+--R  Error  A: (from #\A up to ) Ignored.
+--R  Error  A: Improper syntax.
+--R   2 error(s) parsing 
+--E 8
+
+--S 9 of 20
+i:=1.5
+--R 
+--R
+--R   (7)  1.5
+--R                                                                  Type: Float
+--E 9
+
+--S 10 of 20
+a:=
+  if i > 0 then
+    j:=sin(i*pi())
+    exp(j+1/j)
+  else
+    j:=cos(i*0.5*pi())
+    log(abs(j)**5+1)
+--R 
+--R
+--R   (8)  0.1353352832 3661269189
+--R                                                                  Type: Float
+--E 10
+
+@
+{\bf Problem 2:} again with if then else, in a complex function I 
+noticed a wrong result (the function itself was ok). Simplifying,
+you can produce the same error with something like:
+<<*>>=
+
+--S 11 of 20
+test: (INT,INT) -> List(INT)
+--R 
+--R                                                                   Type: Void
+--E 11
+
+--S 12 of 20
+test(a,b) ==
+  x:=0; y:=0
+  if (a rem b = 0) and b < 0 then
+    x := 1
+    y := 1
+  [x,y]
+--R 
+--R                                                                   Type: Void
+--E 12
+
+--S 13 of 20
+4 rem -2
+--R 
+--R
+--R   (11)  0
+--R                                                     Type: NonNegativeInteger
+--E 13
+
+--S 14 of 20
+test(4,-2)
+--R 
+--R   Compiling function test with type (Integer,Integer) -> List Integer 
+--R
+--R   (12)  [1,1]
+--R                                                           Type: List Integer
+--E 14
+
+@
+returns correctly [1,1], but
+<<*>>=
+
+--S 15 of 20
+4 rem -3
+--R 
+--R
+--R   (13)  1
+--R                                                        Type: PositiveInteger
+--E 15
+
+--S 16 of 20
+test(4,-3)
+--R 
+--R
+--R   (14)  [0,0]
+--R                                                           Type: List Integer
+--E 16
+
+@
+or
+<<*>>=
+
+--S 17 of 20
+4 rem 2
+--R 
+--R
+--R   (15)  0
+--R                                                     Type: NonNegativeInteger
+--E 17
+
+--S 18 of 20
+test(4,2)
+--R 
+--R
+--R   (16)  [0,0]
+--R                                                           Type: List Integer
+--E 18
+
+@
+wrongly returns [0,1]. The same happens if I write
+<<*>>=
+
+--S 19 of 20
+test1: (INT,INT) -> List(INT)
+--R 
+--R                                                                   Type: Void
+--E 19
+
+--S 20 of 20
+test1(a,b) ==
+  x := 0; y := 0
+  if (a rem b = 0) and b < 0 then x := 1 ; y := 1
+  [x,y]
+--R 
+--R                                                                   Type: Void
+--E 20
+
+@
+Why?
+<<*>>=
+)spool 
+)lisp (bye)
+ 
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/input/sqrt3.input.pamphlet b/src/input/sqrt3.input.pamphlet
new file mode 100644
index 0000000..ad20ab9
--- /dev/null
+++ b/src/input/sqrt3.input.pamphlet
@@ -0,0 +1,249 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input sqrt3.input}
+\author{Ralf Hemmecke}
+\maketitle
+\begin{abstract}
+A demo involving the algebraic number $\sqrt{3}$.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+@
+<<*>>=
+)spool sqrt3.output
+)set message test on
+)set message auto off
+)clear all
+ 
+--S 1 of 23
+t1:=(sqrt(3)-3)*(sqrt(3)+1)/6
+--R 
+--R
+--R           +-+
+--R          \|3
+--R   (1)  - ----
+--R            3
+--R                                                        Type: AlgebraicNumber
+--E 1
+
+--S 2 of 23
+tt1:=-1/sqrt(3)
+--R 
+--R
+--R           +-+
+--R          \|3
+--R   (2)  - ----
+--R            3
+--R                                                        Type: AlgebraicNumber
+--E 2
+
+--S 3 of 23
+t2:=sqrt(3)/6
+--R 
+--R
+--R         +-+
+--R        \|3
+--R   (3)  ----
+--R          6
+--R                                                        Type: AlgebraicNumber
+--E 3
+
+--S 4 of 23
+t1+t2
+--R 
+--R
+--R           +-+
+--R          \|3
+--R   (4)  - ----
+--R            6
+--R                                                        Type: AlgebraicNumber
+--E 4
+
+--S 5 of 23
+tt1+t2
+--R 
+--R
+--R           +-+
+--R          \|3
+--R   (5)  - ----
+--R            6
+--R                                                        Type: AlgebraicNumber
+--E 5
+
+--S 6 of 23
+RAN ==> RECLOS FRAC INT
+--R 
+--R                                                                   Type: Void
+--E 6
+
+--S 7 of 23
+x1:=(sqrt(3)$RAN-3)*(sqrt(3)$RAN+1)/6
+--R 
+--R
+--R         1  +-+   1  +-+   1  +-+   1
+--R   (7)  (- \|3  - -)\|3  + - \|3  - -
+--R         6        2        6        2
+--R                                           Type: RealClosure Fraction Integer
+--E 7
+
+--S 8 of 23
+xx1:=-1/sqrt(3)$RAN
+--R 
+--R
+--R          1  +-+
+--R   (8)  - - \|3
+--R          3
+--R                                           Type: RealClosure Fraction Integer
+--E 8
+
+--S 9 of 23
+(x1=xx1)@Boolean
+--R 
+--R
+--R   (9)  true
+--R                                                                Type: Boolean
+--E 9
+
+--S 10 of 23
+s3:=sqrt(3)$RAN
+--R 
+--R
+--R          +-+
+--R   (10)  \|3
+--R                                           Type: RealClosure Fraction Integer
+--E 10
+
+--S 11 of 23
+(s3-3)*(s3+1)/6
+--R 
+--R
+--R           1  +-+
+--R   (11)  - - \|3
+--R           3
+--R                                           Type: RealClosure Fraction Integer
+--E 11
+
+--S 12 of 23
+f3:=sqrt(3,5)$RAN
+--R 
+--R
+--R         5+-+
+--R   (12)  \|3
+--R                                           Type: RealClosure Fraction Integer
+--E 12
+
+--S 13 of 23
+f25:=sqrt(1/25,5)$RAN
+--R 
+--R
+--R          +--+
+--R          | 1
+--R   (13)  5|--
+--R         \|25
+--R                                           Type: RealClosure Fraction Integer
+--E 13
+
+--S 14 of 23
+f32:=sqrt(32/5,5)$RAN
+--R 
+--R
+--R          +--+
+--R          |32
+--R   (14)  5|--
+--R         \| 5
+--R                                           Type: RealClosure Fraction Integer
+--E 14
+
+--S 15 of 23
+f27:=sqrt(27/5,5)$RAN
+--R 
+--R
+--R          +--+
+--R          |27
+--R   (15)  5|--
+--R         \| 5
+--R                                           Type: RealClosure Fraction Integer
+--E 15
+
+--S 16 of 23
+expr1:=sqrt(f32-f27,3)
+--R 
+--R
+--R          +---------------+
+--R          |   +--+    +--+
+--R          |   |27     |32
+--R   (16)  3|- 5|--  + 5|--
+--R         \|  \| 5    \| 5
+--R                                           Type: RealClosure Fraction Integer
+--E 16
+
+--S 17 of 23
+expr2:=(1+f3-f3^2)
+--R 
+--R
+--R           5+-+2   5+-+
+--R   (17)  - \|3   + \|3  + 1
+--R                                           Type: RealClosure Fraction Integer
+--E 17
+
+--S 18 of 23
+expr1-f25*expr2
+--R 
+--R
+--R   (18)  0
+--R                                           Type: RealClosure Fraction Integer
+--E 18
+
+--S 19 of 23
+s:=sqrt(190)$RAN+sqrt(1751)$RAN-sqrt(208)$RAN-sqrt(1698)$RAN
+--R 
+--R
+--R            +----+    +---+    +----+    +---+
+--R   (19)  - \|1698  - \|208  + \|1751  + \|190
+--R                                           Type: RealClosure Fraction Integer
+--E 19
+
+--S 20 of 23
+approximate(s,10^-15)::Float
+--R 
+--R
+--R   (20)  - 0.2341060678 6455900874 E -10
+--R                                                                  Type: Float
+--E 20
+
+--S 21 of 23
+t:=sqrt(190)+sqrt(1751)-sqrt(208)-sqrt(1698)
+--R 
+--R
+--R          +----+    +----+    +---+     +--+
+--R   (21)  \|1751  - \|1698  + \|190  - 4\|13
+--R                                                        Type: AlgebraicNumber
+--E 21
+
+--S 22 of 23
+digits(30)
+--R 
+--R
+--R   (22)  20
+--R                                                        Type: PositiveInteger
+--E 22
+
+--S 23 of 23
+numeric t - approximate(s,10^-30)::Float
+--R 
+--R
+--R   (23)  - 0.5522026336 5 E -29
+--R                                                                  Type: Float
+--E 23
+
+)spool 
+)lisp (bye)
+ 
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/interp/setq.lisp.pamphlet b/src/interp/setq.lisp.pamphlet
index f6e1c05..e9b34ec 100644
--- a/src/interp/setq.lisp.pamphlet
+++ b/src/interp/setq.lisp.pamphlet
@@ -651,8 +651,8 @@
 "Gerhard Schneider      Martin Schoenert       Marshall Schor"
 "Frithjof Schulze       Fritz Schwarz          Nick Simicich"
 "William Sit            Elena Smirnova         Jonathan Steinbach"
-"Christine Sundaresan   Robert Sutor           Moss E. Sweedler"
-"Eugene Surowitz"
+"Fabio Stumbo           Christine Sundaresan   Robert Sutor"
+"Moss E. Sweedler       Eugene Surowitz"
 "Max Tegmark            James Thatcher         Balbir Thomas"
 "Mike Thomas            Dylan Thurston         Barry Trager"
 "Themos T. Tsikas"